"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "nx.draw(petersen_graph(), **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Code Corner"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### `python`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* **list unpacking** operator `*e`: if `e` is a list, an\n",
+ "argument `*e` passes the elements of `e` as individual arguments\n",
+ "to a function call."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* **dictionary unpacking** operator `**opts`: `python` function calls take **positional** arguments and **keyword** arguments. The keyword arguments can be collected in a dictionary `opts` (with the keywords as keys). This dictionary can then be passed into the function call in its \"unwrapped\" form `**opts`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* **set intersection**: if `a` and `b` are sets then `a & b` represents the intersection of `a` and `b`. In a boolean context, an empty set counts as `False`, and a non-empty set as `True`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{3}"
+ ]
+ },
+ "execution_count": 62,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "a = set([1,2,3])\n",
+ "b = set([3,4,5])\n",
+ "a & b"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(False, True)"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bool({}), bool({3})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* `list` [[doc]](https://docs.python.org/3/library/stdtypes.html#list) turns its argument into a `python` list (if possible)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['n', 'e', 't', 'w', 'o', 'r', 'k', 's']"
+ ]
+ },
+ "execution_count": 64,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "list(\"networks\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "source": [
+ "* **list comprehension** [[doc]](https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions) allows the construction of new list from old ones\n",
+ "without explicit `for` loops (or `if` statements)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]"
+ ]
+ },
+ "execution_count": 65,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "[(x, y) for x in range(4) for y in range(4) if x < y]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### `networkx`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* the `read_adjlist` command [[doc]](https://networkx.org/documentation/stable/reference/readwrite/generated/networkx.readwrite.adjlist.read_adjlist.html#networkx.readwrite.adjlist.read_adjlist) constructs a graph from a text file in `adj` format."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* `Graph` constructor and applicable methods [[doc]](https://networkx.org/documentation/stable/reference/classes/graph.html): if `G` is `Graph` object then\n",
+ " * `G.nodes` returns the nodes of a graph `G` (as an iterator),\n",
+ " * `G.edges` returns the edges of a graph `G` (as an iterator),\n",
+ " * ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* `complete_graph` [[doc]](https://networkx.org/documentation/stable//reference/generated/networkx.generators.classic.complete_graph.html)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### `itertools`"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "* `combinations` [[doc]](https://docs.python.org/3/library/itertools.html#itertools.combinations) returns the $k$-element combinations of a given list (as an iterator)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 66,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "['ne', 'nt', 'nw', 'no', 'nr', 'nk', 'ns', 'et', 'ew', 'eo', 'er', 'ek', 'es', 'tw', 'to', 'tr', 'tk', 'ts', 'wo', 'wr', 'wk', 'ws', 'or', 'ok', 'os', 'rk', 'rs', 'ks']\n"
+ ]
+ }
+ ],
+ "source": [
+ "print([\"\".join(c) for c in combinations(\"networks\", 2)])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Slideshow",
+ "hide_code_all_hidden": false,
+ "kernelspec": {
+ "display_name": "Python (CS4423)",
+ "language": "python",
+ "name": "cs4423"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.12.8"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": true,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": true,
+ "toc_position": {},
+ "toc_section_display": true,
+ "toc_window_display": false
+ },
+ "varInspector": {
+ "cols": {
+ "lenName": 16,
+ "lenType": 16,
+ "lenVar": 40
+ },
+ "kernels_config": {
+ "python": {
+ "delete_cmd_postfix": "",
+ "delete_cmd_prefix": "del ",
+ "library": "var_list.py",
+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
+ }
+ },
+ "types_to_exclude": [
+ "module",
+ "function",
+ "builtin_function_or_method",
+ "instance",
+ "_Feature"
+ ],
+ "window_display": false
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}
diff --git a/year4/semester2/CS4423/materials/CS4423-W01-2.pdf b/year4/semester2/CS4423/materials/CS4423-W01-2.pdf
new file mode 100644
index 00000000..3f356400
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diff --git a/year4/semester2/CS4423/materials/CS4423-W02-1.ipynb b/year4/semester2/CS4423/materials/CS4423-W02-1.ipynb
new file mode 100644
index 00000000..4cad542f
--- /dev/null
+++ b/year4/semester2/CS4423/materials/CS4423-W02-1.ipynb
@@ -0,0 +1,786 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "toc": true
+ },
+ "source": [
+ "Table of Contents
\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ " # CS4423 : Week 02 - Lecture 1 - Networks \n",
+ "# More on Graphs, and `networkx`\n",
+ "\n",
+ "[//]: $\\color{red}{\\text{DRAFT}}$\n",
+ "Niall Madden, \n",
+ "School of Mathematical and Statistical Sciences \n",
+ "University of Galway\n",
+ "\n",
+ "(These notes are adapted from Angela Carnevale's work)\n",
+ "\n",
+ "This notebook is at https://www.niallmadden.ie/2425-CS4423/W02/CS4423-W02-1.ipynb\n",
+ "You can read the HTML version at https://www.niallmadden.ie/2425-CS4423/W02/CS4423-W02-1.html\n",
+ "\n",
+ "This version of this notebook was written by Niall Madden, adapted from notebooks by Angela Carnevale.
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## News: \n",
+ "### Labs\n",
+ "\n",
+ "Labs start next week, and an (reintroduction) to Python. This will run:\n",
+ "* Tuesday at 4 in AC215 (slight chance this might get moved to Tuesday at 3), and\n",
+ "* Wednesday at 10am in CA116a. \n",
+ "\n",
+ "These rooms are not labs: BYoD! (Bring Your Own Device)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Website\n",
+ "I now plan to post all notes to https://www.niallmadden.ie/2425-CS4423/ as well as to Canvas."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## `networkx`\n",
+ "Last week we learned a little about the `networkx` package. We'll return to that now, while also revisiting some key ideas about graphs."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As ever, we'll start with importing the `networkx` module, as well as `numpy`: more about that later. And we'll define the `opts` option dictionary."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import networkx as nx\n",
+ "import numpy as np\n",
+ "opts = { \"with_labels\": True, \"node_color\": 'y' } # show labels; yellow noodes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "To create a graph with nodes $1$, $2$, $3$, $4$, $5$, and edges between all even and odd labelled nodes:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "K32 = nx.Graph() # makes THE empty graph\n",
+ "K32.add_edges_from([(1, 2), (1,4), (2,3), (2,5), (3,4), (4,5)])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We'll later learn this is the graph $K_{3,2}$. Now draw it:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nx.draw(K32, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "We can also be lazy, and just give $2$-letter strings for the edges: this implicitly defines the nodes too. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "K33 = nx.Graph([\"A1\", \"A2\", \"A3\", \"B1\", \"B2\", \"B3\", \"C1\", \"C2\", \"C3\"])\n",
+ "nx.draw(K33, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Check basic properties:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "print(f\"K33 has {K33.number_of_nodes()} nodes and {K33.number_of_edges()} edges\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "print(f\"This is the same as saying K33 order {K33.order()} and size {K33.size()}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To list the nodes and edges (as lists)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "list(K33.nodes)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "list(K33.edges)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "A **loop** over a graph `G` will effectively loop over `G`'s nodes. As an example, (recall?) that the **degree** of a node is the number of edges incident to it (or, if you prefer, the number of neighbours)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "for node in K33:\n",
+ " print(f\"node {node} has neighbours {list(K33.neighbors(node))}\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Adding and removing nodes and edges\n",
+ "\n",
+ "We say that \n",
+ "* `G.add_node('v')` adds a node to $G$ called 'v'\n",
+ "* `G.add_nodes_from([2, 3, 5])` adds all the nodes from a list\n",
+ "* `G.add_nodes_from(H])` adds all the nodes from Graph $H$ to Graph $G$\n",
+ "* `G.add_edge('x','y')` add edge from Node $x$ to Node $y$, adding one or both nodes, if needed.\n",
+ "* `G.add_edges_from([(1,5), (2,5), (3,5)])` add edges from a list\n",
+ "* `G.add_edges_from(H.edges)` add edges from another graph\n",
+ "* `G.remove_edge('x','y')` remove edge from $x$ to $y$, but keep the nodes\n",
+ "* `G.remove_node('x')` remove node $x$ and any edge it was incident to."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Neighbours and degree\n",
+ "\n",
+ "(As we've seen) \n",
+ "* The **neighbours** of a node are those that it shares an edge with;\n",
+ "* If nodes $a$ and $b$ are neighbours, we say they are **adjacent**.\n",
+ "* the **degree of a node** is the number of edges incident to it (or, if you prefer, the number of neighbours).\n",
+ "\n",
+ "Let's look at an example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Edges1 = [('Aoife', 'Brian'), ('Aoife', 'Ciara'), ('Aoife', 'Daire'), ('Aoife', 'Ella'), \n",
+ " ('Aoife', 'Finn'), ('Brian', 'Ciara'), ('Brian', 'Finn'), ('Ciara', 'Daire'), \n",
+ " ('Daire', 'Ella'), ('Ella', 'Finn') ]\n",
+ "G1 = nx.Graph(Edges1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nx.draw(G1, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "This is example, which is known as a *wheel graph* is chosen because it exhibits a famous concept in Network Science: *The Friendship Paradox*: your friends (probably) have more friends, on average, than you do!\n",
+ "\n",
+ "Explanation:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "notes"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "#pos = nx.nx_agraph.graphviz_layout(G1)\n",
+ "#nx.draw(G1, pos=pos,**opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Important Graphs\n",
+ "\n",
+ "In this section we'll discuss some important examples of graphs, which we'll return to later as key examples of networks. These include\n",
+ "* Complete Graphs\n",
+ "* Bipartite and complete bipartite graphs\n",
+ "* Path graphs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Complete Graphs\n",
+ "\n",
+ "The [**complete graph**](https://en.wikipedia.org/wiki/Complete_graph)\n",
+ "on a vertex set $X$ is the graph with edge set all of $\\binom{X}{2}$. That is: every node is a neighbour of every other node. It is denoted $K_n$ where $n=|X|$. E.g., if $X=\\{0,1,2,3\\}$, then $K_4$ (\"the complete graph on 4 nodes\") has edges $E=\\{01, 02, 03, 12, 13, 23\\}$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nodes = range(4)\n",
+ "list(nodes) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "E4 = [(x, y) for x in nodes for y in nodes if x < y]\n",
+ "print(E4)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "K4 = nx.Graph(E4)\n",
+ "nx.draw(K4, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "While it is somewhat straightforward to find all $2$-element\n",
+ "subsets of a given set $X$ with a short `python` program,\n",
+ "it is probably more convenient (and possibly efficient) to use a function from the\n",
+ "`itertools` package for this purpose."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from itertools import combinations\n",
+ "nodes5 = range(5)\n",
+ "combinations(nodes5, 2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "print(list(combinations(nodes5, 2)))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "K5 = nx.Graph(combinations(nodes5, 2))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nx.draw(K5, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "`networkx` has a built-in function to create complete graphs: `complete_graph` [[doc]](https://networkx.org/documentation/stable//reference/generated/networkx.generators.classic.complete_graph.html)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [],
+ "source": [
+ "nx.draw(nx.complete_graph(\"NETWORKS\"), **opts)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "nx.draw(nx.complete_graph(22), **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Bipartite Graphs\n",
+ "\n",
+ "A graph is **bipartite** if we can divide the node set, $X$, into two subsets $X_1$ and $X_2$ such that \n",
+ "* $X_1 \\cap X_2 = \\emptyset$ (the sets have no edge in common)\n",
+ "* $X_1 \\cup X_2 = X$ \n",
+ "* For any edge $(u_1,u_2)$ we have $u_1 \\in X_1$ and $u_2 \\in X_2$. That is we only ever have edges between nodes from different sets. \n",
+ "\n",
+ "Such graphs are very common in Network Science, where nodes in the network represent two different types of entities. For example, we might have a graph where nodes represent students and modules, with edges between students and modules they are enrolled in, often called an **affiliation network**."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "Edges2 = [('Aoife', 'CS4423'), ('Aoife', 'CS319'), ('Aoife', 'MA432'), \n",
+ " ('Brian', 'CS4423'), ('Brian', 'CS319'), \n",
+ " ('Ciara', 'CS319'), ('Ciara', 'MA432'), \n",
+ " ('Daire', 'MA432') ]\n",
+ "G2 = nx.Graph(Edges2)\n",
+ "nx.draw(G2, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Somehow that previous graph did not catch the essence of the network: there are two different types of node. We could make that clearer, by colouring the nodes. Here we'll do it manually (later, automatically)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "print(G2.nodes)\n",
+ "color_list= ['c','y','y','y','c', 'c','c'] # y=yellow; c=cyan\n",
+ "nx.draw(G2, node_color=color_list, with_labels=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Complete Bipartite Graphs\n",
+ "\n",
+ "A **complete bipartite graph** is a particular bipartite graph where there is an edge between every node in $X_1$ and every node in $X_2$. Such graphs are denoted $K_{m,n}$ where $|X_1|=m$ and $|X_2|=n$. (We met $K_{2,2}$ and $K_{3,3}$ earlier). \n",
+ "\n",
+ "As usual, there is a built-in generator: `complete_bipartite_graph` [[doc]](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.bipartite.generators.complete_bipartite_graph.html)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "K33 = nx.complete_bipartite_graph(3,3)\n",
+ "nx.draw(K33,**opts) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Path Graphs\n",
+ "\n",
+ "The **Path Graph** with $n$ nodes, denoted $P_n$, is one where two nodes have degree 1, and the other $n-2$ have degree 2:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "P4 = nx.Graph([\"ab\", \"bc\", \"cd\", \"de\"])\n",
+ "nx.draw(P4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "The built-in `nerworkx`generator is called `path_graph` [[doc]](https://networkx.org/documentation/stable/reference/generated/networkx.generators.classic.path_graph.html)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "P10 = nx.path_graph(10)\n",
+ "nx.draw(P10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Exercises\n",
+ "\n",
+ "1. For what values of $n$ is $K_n$ bipartite?\n",
+ "2. For what values of $m$ and $n$ is $K_{m,n}$ bipartite?\n",
+ "3. For what values of $n$ is $P_n$ bipartite?\n",
+ "5. (Based on Q2(a) from the 2023/2024 CS4423 Exam paper) Let $G$ be the graph on the set of nodes \n",
+ "$\\{1, 2, 3, 4, 5, 6\\}$ with edges $1-2$, $1-3$, $2-$4, $3-4$, $3-6$, $4-5$, $4-6$. Draw the graph $G$.\n",
+ "Is $G$ bipartite? Justify your answer. (Note saying $a-b$ is an edge in $G$ is the same as saying $(a,b)$ is an element of its edge set).\n",
+ "\n",
+ "6. (Based on Q1(b) of the 2019/2019 CS4423 paper) At a party with $n=5$ people, some people know each other already while others don’t. Each of the 5 guests is asked how many friends they have at this party. Two report that they have one friend each. Two other guests have two friends each, and the fifth guest has three friends at the party. Understanding friendship as a symmetric relation, is this network possible? Why, or why not?\n",
+ "(*Hint: recall that the sum of all node degrees is twice the number of edges in the graph*).\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finished here Wednesday
"
+ ]
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Slideshow",
+ "hide_code_all_hidden": false,
+ "kernelspec": {
+ "display_name": "Python (CS4423)",
+ "language": "python",
+ "name": "cs4423"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.12.8"
+ },
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+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": true,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": true,
+ "toc_position": {},
+ "toc_section_display": true,
+ "toc_window_display": false
+ },
+ "varInspector": {
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+ },
+ "kernels_config": {
+ "python": {
+ "delete_cmd_postfix": "",
+ "delete_cmd_prefix": "del ",
+ "library": "var_list.py",
+ "varRefreshCmd": "print(var_dic_list())"
+ },
+ "r": {
+ "delete_cmd_postfix": ") ",
+ "delete_cmd_prefix": "rm(",
+ "library": "var_list.r",
+ "varRefreshCmd": "cat(var_dic_list()) "
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+ "nbformat_minor": 1
+}
diff --git a/year4/semester2/CS4423/materials/CS4423-W02-1.pdf b/year4/semester2/CS4423/materials/CS4423-W02-1.pdf
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+++ b/year4/semester2/CS4423/materials/CS4423-W02-2.ipynb
@@ -0,0 +1,984 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "toc": true
+ },
+ "source": [
+ "Table of Contents
\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ " # CS4423-Networks : Week 02 - Lecture 2 [$\\color{red}{\\text{DRAFT}}$]\n",
+ "# From Graphs to Matrices\n",
+ "Niall Madden, \n",
+ "School of Mathematical and Statistical Sciences \n",
+ "University of Galway\n",
+ "\n",
+ "(These notes are adapted from Angela Carnevale's nodes)\n",
+ "\n",
+ "This Jupyter notebook, and a HTML version, can be found at https://www.niallmadden.ie/2425-CS4423/#Week02\n",
+ "\n",
+ "This version of this notebook was written by Niall Madden, adapted from notebooks by Angela Carnevale.
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Preliminaries\n",
+ "### Reminder\n",
+ "\n",
+ "Labs start next week, and an (reintroduction) to Python. This will run:\n",
+ "* Tuesday at 4 in AC215 (slight chance this might get moved to Tuesday at 3), and\n",
+ "* Wednesday at 10am in CA116a. \n",
+ "\n",
+ "These rooms are not labs: BYoD! (Bring Your Own Device)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Notes \n",
+ "(Revised) Notes from yesterday's class are at https://www.niallmadden.ie/2425-CS4423/#Week02. As well as the material we covered, there is a set of exercises at the end of the notebook, including some based on past exam papers."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "source": [
+ "### Modules for this notebook"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "outputs": [],
+ "source": [
+ "import networkx as nx\n",
+ "import numpy as np\n",
+ "opts = { \"with_labels\": True, \"node_color\": 'pink' } # show labels; pink noodes\n",
+ "from itertools import combinations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Important Graphs (continued)\n",
+ "\n",
+ "Yesteryday, we discussed \n",
+ "* Complete Graphs, which can be built using, for example `nx.complete_graph(\"NETWORKS\")`\n",
+ "* Bipartite and complete bipartite graphs, the latter of which can be built using `nx.complete_bipartite_graph(m,n)`. One can also use *list comprehension* to make the edge set: `E = [(x, y) for x in X1 for y in X2 if x < y]`\n",
+ "* Path graphs, built with `nx.path_graph(10)`. Can also use list comprehension to make the edge set (next week's lab)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Cycle Graphs\n",
+ "\n",
+ "Our last example: the **cycle** graph on $n \\geq 3$ nodes, denoted $C_n$, (slightly informally) is formed by adding an edge between to to nodes of degree 1 in a path graph if we delete any one edge is a es is connected, which as a path graph, but with an edge between the two \"end\" nodes. You can make one with `cycle_graph(n)`, but here we'll do it manually.\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "C5 = nx.Graph(['01', '12', '23', '34', '40'])\n",
+ "nx.draw(C5, **opts) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "nx.draw(nx.cycle_graph(6))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "C7 = nx.path_graph(7) # not a cycle graph... yet\n",
+ "C7.add_edge(0,6)\n",
+ "nx.draw(C7)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## New Graphs from old\n",
+ "\n",
+ "### Complement Graph\n",
+ "\n",
+ "The **complement of a graph** $G$ is a graph $H$ with the same nodes as $G$, and two nodes in $H$ are adjacent if and only if they are *not* adjacent in G. \n",
+ "\n",
+ "For example, the complement of a complete graph is an empty graph.\n",
+ "\n",
+ "In `networkx`, the `complement` function returns to complement of a graph."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[(1, 4), (1, 5), (2, 4), (2, 5), (4, 5)]"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "G = nx.Graph([(1, 2), (1, 3), (2, 3), (3, 4), (3, 5)])\n",
+ "G_complement = nx.complement(G)\n",
+ "list( G_complement.edges() ) # This shows the edges of the complemented graph"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "**Tip**: `nx.draw` uses a (semi-random) algorithm, called `spring_layout` for deciding the position of nodes when we draw a graph. Usually, a graph and its complement will be drawn with nodes in different places, making them hard to compare. But we can record the positions determined by the algorithm, and reuse them, as in the next example..."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pos = nx.spring_layout( G)\n",
+ "nx.draw(G, **opts, pos=pos)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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u/vzzT8hkMuzatQupqalwdXWFVCqFh4cHzMzMhI5IRKT2WAZKWFJSEuzs7GBra4s///wTWlpaxXJduVyOxYsXY8qUKXB2dkZwcDBsbGyK5dpCycjIwMGDByGTyXDo0CHI5XK0a9cOUqkUPXv2hLGxsdARiYjUEtcMlLDy5csjMDAQ586dw9y5c4vtumKxGBMmTMBff/2F+Ph42NvbY9++fcV2fSEYGBjAzc0Ne/fuRUJCAlavXo309HT069cPlStXhre3N37//XdkZ2cLHZWISCOxDBRB8+bNMWPGDMyaNQtnz54t1ms3btwYUVFR+Prrr9GjRw+MHTsWb968KdZ7CKFChQoYOnQozpw5g/v372PGjBm4cuUKunTpAktLS/j5+eH8+fNceEhEVIo4TVBEOTk5aNOmDR48eIDo6GiUL1++WK+vUCiwfPlyTJw4EXZ2dggJCUH16tWL9R7KIDY2FjKZDIGBgXj8+DGqVav2buHhV199JXQ8IiKVxDUDpejhw4ewt7dHmzZtsGPHjhI5wz8sLAweHh548eIFNm7ciD59+hT7PZSBXC7HmTNnIJPJsHPnTrx69QqOjo6QSqXw9PSEpaWl0BGJiFQG1wyUImtra2zYsAG7du3Chg0bSuQeLi4uiIqKQvv27eHm5gY/Pz9kZmaWyL2EJBaL0apVK6xfvx4JCQnYvXs3qlWrhqlTp6JKlSpo164dNm/ejOTkZKGjEhGpDY4MFKPhw4dj27ZtCA8PR926dUvkHgqFAmvWrMG4ceNQt25dhIaGasT+/VevXmHXrl2QyWQ4deoUdHV10a1bN0ilUnz77bfQ1dUVOiIRkdLhNIEA0tPT4eLiAm1tbVy6dAn6+voldq+oqCi4u7sjISEB69atg5eXV4ndS9k8fvwYwcHBkMlk79ZpuLm5QSqVonnz5hCLOeBFRARwmkAQhoaGCA4Oxs2bNzFp0qQSvZeDgwMiIyPRtWtXeHt7Y+jQocjIyCjReyqLKlWqYMKECYiKisK1a9cwYsQI/PHHH/j6669RrVo1TJ48GVevXhU6JhGRyuDIQAlYvXo1/Pz8sH//fnTt2rVE76VQKLBhwwaMHj0aNWvWRGhoKOrUqVOi91RGcrkc58+fh0wmQ2hoKF6+fImGDRtCKpXCy8ur2E6JJCJSJZwmEJBCoUDPnj1x9uxZxMTEwMrKqsTveeXKFbi7u+Phw4dYs2YN+vXrV+L3VFZv3rzBH3/8AZlMhn379iErKwstW7aEVCpFnz59in37JxGRsuI0gYBEIhE2btwIfX199O3bF7m5uSV+zwYNGiAsLAx9+vRB//79MWDAAKSlpZX4fZWRrq4uunbtiuDgYDx9+hSbN2+Grq4uhg8fDnNzc/Ts2RM7d+5Uy90YRESFwTJQQipWrIiAgACcOnUKCxYsKJV7GhsbY+vWrdi8eTNCQ0Ph6uqKa9eulcq9lVWZMmXQv39/HD16FI8fP8b8+fPx+PFjuLm5wdzcHIMGDcLJkydLpbARESkrloES1KpVK/z444+YPn06Ll68WGr39fX1RVhYGEQiEVxcXLBp0yYe7wvAwsICY8eORVhYGP7++2+MGTMGp0+fRtu2bWFtbf1uUSL/vyIiTcM1AyUsJycHLVu2RHx8PKKjo1G2bNlSu3d6ejpGjx6NjRs3QiqVwt/fn08I/A+FQoHLly8jICAAISEhePbsGerWrQupVApvb2/Y2toKHZGIqNC4gFCJ3L9/H3Z2dujUqRMCAwNL5Ljiz5HJZBg2bBisrKwQGhoKOzu7Ur2/qsjOzsbx48chk8mwZ88epKeno1mzZpBKpXB3d0fFihWFjkhEVCBcQKhEbG1tsW7dOgQHB2Pr1q2lfn+pVIqIiAjo6+ujUaNGWLt2LYfCP0JHRwfffvstAgICkJiYCJlMhjJlymDUqFEwNzdH165dERISgvT0dKGjEhEVK44MlKLBgwcjODgYERERqF27dqnfPyMjA+PHj4e/vz/c3d2xfv16/vvMh8TERISGhkImk+HixYswNjZGr169IJVK0aZNG2hrawsdkYjoozhNoITS0tLg5OQEQ0NDXLhwAXp6eoLkCA0NxeDBg1G5cmWEhobC0dFRkByq6O7duwgMDIRMJsPNmzdhZmYGT09PSKVSODs7l/oUEBHR53CaQAkZGRkhKCgI165dw5QpUwTL4e7ujsjISJQtWxZNmjTBypUrOW2QTzVq1MD06dNx48YNhIWFwcvLCyEhIXB1dUWdOnUwe/Zs3L17V+iYREQFwjJQyhwcHLBgwQIsWbIEhw8fFiyHRCLB+fPnMWzYMIwaNQp9+vTBq1evBMujakQiEZydnbFkyRI8fvwYR48eRZMmTbBw4UJIJBI0btwYK1asQGJiotBRiYi+iNMEAlAoFOjatSsuX76M2NhYmJubC5pn9+7dGDhwIMqXL//ut1wqnIyMDBw4cAABAQE4fPgwFAoFvvnmG/j4+KB79+7c2klEpYrTBEpMJBJh8+bN0NLSQr9+/SCXywXN06tXL0RFRcHU1BTNmzfHkiVLOG1QSAYGBnB3d8f+/fuRkJCAlStX4vXr1/Dx8YGZmRmkUikOHTqE7OxsoaMSEb3DMiAQU1NTbN++HcePH8eiRYuEjoNq1arh7NmzGDVqFMaPH4/u3bvj5cuXQsdSaRUrVsTw4cPx119/4d69e5g2bRqio6PRuXNnWFlZ4bvvvsPFixdZvIhIcJwmENjkyZOxaNEinD9/Hi4uLkLHAQAcOHAA/fv3h7GxMYKDg9G0aVOhI6kNhUKBmJgYyGQyBAUF4cmTJ6hRowa8vb0hlUoF2XJKROqLWwtVRHZ2Npo3b44XL14gKioKJiYmQkcCADx8+BCenp64fPky5s2bhwkTJkAs5kBSccrNzcWZM2cgk8mwc+dOJCcnw8nJCVKpFJ6enrCwsBA6IhGpOK4ZUBE6OjoIDAxEYmIi/Pz8hI7zjrW1NU6fPo0JEybghx9+QJcuXfDs2TOhY6kVLS0ttG7dGhs2bEBCQgJ27twJa2trTJ48GVWqVEH79u2xdetWpKSkCB2ViNQcy4ASqFGjBtasWYPt27dj+/btQsd5R0dHB7/++isOHTqEsLAw2Nvb48yZM0LHUkv6+vro3bs3du/ejYSEBKxduxbZ2dkYMGAAzMzM4OHhgf379+PNmzdCRyUiNcRpAiXSv39/7N69G1FRUZBIJELHec+TJ0/g5eWFc+fOYfbs2ZgyZQqnDUrBo0ePEBwcjICAAMTGxqJChQpwc3ODj48PmjZtyn8HRPRZXDOgglJTU+Ho6Ihy5crh3Llz0NXVFTrSe3JycjBr1izMnTsX7dq1w/bt22FmZiZ0LI1x9epVyGQyBAYG4uHDh7CxsXm38LBevXpCxyMiJcQyoKIiIiLQpEkTjBs3DvPnzxc6zkcdO3YMPj4+EIvFkMlkaNOmjdCRNIpcLse5c+cgk8kQGhqKpKQk2NnZQSqVwsvLC1WqVBE6IhEpCS4gVFFOTk745ZdfsGDBAhw9elToOB/1zTffIDo6Gl999RXatWuHmTNnIjc3V+hYGkMsFqNFixbw9/dHQkIC9u7di1q1amHGjBmwtrZGmzZtsHHjRh4vTUT5xpEBJSSXy/Htt98iJiYGsbGxqFy5stCRPio3Nxdz587FrFmz0LJlSwQGBnI7nIBSUlKwe/duyGQynDx5Ejo6OujcuTOkUik6d+4s2FMyiUg4nCZQcQkJCbCzs4OTkxMOHjyo1AvFTp06BS8vL+Tm5iIgIADt27cXOpLGi4uLQ3BwMGQy2bsnVLq5uUEqlaJly5ZK/fNERMWH0wQqztzcHFu3bsXhw4exfPlyoeN8VqtWrRATEwMHBwd07NgRP/74I3JycoSOpdEsLS0xfvx4RERE4MaNGxg1ahROnDiB1q1bw8bGBpMmTUJMTAyPQiYiABwZUHoTJkzA8uXLcfHiRTg6Ogod57Pkcjnmz5+P6dOno2nTpggMDORiNiWiUChw8eJFyGQyhISE4Pnz56hXrx6kUim8vb1hY2MjdEQiKmacJlATb968QZMmTfD69WtERESoxCNwz549C09PT2RmZmLbtm3o1KmT0JHoP7Kzs3H06FHIZDLs3bsXGRkZaNGiBaRSKdzc3FChQgWhIxJRMeA0gZrQ1dV990Cb0aNHCx0nX5o3b47o6Gg0atQInTt3xqRJk/jIXiXzdnHh26Owt2/fDiMjI/j5+cHc3Bzdu3dHaGgoMjIyhI5KRKWAZUAF1KpVC6tWrcLmzZsRHBwsdJx8qVSpEg4cOIDffvsNS5YsQcuWLfHgwQOhY9FHGBsbw8fHB4cPH8aTJ0+wcOFCJCQkwMPDA2ZmZvD19cWxY8e4fZRIjXGaQEUoFAr4+Pjg4MGDiI6ORrVq1YSOlG8XLlyAp6cnUlNTsXnzZnTv3l3oSJQPt2/fRmBgIGQyGW7fvg0LCwt4enpCKpXC0dERIpFI6IhE9AVcM6CGUlJSYG9vDzMzM5w5cwY6OjpCR8q3ly9fYsCAAdi/fz/Gjh2L+fPnK91xy/RxCoUC4eHhkMlkCAoKQmJiImrXrg2pVAqpVIrq1asLHZGIPoFrBtRQmTJlEBQUhPDwcMycOVPoOAVSoUIF7N27F0uXLsWqVavQvHlz3Lt3T+hYlA8ikQguLi5YunQpnjx5giNHjsDV1RULFixAjRo10KRJE6xatYqPuCZSYSwDKqZRo0b4+eef8csvv+DkyZNCxykQkUiEMWPG4Ny5c3j+/DkcHBywa9cuoWNRAWhra6NDhw7Ytm0bnj59iqCgIFSqVAljx46FhYXFu0WJaWlpQkclogLgNIEKksvlaN++PW7cuIGYmBhUqlRJ6EgF9urVKwwePBi7du2Cn58fFi5cCH19faFjUSE9f/4coaGhkMlkOH/+PIyMjNCjRw/4+PigXbt20NbWFjoikUbimgE1FxcXBzs7OzRp0gT79u1TycVcCoUCq1evxvjx41GvXj2EhoZCIpEIHYuK6N69e+8WHt64cQOVK1eGh4cHpFIpXF1dVfJnlUhVcc2AmrO0tMTmzZtx4MABrFq1Sug4hSISieDn54eLFy8iNTUVjo6OKrN1kj6tWrVq+PHHH3Ht2jVERkbCx8cHO3fuROPGjVGrVi389NNPuHXrltAxiehfODKg4saMGYO1a9fi0qVLsLOzEzpOoaWkpGDYsGEIDg7G0KFDsXTpUhgYGAgdi4pJbm4uTp06BZlMhl27diElJQUuLi6QSqXw8PCAubm50BGJ1BKnCTREZmYmGjdujKysLERERMDQ0FDoSIWmUCiwYcMGjB49GjVr1kRoaCjq1KkjdCwqZhkZGfj9998hk8nw+++/Izc3F+3atYNUKkXPnj1hYmIidEQitcFpAg2hr6+P4OBgPHz4EOPGjRM6TpGIRCIMGTIEly5dwps3b+Ds7Izt27cLHYuKmYGBAfr06YM9e/YgISEBa9asQWZmJvr37w8zMzN4enri4MGDPMKaqBSxDKiBOnXqYNmyZVi3bh127twpdJwia9iwIcLDw9GrVy/069cPAwcO5FY1NVWhQgUMHToUp0+fxoMHD/DTTz/h+vXr6Nq1KywsLDBy5EicO3eOj1omKmGcJlATCoUCHh4eOHbsGKKjo9XicbQKhQJbtmyBn58fqlWrhtDQUNSrV0/oWFQKYmNjIZPJEBgYiMePH8PW1hbe3t6QSqWoW7eu0PGIVAbXDGigV69ewd7eHlWqVMGpU6fUZm/39evX4ebmhnv37mHVqlXw9fXl9jQNIZfL8ddff0Emk2HHjh149eoVHBwcIJVK4enpCSsrK6EjEik1rhnQQOXKlUNgYCAuXryIOXPmCB2n2NStWxdhYWHw8vLCwIED0a9fP7x+/VroWFQKxGIxvv76a6xbtw4JCQnYs2cPqlevjh9//BFVq1ZF27ZtsWnTJiQnJwsdlUilsQyomaZNm2LmzJn4+eefcebMGaHjFBtDQ0Ns3LgR27dvx549e+Ds7IzY2FihY1Ep0tPTQ48ePbBz5048ffoUGzZsAAAMHjwYZmZmcHNzw969e5GVlSVwUiLVw2kCNZSbm4u2bdvi7t27iImJQYUKFYSOVKz+/vtveHh44ObNm1i+fDmGDBnCaQMN9uTJEwQHB0MmkyEqKgrlypWDm5sbpFIpWrRoAbGYv/OQ5uI0gQbT0tJCQEAA0tPTMXjwYLVbiV2nTh1cvHgRvr6+GDZsGLy9vZGSkiJ0LBKIlZUVvv/+e0RGRuLatWsYOXIkjh07hlatWsHW1hY//PADrly5InRMIqXGkQE1tnfvXvTs2RNr1qzB8OHDhY5TIkJCQjBkyBCYmZkhNDQUDg4OQkciJaBQKHD+/HnIZDKEhobixYsXaNCgAaRSKby8vGBtbS10RKJSwZEBQo8ePTBy5EiMGzcO165dEzpOifDw8EBkZCTKlCmDxo0bY9WqVWo3EkIFJxKJ0KxZM6xevRpxcXE4cOAA6tati1mzZsHGxubdosSkpCShoxIpBY4MqLmMjAy4uroCAC5fvqy25/1nZWVhwoQJWLlyJXr37o0NGzagXLlyQsciJZOamoo9e/ZAJpPh+PHj0NLSQufOnSGVStGlSxc+RpvUDkcGCEDe0a9BQUG4c+cOJkyYIHScEqOnp4cVK1Zg586dOH78OBwdHREWFiZ0LFIyJiYm6NevH/744w88efIEv/32Gx4/fgw3NzeYmZlh4MCBOHHiBHJzc4WOSlSqWAY0QP369bFkyRKsXr0ae/fuFTpOierduzeioqJQqVIlNGvWDEuXLuW0AX2Uubk5xowZg7CwMNy8eRNjx47FmTNn0K5dO1hbW2PChAmIiorizw9pBE4TaAiFQoHevXvj9OnTiImJQZUqVYSOVKLevHmDyZMnY8mSJejWrRs2b96sdlssqfgpFApcvnwZMpkMwcHBePbsGb766itIpVJ4e3ujWrVqQkckKhAeR0wfePnyJezs7FCjRg2cOHECWlpaQkcqcfv374evry9MTEwQHByMJk2aCB2JVER2djaOHz8OmUyGvXv3Ii0tDU2bNoVUKoW7uzsqVaokdESiL+KaAfpAhQoVEBAQgL/++gu//PKL0HFKRbdu3RAVFQUrKyu0bNkSv/32G+RyudCxSAXo6Ojg22+/RUBAAJ4+fQqZTIZy5cph9OjRsLCwQNeuXREcHIz09HShoxIVGcuAhvn6668xbdo0zJw5E+fOnRM6TqmwsbHB6dOnMX78eEyaNAldu3bF8+fPhY5FKsTIyAje3t74/fffER8fj6VLl+L58+fw8vKCmZnZu0WJOTk5QkclKhROE2ignJwctGrVCo8ePUJMTIxGbcE7dOgQ+vXrB319fQQFBaFFixZCRyIVdvfuXQQGBkImk+HmzZswMzODh4cHpFIpXFxceEw2CY7TBPRJ2trakMlkSElJwdChQzVqtXSnTp0QHR2N6tWro3Xr1pg3bx6nDajQatSogenTp+PGjRsIDw+Ht7c3QkND0ahRI9SuXRuzZs3CnTt3hI5J9EUsAxrKxsYG69evx44dO7Bp0yah45SqKlWq4OTJk5g8eTKmTZuGjh074unTp0LHIhUmEong5OSExYsX4/Hjxzh69CiaNm2KRYsWoWbNmmjUqBGWL1/OnzNSWpwm0HBDhw6FTCZDeHg4vvrqK6HjlLpjx47Bx8cHYrEYgYGBaN26tdCRSI1kZGTgwIEDkMlkOHz4MORyOdq1awcfHx/06NEDxsbGQkckNcethZQv6enpcHZ2hq6uLi5evKiRx7HGx8dDKpXi9OnTmDFjBqZNm6YR2y6pdL148QI7duyATCbD2bNnYWhoiO7du0MqlaJ9+/bQ0dEROiKpIa4ZoHwxNDREUFAQ/v77b/zwww9CxxGEhYUFjh07hhkzZmDWrFn45ptvEB8fL3QsUjMVK1bE8OHD8ddff+HevXuYNm0aYmNj0aVLF1haWsLPzw/nz5/XqDU8pDw4MkAAgBUrVmD06NE4cOAAunTpInQcwfz555/w9vaGXC5HQEAAvvnmG6EjkRpTKBSIjY2FTCZDYGAgnjx5gurVq8Pb2xtSqRR16tQROiKpOE4TUIEoFAp069YNFy9eRExMDCwtLYWOJJinT5+ib9++OH78OKZOnYqZM2dCW1tb6Fik5uRyOc6cOYOAgADs3LkTycnJcHR0hFQqhaenp0b/N0mFxzJABfb8+XM0bNgQX331FY4eParR8+ZyuRy//vorpk+fjmbNmiEwMFDtn+dAyiMzMxOHDh2CTCbDwYMHkZOTgzZt2kAqlaJXr178e5jyjWsGqMAqVaqEgIAA/Pnnn/jtt9+EjiMosViMqVOn4tSpU/jnn39gb2+Pw4cPCx2LNIS+vj569eqFXbt24enTp1i3bh1yc3MxcOBAmJmZwd3dHfv27cObN2+EjkpqgmWA3tOmTRtMnjwZ06dPx6VLl4SOI7gWLVogOjoarq6u6NSpE3744QdkZ2cLHYs0SLly5TBo0CCcPHkSDx8+xOzZs3Hr1i306NED5ubmGDZsGP766y8enkVFwmkC+kB2djZatGiBxMREREVFoWzZskJHEpxcLseiRYswZcoUuLq6Ijg4GNbW1kLHIg127dq1dwsPHzx4AGtr63cLD+vXry90PFISXDNARXLv3j3Y29ujc+fOkMlkPGP9fy5cuABPT0+kpqZiy5Yt6Natm9CRSMPJ5XKcP38eAQEB2LFjB16+fImGDRtCKpXCy8sLVatWFToiCYhrBqhIqlWrBn9/fwQFBWHbtm1Cx1EaTZo0QVRUFFq0aIHu3btj/PjxnLclQYnFYjRv3hz+/v6Ij4/Hvn37UKdOHfz000+wsbFB69atsWHDBrx69UroqKTEODJAnzVw4ECEhoYiMjIStWrVEjqO0lAoFFi2bBkmTZoEe3t7hISEoFq1akLHInonJSUFe/bsgUwmw4kTJ6CtrY3OnTtDKpWic+fOGnnaqCbiNAEVi9evX8PJyQnGxsa4cOECdHV1hY6kVMLCwuDu7o6kpCRs2rQJvXr1EjoS0Qfi4+MRHBwMmUyGiIgIlC1bFr1794aPjw++/vpriMUcJFZXnCagYmFsbIygoCBcuXIFU6dOFTqO0nFxcUFUVBTatm2L3r17Y9SoUcjKyhI6FtF7LCwsMG7cOISHh+PGjRsYPXo0Tp06hTZt2sDa2hoTJ05EdHQ0j0LWYBwZoHxZsmQJxo8fj8OHD6Njx45Cx1E6CoUCq1evxvjx41G/fn2EhIRAIpEIHYvokxQKBS5evAiZTIaQkBA8f/4cdevWhVQqhbe3N2xtbYWOSMWA0wRUrORyObp06YKIiAjExsbCzMxM6EhKKTIyEu7u7khMTMT69evh4eEhdCSiL8rOzsaxY8cgk8mwd+9epKeno3nz5pBKpXBzc0PFihWFjkiFxGkCKlZisRhbtmyBSCRC//79ecDJJzg6OiIyMhKdOnWCp6cnhg8fjoyMDKFjEX2Wjo4OOnXqBJlMhqdPnyIgIADGxsb47rvvYGFhgW7duiEkJATp6elCR6USwjJA+Va5cmVs27YNf/zxB5YsWSJ0HKVVpkwZBAUFYe3atdiyZQsaN26MmzdvCh2LKF+MjY0hlUpx+PBhxMXFYdGiRUhMTISnpyfMzMzg6+uLY8eOITc3V+ioVIw4TUAFNmnSJCxduhTnz5+Hs7Oz0HGUWmxsLNzd3fH48WP4+/vDx8dH6EhEhXLnzh0EBgZCJpPh1q1bMDc3h6enJ6RSKZycnHgwmZLimgEqMW/evEGzZs3w6tUrREZGwsTEROhISu3169cYMWIEAgICMHDgQKxYsQKGhoZCxyIqFIVCgfDwcMhkMgQHB+Pp06eoXbv2u6OQa9SoIXRE+heWASpRd+7cgYODA3r16oWtW7cKHUfpKRQKbNmyBX5+fqhevTpCQ0NRt25doWMRFUlOTg5OnjwJmUyG3bt34/Xr12jcuDGkUik8PDxgampa+qFyc4GMLEAuB8RiwEAP0ODHsbMMUInbvn07+vXrh4CAAEilUqHjqIRr167B3d0d9+7dw6pVq+Dr68vhVVIL6enp2L9/P2QyGY4cOQKFQoH27dtDKpWiR48eMDIyKrmbp2UA8c+AF8lA5kfO+dDXAyqWBSxMASODksuhhFgGqFT07dsX+/btQ1RUFIcH8yktLQ2jRo3C5s2b0bdvX6xevRrGxsZCxyIqNs+fP8eOHTsgk8lw7tw5GBoaokePHpBKpfjmm2+go6NTPDfKyAJu3weSUvP/nvImQE3bvBEDDcAyQKUiJSUFjo6OqFChAs6ePcvjigtg+/btGDFiBKpWrYqQkBA0bNhQ6EhExe7evXsICgpCQEAAbty4AVNTU3h4eEAqlaJRo0aFHxmLfwbceQjIC3FqolgESKzzRgrUHM8ZoFLxdhtdVFQUZsyYIXQcldK3b1+Eh4dDR0cHjRo1wrp160r+ONjcXOB1OpDyOu9/uT2MSli1atUwdepUXLt2DZGRkejXrx92796NJk2aoGbNmpgxY0bBt94+iANuPShcEQDy3nfrQd51CABHBqiYLFiwAJMnT8bRo0fRrl07oeOolIyMDIwbNw5r166Fp6cn1q5dW7z/nXE+lZRMbm4uTp8+DZlMhp07dyIlJQVOTk7w8fGBp6cnzM3NP/3m+Gd5H+TFpZaNWo8QcJqASpVcLkeHDh1w9epVxMbGCrOKWMUFBwdj6NChMDMzQ2hoKBwcHIp2Qc6nkgrIzMzEwYMHIZPJcOjQIeTk5KBt27aQSqXo2bPn+585GVlA+NVPjgikpqfh520bEX3nFqJu38Tz5Ff4qf8QzBww9NMBxCLAub7a/sxzmoBKlVgsxrZt25CbmwtfX18+/awQPD09ERERARMTEzRu3BirV68u/P+P8c/y/tIsSBEA8l4ffjXv/USlQF9fH3369MGePXuQkJAAf39/vHnzBr6+vjAzM4OHhwcOHDiAN2/e5JXbz0wNvEhOxroDe5CV/QY9mn+dvwByRd51NRzLABUbCwsLbNmyBYcOHcLy5cuFjqOSatasifPnz2PIkCHw8/ODu7s7kpOTC3YRzqeSiipfvjyGDBmCU6dO4eHDh5g1axZu3LiBbt26oZVLoy+WWxtzCyQdPInTy9bhlyHf5f/GSal502kajGWAilWnTp0wduxYTJo0CVFRUULHUUn6+vpYuXIldu7ciWPHjsHBwQFhYWH5e3P8M+B+MX2I34/jCAEJpmrVqpg0aRJiY2MRGxuL38ZPQs4XFryKRKKi7U7QYCwDVOx+/fVX1K1bF15eXkhLSxM6jsrq3bs3IiMjUalSJTRr1gzLli37/LRBRlbeVquPiL59E50nj4W1excYtG+OCl3bosnIgQg4eujzIe48zLsukYAaNGiAZnXqQ7skTxJ8UcARODXDMkDFTk9PD8HBwXj06BHGjBkjdByVVr16dZw9exZ+fn4YO3YsevbsiZcvX378xZ+ZT331+jWqmpph3uCRODR/KbZNmQlbcwv0nfcT5mzb+OkAnE8lZZCT+/GdMMUpM0ujt9pqCx2A1FPt2rWxcuVKDBw4EN988w08PDyEjqSydHV1sWTJErRq1Qq+vr5wcHBASEgIGjdu/P8vSsv47HxqKwcntHJweu/PujRtgXvxcVh3cA+m9Rv06QBv51O57ZCEUtJF4K2MLMBYMx8ixpEBKjG+vr7w9PTE0KFDcf/+faHjqLzu3bsjOjoalpaWaNGiBX777TfI5fK8LxZyvrNS2XL5G3rV8PlUEtjbn3N1uY8SYhmgEiMSieDv748KFSrA29sbOTk5QkdSeTY2Njhz5gzGjRuHSZMmoVu3bnj+/Hm+5zvlcjlycnLw7FUSVu/dgT/CLuAHr/5ffqOGz6eSwMSl9FFVWvdRQpr7nVOpKFu2LAIDA3H58mXMmjVL6DhqQUdHBwsWLMDBgwdx8eJFNGvcGIrMzHy9d+SS+dBp1wSVe7THuFVLsHz0BAzr1uvLb9Tw+VQSWGkdCKSmBw/lB9cMUIlr0qQJZs+ejWnTpqFt27Zo1aqV0JHUQufOnREdHY3p476HCPnbTjXVZwAGd+6OxFdJOHD+L3y37DekZWRggmffL79Zg+dTSWBaWnnHZudj7cDhS+eQlpGJ1Iy8nUzXH9zDzlMnAACdGjeDob7+x9+or5d3Hw3F44ipVOTm5uKbb77BzZs3ERMTg0qVKgkdSW3kJCVDO/Z2od47YvGv2PD7XsTtOgzTcuU//2KHOkAZPmqZBHLnIfAk8Ysvs/XohgdP4z/6tXtB+2BrYfnxN1pVznuSoZrJ7+c3RwaoVGhpaWH79u2ws7PDoEGDsHfv3sIfDkLv0S7Cs+Fdv6oL//278E/cky+XAQ2eTyUlYGGarzJwP2R/4a+vwfhfN5UaKysrbNq0Cfv378eaNWuEjqM+ijDP+WdUBMRiMapbWpXofYiKzMgg70FaJaG8icZvneXIAJWqbt264bvvvsP48ePRokULNGjQQOhIqi8f86lDF85FGUMjuH5VD2blK+B5cjJ2nDqOkD+PYaJn3y+PCmj4fCopiZq2n31qYaGIRXnX1XBcM0ClLjMzE66ursjNzUVYWBgMDbkorci+MJ+6+fB+bD58EDce3MOr16kwNjCEXY2aGNy5O3zad/ry9dV0PpVUUPyzvAdpFZdaNmo9RZDfz2+WARLE9evX4ezsjH79+sHf31/oOKovLQMIv1Zy13eup/HDqKREHsQVzwO5bK0AG4uiX0eJ5ffzm2sGSBB169bF0qVLsXbtWuzevVvoOKqP86mkSWws836jFxdyEbJYlPd+NS8CBcEyQIIZMmQIevfujUGDBuHhw48/bY8KoKZt4f9y/BTOp5KysjAFnOsXvASXN8l7nxpPDRQGpwlIUElJSbCzs4OtrS1OnjwJbW2uaS0SzqeSJkrLyPvZf5H8wUJauUIBsYE+ULFs3s+yho1ycZqAVEL58uURGBiIc+fOYe7cuULHUX0WpoDtJw5VKShbKxYBUg1GBnkLXBs1AJo7AE51AYc62HLlMqp4dIHCtX7e1zWsCBQEywAJrnnz5pgxYwZmz56Nv/76S+g4qo/zqaTJtLTyjs0uY4wyluaIT0zMe5gXfRbLACmFH3/8Ec2aNYNUKkVSUpLQcVRfAedTs//3REl5WWPOp5LakEgkAIA7d+4InET5sQyQUtDW1kZAQABev36NIUOGIB9LWehLDPSAhrXztgVaVc47OOgjFPp6uPryKRoO8kKTYf1xL6EYtmwRKYEaNWoAYBnID67WIqVhbW2NDRs2oHfv3li/fj2GDh0qdCT18HY+VYK8xxBnZAFyed6zBgz0INLSgkOjBthgYwEPDw84ODhg8+bN6Nmzp9DJiYrEyMgIFhYWLAP5wJEBUiq9evXCsGHDMHbsWFy/fl3oOOrnX/OpMDZ874hhV1dXREVFoW3btujVqxdGjx6NrKwvPzKWSJlJJBKWgXxgGSCls3jxYlSrVg2enp7IzMwUOo5GKVeuHHbu3IkVK1Zg7dq1aNq0Kf8iJZXGMpA/LAOkdAwNDREcHIxbt25h4sSJQsfROCKRCN999x3Onz+P5ORkODo6IjQ0VOhYRIXCMpA/LAOklBo0aIDFixdj5cqV2L+/kM8npyJxcnJCZGQkOnXqBA8PD4wYMQIZGRlCxyIqEIlEgpcvX+Lly5dCR1FqLAOktEaMGIHu3btjwIABePLkidBxNFKZMmUQFBQEf39/bN68GY0bN8bNmzeFjkWUb2+3F969e1fgJMqNZYCUlkgkwsaNG2FgYAAfHx/k5uYKHUkjiUQiDBs2DJcuXUJmZiacnJwgk8mEjkWUL9xemD8sA6TUKlasiICAAJw+fRrz588XOo5Gs7OzQ0REBHr27AkfHx8MHjwY6enpQsci+qyyZcvC1NSUZeALWAZI6bVq1Qo//vgjZsyYgQsXLggdR6MZGxtj27Zt2LhxIwIDA+Hq6sotoKT0uIjwy1gGSCX89NNPcHV1hZeXF169eiV0HI0mEokwcOBAhIWFQS6Xw8XFBVu2bBE6FtEnsQx8GcsAqQRtbW0EBgbi1atXGD58OI8rVgL16tVDWFgYPDw8MGDAAPTv3x+vX78WOhbRB1gGvoxlgFSGra0t1q5di5CQEP4mqiSMjIywadMmbNu2DTt37oSLiwuuXLkidCyi90gkEiQmJiIlJUXoKEqLZYBUioeHBwYNGoTvvvuOW9yUSN++fREREQEdHR24urpiw4YNHL0hpcHthV/GMkAqZ9myZahatSo8PT15dr4SqVOnDi5duoS+fftiyJAhkEqlSE1NFToWER9lnA8sA6RyjIyMEBwcjOvXr2Py5MlCx6F/MTAwwLp16xAYGIgDBw7A0dERUVFRQsciDVehQgWUL1+eZeAzWAZIJdnb22PBggVYunQpDh06JHQc+g8vLy9ERkbC2NgYTZo0werVqzltQILiIsLPYxkglTV69Gh07twZvr6+iI+PFzoO/UfNmjVx4cIFDB48GH5+fnB3d0dycrLQsUhDsQx8HssAqSyRSITNmzdDS0sL/fr1g1wuFzoS/Ye+vj5WrlyJHTt24OjRo3B0dER4eLjQsUgDsQx8HssAqTRTU1MEBATgxIkTWLhwodBx6BP69OmDqKgoVKhQAU2bNsWyZcs4bUClSiKRIC4uDmlpaUJHUUosA6Ty2rZti0mTJuHHH3/E5cuXhY5Dn1C9enWcPXsWfn5+GDt2LHr16oWkpCShY5GGeLuj4J9//hE4iXJiGSC18PPPP8PR0RHe3t48WESJ6enpYcmSJdi7dy9OnToFBwcHXLp0SehYpAG4vfDzWAZILejo6CAwMBCJiYnw8/MTOg59Qffu3REdHQ0LCws0b94cixYt4poPKlGmpqYwMTFhGfgElgFSGzVq1IC/vz8CAgKwfft2oePQF9jY2ODMmTMYO3YsJkyYgG7duuHFixdCxyI1JRKJuIjwM1gGSK14e3ujX79+GDlyJG7fvi10HPoCHR0d/Pbbbzh48CAuXrwIe3t7nDt3TuhYpKZYBj6NZYDUzsqVK2Fubg4vLy+8efNG6DiUD507d0Z0dDRsbW3x9ddf45dffuG0ARU7loFPYxkgtWNiYoLg4GDExsZi2rRpQsehfKpSpQr+/PNPTJo0CVOnTkWnTp2QmJgodCxSIxKJBI8ePUJmZqbQUZQOywCpJScnJ/zyyy/47bffcPToUaHjUD5pa2tj3rx5OHLkCCIjI2Fvb4/Tp08LHYvUhEQigUKhwL1794SOonRYBkhtjRs3Dh06dEC/fv3w9OlToeNQAXTo0AHR0dGoXbs22rRpg9mzZyM3N1foWKTiuL3w01gGSG2JxWJs3boVCoUCvr6+nINWMZaWljh+/DimTZuGmTNnokOHDkhISBA6FqkwCwsLGBgYsAx8BMsAqTUzMzNs3boVR44cwbJly4SOQwWkpaWFWbNm4fjx47h69Srs7e1x4sQJoWORiuL2wk9jGSC117FjR3z//ff44YcfEBkZKXQcKoQ2bdogJiYGDRo0wDfffIMZM2YgJydH6FikglgGPo5lgDTCvHnz0LBhQ3h6euL169dCx6FCMDMzw5EjRzB79mzMnTsXbdu2RVxcnNCxSMWwDHwcywBpBF1dXQQFBSEuLg6jRo0SOg4VkpaWFqZNm4aTJ0/izp07sLOzw5EjR4SORSpEIpHg/v37PIPkP1gGSGPUrFkTq1atwpYtWxAUFCR0HCqCr7/+GtHR0XB2dsa3336LKVOmIDs7W+hYpAIkEgnkcjkePHggdBSlwjJAGqVfv37w9vbG8OHD+ShTFWdqaorff/8dv/76K3777Te0atUKjx49EjoWKTluL/w4lgHSKCKRCGvWrEHFihXh7e3N3yZVnFgsxg8//IAzZ87g0aNHsLe3x8GDB4WORUqsSpUq0NPTYxn4D5YB0jhlypRBUFAQIiIi8NNPPwkdh4pB06ZNERUVhWbNmqFr1674/vvvOSdMHyUWi1G9enWWgf9gGSCN1KhRI/z888/49ddfuW9dTVSsWBH79u3DokWLsHz5crRs2RL3798XOhYpIe4o+BDLAGmsSZMmoU2bNujbty+ePXsmdBwqBiKRCOPHj8fZs2eRkJAABwcH7N27V+hYpGRYBj7EMkAaSywWY9u2bcjOzsbAgQOhUCiEjkTFpFGjRoiKikLr1q3Rs2dPjBkzBllZWULHIiUhkUhw7949Hlz1LywDpNEsLS2xZcsWHDx4ECtXrhQ6DhWj8uXLY9euXVi+fDn8/f3RrFkz3L17V+hYpAQkEgmys7O5++RfWAZI43Xu3BmjR4/GhAkTEBMTI3QcKkYikQijRo3C+fPnkZSUBEdHR+zYsUPoWCQwbi/8EMsAEYD58+fjq6++gqenJ9LS0oSOQ8XMyckJkZGR6NixI9zd3TFy5EhkZmYKHYsEYm1tDW1tbZaBf2EZIAKgr6+P4OBgPHz4EOPGjRM6DpWAsmXLIjg4GGvWrMGmTZvQuHFj3Lp1S+hYJABtbW1Uq1aNZeBfWAaI/qdOnTpYvnw51q9fz6FkNSUSiTB8+HBcunQJGRkZcHJyQmBgoNCxSADcUfA+lgGifxk4cCDc3NwwZMgQnl2uxuzs7BAeHo7u3btDKpViyJAhSE9PFzoWlSKWgfexDBD9i0gkwrp161CuXDl4e3tz65EaMzExwfbt27FhwwbIZDI0atQIN27cEDoWlRKJRIK7d+9CLpcLHUUpsAwQ/Ue5cuUQGBiIS5cuYfbs2ULHoRIkEokwaNAgXL58Gbm5uXB2dsbWrVuFjkWlQCKRICsrC0+ePBE6ilJgGSD6iKZNm2LmzJmYO3cuTp8+LXQcKmH169dHWFgY3N3d4evrC19fX+4qUXPcXvg+lgGiT5gyZQpatGgBHx8fvHjxQug4VMKMjIywefNmbN26FTt27ICzszOuXr0qdCwqIba2thCLxSwD/8MyQPQJWlpaCAgIQHp6OgYPHszjijVEv379EB4eDm1tbbi4uGDDhg38d6+GdHV1YWNjwzLwPywDRJ9RpUoVbNy4EXv37oW/v7/QcaiUfPXVV7h8+TL69u2LIUOGwMfHB6mpqULHomLGHQX/j2WA6At69OiBkSNHYvz48Rw21iAGBgZYt24dZDIZ9u/fD2dnZ0RHRwsdi4oRy8D/YxkgyoeFCxdCIpHA09MTGRkZQsehUuTt7Y2IiAgYGhqicePGWLNmDacN1MTbMsB/nywDRPliYGCA4OBg3L17F99//73QcaiU1apVCxcuXMCgQYMwcuRIeHp6Ijk5WehYVEQSiQTp6elISEgQOorgWAaI8qlevXpYsmQJ1qxZgz179ggdh0qZvr4+Vq1ahdDQUBw5cgSOjo4IDw8XOhYVAbcX/j+WAaICGDZsGHr27IlBgwbxWegays3NDZGRkShfvjyaNm2K5cuXc5hZRVWvXh0ikYhlACwDRAUiEomwYcMGGBkZwcfHB7m5uUJHIgHUqFED586dw8iRIzFmzBj07t0bSUlJQseiAtLX10eVKlVYBsAyQFRgFSpUgEwmw9mzZzFv3jyh45BA9PT0sHTpUuzZswd//vknHBwccOnSJaFjUQFxR0EelgGiQmjZsiWmTZuGmTNn4ty5c0LHIQH16NEDUVFRMDc3R/PmzbFo0SJOG6gQloE8LANEhTR9+nQ0adIE3t7eHCLWcLa2tjhz5gzGjBmDCRMmoFu3bjzCWkVwe2EelgGiQtLW1oZMJkNKSgqGDRum8X+ZaDpdXV0sXLgQBw4cwPnz5+Hg4MBRIxUgkUiQkpKC58+fCx1FUCwDREVgY2OD9evXY8eOHdi4caPQcUgJdOnSBdHR0bC2tsbXX3+NX3/9FXK5XOhY9AncXpiHZYCoiPr06YMhQ4Zg9OjRuHHjhtBxSAlUrVoVp06dwqRJkzBlyhR07twZz549EzoWfUSNGjUAsAywDBAVg6VLl8LW1haenp7IzMwUOg4pAW1tbcybNw9HjhxBREQE7O3tcebMGaFj0X8YGRnBwsKCZUDoAETqwNDQEEFBQbh58yYmTZokdBxSIh06dEB0dDRq1qyJ1q1bY86cOTyfQslwRwHLAFGxsbOzw8KFC7FixQocOHBA6DikRCwtLXH8+HFMmzYNM2bMQIcOHXgevhJhGWAZICpWfn5+6Nq1KwYMGIC4uDih45AS0dbWxqxZs3Ds2DFcvXoV9vb2OHHihNCxCCwDAMsAUbESiUTYtGkTdHV1eVwxfVTbtm0RHR2N+vXr45tvvsFPP/3EnxOBSSQSvHz5Ei9fvhQ6imBYBoiKWaVKlRAQEIBTp05hwYIFQschJWRubo4//vgDs2bNwpw5c9C2bVuOJAno7fbCu3fvCpxEOCwDRCWgTZs2mDJlCqZPn46LFy8KHYeUkJaWFqZPn46TJ0/i9u3bsLe3xx9//CF0LI3E7YUsA0QlZubMmXBxcYG3tzeSk5OFjkNK6uuvv0Z0dDQcHR3RsWNHTJkyBTk5OULH0ihly5aFqakpywARFT8dHR0EBgbixYsXGD58OI8rpk8yNTXFoUOH8Msvv+C3335Dq1at8OjRI6FjaRRNX0TIMkBUgqpVqwZ/f38EBwdj69atQschJSYWizF58mScPn0aDx48gL29PX7//XehY2kMlgEiKlFeXl4YMGAAvvvuO9y6dUvoOKTkmjVrhujoaDRt2hRdunTBxIkTkZ2dLXQstccyQEQlbvny5bCysoKnpyeysrKEjkNKrmLFiti/fz8WLVqEpUuXokWLFnjw4IHQsdSaRCJBYmIiUlJShI4iCJYBolJgbGyMoKAgXL16FVOnThU6DqkAkUiE8ePH4+zZs0hISIC9vT327t0rdCy1penbC1kGiEqJo6Mj5s+fj8WLF+Pw4cNCxyEV0ahRI0RFRaFVq1bo2bMnxo4dy9GlEqDpjzJmGSAqRWPGjMG3336L/v3782x6yrfy5ctj9+7dWLZsGVavXo1mzZrhn3/+ETqWWqlQoQLKly/PMkBEJU8sFmPLli0Qi8Xo378/5HK50JFIRYhEIowePRrnz59HUlISHBwcsHPnTqFjqRVNXkTIMkBUyipXroxt27bh6NGjWLx4sdBxSMU4OzsjMjISHTp0gJubG/z8/JCZmSl0LLXAMkBEpap9+/aYOHEipkyZgrCwMKHjkIopW7YsQkJCsHr1amzcuBFNmjTB7du3hY6l8lgGiKjUzZkzB/b29vDy8kJqaqrQcUjFiEQijBgxAhcvXkRaWhocHR0RFBQkdCyVJpFIEBcXh7S0NKGjlDqWASKB6OrqIigoCE+fPoWfn5/QcUhF2dvbIyIiAt26dYO3tzeGDh2KjIwMoWOppLc7CjRxcSbLAJGAJBIJ1qxZg+3btyMgIEDoOKSiTExMEBAQgA0bNmD79u1wdXXF33//LXQslaPJ2wtZBogE5uPjAx8fH4wYMUJjDzyhohOJRBg0aBDCwsKQk5MDJycnbNu2TehYKsXU1BQmJiYsA0QkjFWrVsHMzAxeXl548+aN0HFIhdWvXx/h4eFwc3ND//79MWDAAI2cAy8MkUiksYsIWQaIlECZMmUQFBSEqKgoTJ8+Xeg4pOKMjIywZcsWbNmyBaGhoXBxccHVq1eFjqUSWAaISFAuLi6YN28eFixYgGPHjgkdh9RA//79ERYWBi0tLbi6umLjxo1QKBRCx1JqLANEJLjvv/8e33zzDfr164fExESh45AaqFu3Li5dugSpVIrBgwejb9++3Mr6GRKJBI8ePdK4g5xYBoiUiFgsxtatW5GbmwtfX18eV0zFwtDQEOvXr4dMJsO+ffvg7OyMmJgYoWMpJYlEAoVCgXv37gkdpVSxDBApGQsLC2zZsgWHDx/G8uXLhY5DasTb2xsREREwMDBAo0aN4O/vz2mD/9DU7YUsA0RKqFOnThg3bhwmTZqEqKioj78oNxd4nQ6kvM7739zc0g1JKqlWrVq4ePEiBg4ciBEjRsDT0xMpKSlCx1IaFhYWMDAw0LgyIFLkoxampKSgbNmySE5ORpkyZUojF5HGy8rKQpMmTZCWloaIiAgYGxsDaRlA/DPgRTKQ+ZFn2uvrARXLAhamgJFB6YcmlRIaGoohQ4bA1NQUISEhcHJyEjqSUmjYsCFatGiBVatWCR2lyPL7+c2RASIlpaenh6CgIDx+/Bg//zgNiL0JhF8DniR+vAgAeX/+JDHvdbE3gYxPvI4IgLu7OyIjI1GuXDk0bdoUK1as4LQBNHNHAcsAkRKrXbs2/tgqw8zOfSB/WcCh3KRUIPxq3kgC0SfUqFED586dw/DhwzF69Gj06dMHr169EjqWoFgGiEi5PIhDc9Mq0NfVg1gkKvj75Qrg1gPgQVzxZyO1oaenh2XLlmH37t04efIkHBwccPnyZaFjCUYikeD+/fsadRooywCRsop/BtzP+xAXFaYI/Nv9OI4Q0Bf17NkTUVFRqFy5Mpo1a4bFixdr5LSBRCKBXC7HgwcPhI5SalgGiJRRRhZw5+FHv3QyMgwD589Gnb59YNSxBaz6dEL3H79HxM0bn7/mnYdcQ0BfZGtri7/++gtjxozB999/j+7du+Ply5dCxypVmri9kGWASBndvp83xP8Ra/btwv2EeIzp44lDvy7Fsu++R2JSEhqPHICTkWGfvqZckXddoi/Q1dXFwoULsX//fpw7dw729vY4f/680LFKTZUqVaCnp6dRZUBb6ABE9B9pGXmL/z5h1dhJqFy+wnt/1tG1CSTSnpgXsBltHF0+fe2k1Lzrc9sh5UPXrl0RHR0NT09PtGzZEnPnzsXEiRMhFqv375FisRjVq1fXqDKg3v9GiVTRF+b2/1sEAMDY0BB1bavj0bOnRb4+0b9VrVoVp06dwsSJEzF58mR06dIFz56p/8+Qpu0oYBkgUjYvkgv8luTXrxF562/Us61eItcnzaajo4NffvkFhw8fRlhYGOzt7XHmzBmhY5UolgEiEk5O7qcPFPoMv6XzkZaZgR99Bn75xZlZPLqYCqVjx46Ijo6GRCJB69atMWfOHOSq6c+SRCLBvXv3kJOTI3SUUsEyQKRMClEEpm9cA9nxI1jiNx5Otb/K35u4q4AKycrKCidOnMCPP/6IGTNmoGPHjnj6NB/TUypGIpEgOzsbjx49EjpKqWAZIFImBXxk8awt6zFn+ybMHTwS3/VyL7H7EP2btrY2Zs+ejaNHj+LKlSuwt7fHyZMnhY5VrDRteyHLAJEyKcAq7Vlb1mPmlnWY6TsUU30GFOg2N2/f0ZjhTyo57dq1Q3R0NOrWrYt27drhp59+UptpA2tra2hra7MMEJEADPTy9bKft23AzC3rMK3vQPzkO6RAt5DL5XBq0RRlypRBs2bNMG7cOAQGBuL27dsaedocFY25uTmOHj2KWbNmYc6cOWjXrh3i4lT/+GttbW1Uq1ZNY8oAH2FMpGwuXfns2oFFIQGYsGYZOro2wU/9PywCjes1+Ozl5Xo6OJ+TisuXLyMsLAxhYWG4e/cuAKBcuXJwcXF594+rqyssLS2L9v2Qxjh16hS8vb2Rk5ODgIAAtG/fXuhIRdKpUyfo6Ohg3759QkcptPx+frMMECmbOw/zHkP8Ca3GDMPpmMhPfl1x6jOnEAKAVWVAYv3eH7148QLh4eHvysHly5eRkJAAALC0tHxXDFxcXODs7Izy5cvn//shjZKYmIi+ffvi6NGjmDJlCmbPng1tbdU832706NE4ceIErl27JnSUQmMZIFJVaRlAeAn+5eNc74snECoUCjx58uRdMQgLC0N4eDiSk/POKJBIJO/KgYuLCxwcHGBoaFhymUmlyOVyLFiwANOmTUOTJk0QFBSEKlWqCB2rwJYvX45JkyYhPT1dZU9dZBkgUmWxNz97JHGhlTcBGtYu1Fvlcjlu3779bvQgLCwMkZGRyMrKgpaWFurXr//e9EK9evWgo6NTzN8AqZKzZ8/Cy8sLGRkZ2LZtGzp16iR0pAI5dOgQOnfujIcPH6Jq1apCxykUlgEiVZaRBYRf/eTDigpFLAKc6+d7kWJ+ZGdn4+rVq++NIFy7dg25ubnQ19eHg4PDeyMIEolEZX/DosJ58eIF+vfvj99//x0TJ07E3LlzVaYk3rp1C7Vr18bJkyfRunVroeMUCssAkaqLfwbcKsbnqdeyASxMi+96n5Ceno6oqKj3Fii+XZFdrlw5ODs7vzeCYGVlVeKZSFhyuRxLlizB5MmT4ezsjODgYNjY2Agd64vevHkDAwMD+Pv7Y8iQgu3aURYsA0Tq4EEccL8YtmnZWgE2FkW/TiG9fPny3QLFtyUhPj4eAGBhYfHBAsUKFT58GBOpvosXL8LT0xMpKSnYvHkzunfvLnSkL6pevTrc3Nwwf/58oaMUCssAkbqIf5a3w6AwUwZiUd7OgVIYESiojy1QfPXqFQCgRo0a700vODo6coGimkhKSsLAgQOxd+9ejBkzBgsWLICurq7QsT6pffv2MDExwa5du4SOUigsA0TqJCMLuH2/YIsKy5sANW2LdY1ASZLL5bhz58572xujoqKQmZkJLS0t1KtX770RhPr166vM3DO9T6FQYMWKFZgwYQLs7OwQEhKC6tXz8cRNAYwcORLnzp1DTEyM0FEKhWWASB2lZeSNFLxI/vjBRPp6QMWyeSMBX9g+qAqys7Nx7dq190YQrl69+m6Bor29/XsjCDVr1uQCRRUSHh4ODw8PPH/+HJs2bULv3r2FjvSBxYsXY/r06Xj9+jVEIpHQcQqMZYBI3eXm5o0YyOV5zzQw0AO0tIROVeLeLlD89wjC2wWKZcuWfbdA8W1JsLKyUsm/xDVFcnIyBg8ejJ07d8LPzw8LFy6Evr6+0LHe2b9/P7p37464uDhYWAi37qawWAaISGMkJSV9sEDx7fn45ubm75UDFxcXLlBUMgqFAv7+/hg3bhzq1q2LkJAQ1KxZU+hYAIDr16+jXr16OHPmDFq0aCF0nAJjGSAijfZ2geK///n3AsV/P4PB0dERRkZGwgYmREdHw93dHfHx8Vi/fj08PT2FjoTMzEwYGhpi48aNGDCgYE8HVQb5/fxWzQOjiYi+wMrKClZWVujRoweAvN8+/7tAcd++fcjIyIBYLP5ggWKDBg24QLGU2dvbIyIiAsOGDYOXlxf+/PNPLF26FAYGwq1/0dfXR5UqVdT+6YUcGSAijZWTk4Nr1669d0DSlStXkJubCz09PTg4OLw3glCrVi0uUCwFCoUCGzduxKhRo1CzZk2EhoaiTp06guVp06YNTE1NERISIliGwuI0ARFRIaSnpyM6Ovq9EYTbt28DAMqUKfPBAsUqVapwgWIJuXLlCtzd3fHo0SOsWbMGffv2FSTH0KFDERERgYiICEHuXxQsA0RExSQpKQkRERHvLVB88uQJAMDMzOyDBYoVK1YUOLH6eP36Nfz8/LBt2zYMGDAAK1asKPX1HQsWLMDcuXPx6tUrlSt+LANERCUoLi7ugwWKSUlJAPKOsP338xe4QLHotmzZAj8/P9ja2iI0NBT16tUrtXvv3r0bvXv3RmJiIkxNle80z89hGSAiKkUKhQJ37959b3ohMjLy3QLFunXrfrBAUZmP4VVG169fh7u7O/755x+sXLkSAwYMKJXf1GNjY2FnZ4fz58+jSZMmJX6/4sQyQEQksJycHFy/fv29BYqxsbHvFija29u/N4LABYpflp6ejtGjR2Pjxo3w8fHBmjVrYGxsXKL3TEtLg7GxMbZt2ybYuoXCYhkgIlJCGRkZHyxQvHXrFoC8BYpOTk7vjSBUrVpV5eapS4NMJsOwYcNgZWWF0NBQ2NnZlej9LC0tMWTIEMyaNatE71PcWAaIiFTEq1evEBER8d4IwuPHjwEAlStXfm9xoouLCypVqiRwYuVw69YtuLu74++//8ayZcswdOjQEitOLVu2RNWqVSGTyUrk+iWFZYCISIXFx8e/tzjx8uXL7xYoVqtW7YMFiiU9VK6sMjMzMW7cOPj7+8PDwwPr1q0rkc+pgQMH4tq1a7h06VKxX7sksQwQEakRhUKBf/75573tjZGRkUhPT4dYLMZXX3313ghCw4YNNWqBYmhoKAYPHozKlSsjNDQUjo6OxXr9efPmYdGiRXjx4kWxXreksQwQEam5nJwc3Lhx44MFijk5OdDV1f1ggWLt2rXVeoHi3bt34e7ujqtXr2LRokXw8/MrtmmD0NBQeHh44MWLFyr1oCuWASIiDZSRkYGYmJj3RhBu3rwJADAxMYGTk9N7IwjW1tZqtUAxKysLEydOxIoVK9CrVy9s3LgR5cqVK/J1IyMj4eTkhMuXL8PFxaXoQUsJywAREQEAkpOTP1ig+OjRIwCAqanpBwsUVe1gnY/ZvXs3Bg4ciPLlyyMkJASurq5Ful5ycjLKlSuHwMBAeHl5FVPKkscyQEREn5SQkPDe4sSwsDC8fPkSAGBra/vBAkUTExOBExfcvXv34OnpiaioKMyfPx9jx44t0ihI5cqVMWrUKEyfPr0YU5YslgEiIso3hUKBe/fuvVcOIiIikJ6eDpFI9NEFinp6ekLH/qI3b95gypQpWLx4Mbp164bNmzcXes6/adOmqFmzJrZu3VrMKUsOywARERXJ2wWK/97iGBMT826Bop2d3QcLFLW0tISO/VEHDhxA//79YWxsjJCQkEIdK9yvXz/cvXsX586dK4GEJYNlgIiIil1mZuYHCxT//vtvAICxsfEHCxRtbGyUZoHiw4cP4eXlhUuXLmHevHmYMGFCgXZXzJ49G5s3bMS96zcAuRwQiwEDPUBJCxDAMkBERKXk7QLFf48gPHz4EEDeAsV/L050cXFB5cqVBcuanZ2N6dOnY/78+fj222+xdevWLy+YTMsA4p8h9cFjGIm1PywQ+npAxbKAhSlgZFBy4QuBZYCIiATz9OnTDxYovj2wx8bG5r3nLzg5OZX6AsUjR46gb9++0NXVRXBwMFq0aPHhizKygNv3gaTU/F+4vAlQ0zZvxEAJsAwQEZHSUCgUuH///gcLFNPS0iASiVCnTp33phfs7OxKfIHikydP4O3tjbNnz2L27NmYMmXK///WH/8MuPMQkH/xI/JDYhEgsc4bKRAYywARESm13Nzc9xYoXr58GbGxscjOzoaOjs67BYpvS0KdOnWKfYFiTk4OZs2ahblz56Jdu3bYvn07zDJzgftxRb+4rSVgY1n06xQBywAREamczMxMxMbGfrBAUaFQwNjYGI6Oju+NINja2hbLAsXjx49DKpXCp21HLBo2qhi+k/+pZSPoCAHLABERqYWUlJT3Fihevnz53QLFSpUqfbBA0czMrFD3SXz4CGVvPYautna+CsaGg3sxZOFcGOkb4PWRMx9/kVgEONcXbA0BywAREamtxMTEDxYoPn/+HABgbW39wQLFfH12xd6EIikV+RlnePIsEfV8PWBkYIDk168/XQaAvEWFDWvn7xsrZiwDRESkMRQKBR48ePDe8xfCw8PfW6D479EDOzs76Ovr//8F0jKA8Gv5vl/XKeMgEolQwaQMdp4++fkyAADO9QTZdpjfz2/tUsxERERUIkQiEWxtbWFrawt3d3cAeQsU//777/dGD4KCgt4tUGzYsOG7EYRude1RAcjXqEDA0UM4HROF61tCMG3jmvwFjH+Wt8NASbEMEBGRWtLS0kK9evVQr149+Pr6Ash7xHFsbOy7cnDmzBmsXbsWtwJ2oaJV1S9eMzHpJcauXIxfh/qhSuUCrE14kQxICvmNlAKWASIi0hh6enrvpgreSn2VDOPoW/l6/8gl81Hb2gYjuvcp2I0zs4DcXKU9uphlgIiINJqJtg6Qj90Du06fxIELfyFqfUDhtjNmZAHGhoVIWPJYBoiISLPJ5V98yev0dPgtnY9RPd1hWdEUr1Lzjih+k5MDAHiVmgodbW0YGXxmkWA+7iMUlgEiItJs+Xhy4fPkV3ia9BKLQmVYFCr74Ovlu7ZB92ZfY+/chUW6j1BYBoiISLPl40Ag8woV8ecS/w/+/NfALTgdE4XD85ehUtmyRb6PUFgGiIhIs2lp5T2GODPrky/R19NDKwenD/58y5ED0BKLP/q1/1xAaRcPAoDyjlkQERGVlopf+K1e2a9fRDyBkIiIqIAnEBaYkp9AyJEBIiIiI4O8ZwiUhPImghSBgmAZICIiAoCatnlPGSxOYlHedZUcywARERGQt9q/uJ8fILFW6l0Eb7EMEBERvWVhCthaFs+1bK3yrqcCuLWQiIjo32wsAV0d4M5DQP7FNfYfEovyRgRUpAgALANEREQfsjAFypUBbt8HklLz/77yJnlrBFRgauDfWAaIiIg+xkAPaFg7b9th/LO8xxB/7GAifb28cwQsTJV+18CnsAwQERF9jpFB3rC/BHmPIc7IynvokFicVxiU+GTB/GIZICIiyi8tLaV9DHFRcDcBERGRhmMZICIi0nAsA0RERBqOZYCIiEjDsQwQERFpOJYBIiIiDccyQEREpOFYBoiIiDQcywAREZGGYxkgIiLScCwDREREGo5lgIiISMOxDBAREWk4lgEiIiINxzJARESk4VgGiIiINJx2fl6kUCgAACkpKSUahoiIiIrP28/tt5/jn5KvMpCamgoAqFq1ahFjERERUWlLTU1F2bJlP/l1keJLdQGAXC5HXFwcTExMIBKJijUgERERlQyFQoHU1FRYWlpCLP70yoB8lQEiIiJSX1xASEREpOFYBoiIiDQcywAREZGGYxkgIiLScCwDREREGo5lgIiISMOxDBAREWm4/wNK2/KvcGfGhQAAAABJRU5ErkJggg==",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "nx.draw_networkx(G_complement, **opts, pos=pos)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Line Graphs\n",
+ "\n",
+ "A graph, $G$, is made from \"things\" that have connections to each other. The \"things\" are nodes, and their connections are represented by an edge.\n",
+ "\n",
+ "But we can think of edges as \"things\" too, with connections to any other edge that has a vertex in common. This leads to the idea of a _line graph_.\n",
+ "\n",
+ "The **line graph** of $G$, is denoted $L(G)$: every node in $L(G)$ corresponds to an edge in $G$, and for every two edges in $G$ that have a node in common, $L(G)$ has an edge between their corresponding nodes."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "#### Examples"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "G = nx.Graph([\"AB\", \"AC\", \"AD\", \"BD\"])\n",
+ "nx.draw(G, **opts)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "LG = nx.line_graph(G)\n",
+ "nx.draw(LG, **opts, node_size=800) # large nodes to label easier to read"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "#### Line graph of $C_4$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "G = nx.cycle_graph(4)\n",
+ "nx.draw(G, **opts)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "LG = nx.line_graph(G)\n",
+ "nx.draw(G, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Petersen Graph\n",
+ "\n",
+ "Everyone who has a favourite graph has as their favourite graph the [Petersen Graph](https://en.wikipedia.org/wiki/Petersen_graph). It is a graph on $10$ nodes with $15$ edges.\n",
+ "\n",
+ "One way to construct it, is as the **complement** of the **line graph** of the complete graph $K_5$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "K5 = nx.complete_graph(5)\n",
+ "nx.draw(K5, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Next we make the line graph, $L(K_5)$:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false,
+ "slideshow": {
+ "slide_type": "-"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "LK5 = nx.line_graph(K5)\n",
+ "nx.draw(LK5, **opts, node_size=800)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "And (almost) finally, we take the complement of $L(K_5)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "hideCode": false,
+ "hidePrompt": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "Petersen = nx.complement(LK5)\n",
+ "nx.draw(Petersen, **opts, node_size=800)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "While the graph is correct, we have to be quite careful with the positioning of the nodes to get a proper view of the graph:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pos = nx.circular_layout(Petersen)\n",
+ "pos[(0,1)]=[0,5]; pos[(0,2)]=[3,1]; pos[(0,3)]=[2,-2]; pos[(0,4)]=[-3,-4]\n",
+ "pos[(1,2)]=[3,-4]; pos[(1,3)]=[-2,-2]; pos[(1,4)]=[-3,1]\n",
+ "pos[(2,3)]=[-5,2]; pos[(2,4)]=[0,3]\n",
+ "pos[(3,4)]=[5,2]\n",
+ "nx.draw(Petersen, pos=pos,node_size=800, width=3, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Matrices of Graphs\n",
+ "\n",
+ "There are various ways the represent a network/graph, including:\n",
+ "* The node set and edge set, or\n",
+ "* a drawing of the graph.\n",
+ "But, computationally, the most useful way is as a matrix. Three important matrix representations are\n",
+ "1. **The Adjacency Matrix** (most important)\n",
+ "2. **Incidence Matrix** (has its uses)\n",
+ "3. **The Graph Laplacian** (the coolest)\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "## Adjacency Matrix\n",
+ "\n",
+ "**Definition** The __adjacency matrix__ of a graph, $G$ of order $n$, is a square $n\\times n$ matrix, $A=(a_{ij})$, \n",
+ "with rows and columns corresponding to the nodes of the graph. That is, we number the nodes $1, 2, \\dots, n$. Then $A$ is given by \n",
+ "$$\n",
+ " a_{ij}=\\begin{cases} 1 & \\mbox{if node $i$ and $j$ are joined by an edge},\\\\\n",
+ "0 &\\mbox{otherwise}.\\end{cases}\n",
+ "$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example\n",
+ "Let $G=G(X,E)$ be the graph with $X=\\{a,b,c,d,e\\}$ and edges $a-b$, $b-c$, $b-d$, $c-d$ and $d-e$.\n",
+ "Then $$A = \n",
+ "\\begin{pmatrix}\n",
+ "0&1&0&0&0\\\\\n",
+ "1&0&1&1&0\\\\\n",
+ "0&1&0&1&0\\\\\n",
+ "0&1&1&0&1\\\\\n",
+ "0&0&0&1&0\n",
+ "\\end{pmatrix}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "### Example\n",
+ "The adjacency matrix of $K_4$ is \n",
+ "$$ A = \\begin{pmatrix} \n",
+ "0 & 1 & 1 &1 \\\\\n",
+ "1 & 0 & 1 &1 \\\\\n",
+ "1 & 1 & 0 &1 \\\\\n",
+ "1 & 1 & 1 &0 \n",
+ "\\end{pmatrix}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Properties of Adjacency matrices \n",
+ "1. $\\sum_{i=1}^N \\sum_{j=1}^N a_{ij} = \\sum_{u \\in X} \\mathrm{deg}(u)$, where $\\mathrm{deg}(u)$ is the degree of $u$.\n",
+ "2. All graphs we've seen so far are _undirected_. For all such graphs, $A$ is symmetric: $A=A^T$; equivalently $a_{ij}=a_{ji}$\n",
+ "4. $a_{ii}=0$ for all $i$.\n",
+ "3. In real-world examples, $A$ would usually be **sparse**, which means that $\\sum_{i=1}^N \\sum_{j=1}^N a_{ij} \\ll n^2$. (I.e., the vast majority of the entries are zero)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Sparse matrices\n",
+ "Sparse matrices have huge importance in computational linear algebra. The main idea is that it is much more efficient to just store the location of the non-zero entries. That is what `networkx` does:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Coords\tValues\n",
+ " (0, 1)\t1\n",
+ " (0, 3)\t1\n",
+ " (1, 0)\t1\n",
+ " (1, 2)\t1\n",
+ " (2, 1)\t1\n",
+ " (2, 3)\t1\n",
+ " (3, 0)\t1\n",
+ " (3, 2)\t1\n"
+ ]
+ }
+ ],
+ "source": [
+ "C4 = nx.cycle_graph(4)\n",
+ "A_C4 = nx.adjacency_matrix(C4)\n",
+ "print(A_C4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "This matrix is internally represented as a `scipy` sparse matrix. It needs to be converted (e.g. by the `toarray` method) in order to be displayed as a matrix as usual.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "scipy.sparse._csr.csr_array"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(A_C4)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "numpy.ndarray"
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "type(A_C4.toarray())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[0 1 0 1]\n",
+ " [1 0 1 0]\n",
+ " [0 1 0 1]\n",
+ " [1 0 1 0]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(A_C4.toarray())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Another example\n",
+ "Here is another example, we introduce to look at the idea of creating a graph from a matrix:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "G = nx.Graph([\"ab\", \"bc\", \"bd\", \"cd\", \"de\"])\n",
+ "nx.draw(G, **opts)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[0 1 0 0 0]\n",
+ " [1 0 1 1 0]\n",
+ " [0 1 0 1 0]\n",
+ " [0 1 1 0 1]\n",
+ " [0 0 0 1 0]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "A = nx.adjacency_matrix(G)\n",
+ "print(A.toarray())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "source": [
+ "Now let's make a graph from that matrix:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "H = nx.from_numpy_array(A.toarray())\n",
+ "nx.draw(H, **opts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So the graph is more or less the same, but the labels have changed!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
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+ },
+ "source": [
+ "#### More about Adjacency Matrices\n",
+ "\n",
+ "Next week we'll learn more about these matrices. In particular, even though they are created just as a table of numbers representing a graph, matrix algebra is really important! Examples:\n",
+ "* Matrix-vector products can tell us about neighbours of a vertex\n",
+ "* Matrix-matrix produces can let us compose the actions to two networks\n",
+ "* Matrix powers tell us about paths of given lengths\n",
+ "* Even the eigenvalues of $A$ give us information about the network"
+ ]
+ },
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+ "metadata": {
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+ "source": [
+ "## Exercises\n",
+ "\n",
+ "1. For what values of $n$ is $C_n$ bipartite?\n",
+ "2. In this class we looked at a few graph generators in `networkx`. Explore the following: `barbell_graph`, `ladder_graph`, `lollipop_graph`, `star_graph` and `wheel_graph`.\n",
+ "3. We say two graphs are **equal** if they have the same node and edge sets. We say they are **isomorphic** if there is a relabling of their nodes that makes them equal. Verify that $C_5$ is isomorphic to its complement.\n",
+ "4. Convince yourself that $C_n$ is always isomorphic to $L(C_n)$, the line graph of $C_n$.\n",
+ "5. Is the Petersen graph bipartite?\n",
+ "6. Write down the adjacency matrix of $K_{3,3}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finished here Thursday
"
+ ]
+ }
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diff --git a/year4/semester2/CS4423/materials/CS4423-W02-2.pdf b/year4/semester2/CS4423/materials/CS4423-W02-2.pdf
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