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Created November 9, 2020 00:11
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CS166 - Introduction to Networks
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction to networks\n",
"\n",
"#### Sayama Exercise 15.2.\n",
"Calculate the following:\n",
"- The number of edges in a complete graph made of $n$ nodes.\n",
"- The number of edges in a regular graph made of $n$ nodes each of which has degree $k$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import networkx as nx\n",
"import matplotlib.pyplot as plt\n",
"import itertools as it"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1.\n",
"A complete graph has an edge between every possible pair of nodes. Assuming a complete graph with multiple edges connecting a given pair of nodes would still be a complete graph, we have that the minimum number of edges in a complete graph is for the case in which only 1 edge connects each pair of nodes. Thus, there are\n",
"\n",
"$$E \\geq \\frac{n(n-1)}{2}$$\n",
"\n",
"edges in a complete graph of $n$ nodes. This is derived from the observation that for every node added to a complete graph, we must add one edge for every preexisting node. Thus, we have the sum of the natural numbers from 0 to $n$ as our number of edges."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2.\n",
"In a regular graph, we could compute the sum of the degrees of all nodes as simply $nk$, since all $n$ nodes have degree $k$. Since every edge contributes an additional 2 to the total sum of degrees, since it adds one for each node it is connected to, we know that $nk = 2E$, where $E$ is the number of edges in the graph. Thus, we can use this equation to conclude that the number of edges in a graph as described is $E = \\frac{nk}{2}$.\n",
"\n",
"An interesting observation is that this equation implies we cannot have regular graphs with odd $n$ and $k$ simultaneously (at least not if we want an integer number of edges), since the denominator would make the number of edges a fraction."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Sayama Exercise 15.3\n",
"\n",
"Draw each of the graphs mentioned in Sayama Exercise 15.3. You can use the NetworkX library for exercise, or you can draw the graphs manually.\n",
"\n",
"- A complete graph made of four nodes.\n",
"- A complete graph made of five nodes.\n",
"- A bipartite graph made of a two-node group and a three-node group in which all possible inter-group edges are present.\n",
"- A bipartite graph made of two three-node groups in which all possible inter-group edges are present.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Complete graph of 4 nodes\n",
"g = nx.Graph()\n",
"n = range(4)\n",
"\n",
"g.add_nodes_from(list(n))\n",
"\n",
"edges = list(it.product(list(n), list(n)))\n",
"\n",
"g.add_edges_from(edges)\n",
"\n",
"nx.draw(g)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Complete graph of 5 nodes\n",
"g = nx.Graph()\n",
"n = range(5)\n",
"\n",
"g.add_nodes_from(list(n))\n",
"\n",
"edges = list(it.product(list(n), list(n)))\n",
"\n",
"g.add_edges_from(edges)\n",
"\n",
"nx.draw(g)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from networkx.algorithms import bipartite\n",
"\n",
"B = nx.Graph()\n",
"\n",
"lst1 = list(range(2))\n",
"lst2 = [\"a\", \"b\", \"c\"]\n",
"\n",
"# The code below was inspired by the Stack Overflow question/answers at\n",
"# https://stackoverflow.com/questions/35472402/how-do-display-bipartite-graphs-with-python-networkx-package\n",
"\n",
"B.add_nodes_from(lst1, bipartite=0)\n",
"B.add_nodes_from(lst2, bipartite=1)\n",
"\n",
"B.add_edges_from(list(it.product(lst1, lst2)))\n",
"\n",
"nx.draw(B, with_labels = True)\n",
"plt.show()\n",
"\n",
"# Separate by group\n",
"left, right = nx.bipartite.sets(B)\n",
"positions = {}\n",
"\n",
"positions.update((node, (1, index)) for index, node in enumerate(left))\n",
"positions.update((node, (2, index)) for index, node in enumerate(right))\n",
"\n",
"nx.draw(B, pos = positions, with_labels = True)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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CV8WXkFuOSRtiUSdr/SZ2a0tz7JkR3qqTW5ojlUqRnp6uUYh37tyBt7e3RiF6eHjQVgmiV7/99huWLFmC+Ph4g3s2I8dx8PT0xMGDBxEUFMQ6DuEhXhUf0PRZnY+i7bM6m1NbW4u0tDSNQiwsLISvr69GIbq5udFGXqJ1NTU1CAgIwNatW/HYY4+xjtOkmJgYeHh4GNxolPAD74oPMNynMzSnuroaqampGoVYVlYGPz8/jUJ0dXWlKSDSZosXL0ZWVhZ2797NOkqzDh48iNWrV+PEiROsoxAe4mXxAUBiXjnWnsnE6fRiKBVKyO77Lhufx/eYrwNiIr20Mr2pC5WVlUhJSdEoxMrKSgQEBKiKsLEUnZycqBDJQ0kkEgwdOtTgFrQ8qLq6Gr169UJ+fj49notoHW+Lr1FpdT0WrPoFWffq4RfcD3ZCS/j16oTnwgz7CewPc+/evSYLUSqVNlmIPXv2pEIk4DgO0dHRiIqKwjvvvMM6ziONGjUKCxYswJNPPsk6CuEZ3hcfAMyePRu+vr6YN28e6yg6VVpaiuTkZI1CVCgUahvyGwuxR48erCMTPTpw4AA+/PBDg1zQ0pRvv/0WOTk5WLNmDesohGdMoviioqLw1ltvYdy4cayjMFFUVNRkIZqbmzdZiN26dWMdmWhZ44KWbdu2ITIyknWcFklKSsJTTz2Fmzdv0owF0SqTKD43NzecPHkSnp6erKMYDI7jUFBQ0GQhWltbN1mIdISU8frggw9w69Yt7Ny5k3WUFuM4Di4uLjh9+jS8vb1ZxyE8wvvik0qlsLe3R3V1NW0ebwGO43Dnzh2NQkxJSYGdnZ1GIQYEBMDOzo51bPIQ6enpGDZsGBITE9G7d2/WcVrl9ddfR2hoKObOncs6CuER3hdfcnIynn32WaSlpbGOYtSUSiVyc3M1CjE1NRXdunVTK8TAwEAEBATQajwD0LigZezYsXj77bdZx2m1ffv2YfPmzTh8+DDrKIRHeF98v//+OzZt2oQ///yTdRReUiqVyMnJURVhYymmp6fD0dFRY4To5+cHGxsb1rFNxv79+/Hxxx/jxo0bRrGg5UHl5eVwdXVFYWEhPSGFaA3vi++bb75BYWEhvvvuO9ZRTIpCoUBWVpbGCDEjIwNOTk4ahejr6wuhUPjoNyYtVlNTA39/f2zfvh0ikYh1nDYbPnw4PvroI0RFRbGOQniC98X3xhtvoH///njzzTdZRyEA5HI5MjMzNQoxKysLrq6uGoXo4+NDT7poo/fffx+5ubnYsWMH6yjt8sUXX6CsrAzLly9nHYXwBO+LTyQS4eOPPzaY542RpjU0NCAjI0OjEG/dugV3d3eNe4je3t5GOXWnL40LWpKSktCrVy/Wcdrl+vXrmDJlClJSUlhHITzB++Lr3bs3Ll++DBcXF9ZRSBvU19cjPT1doxDz8vLg5eWlUYienp4mv3qX4ziMHTsW48aNw1tvvcU6TrsplUr07NkTV69eRZ8+fVjHITzA6+KrqqqCo6Mjqqur6SkHPFNXV4e0tDSNQiwoKICPj4/GlKm7u7vJ/B3Yt28fPv30U8TFxfFmVDxlyhQMHz4cM2fOZB2F8ACvi+/GjRt45ZVXkJiYyDoK0ZOamhqkpqZqFGJJSYnqSRf3/+nTpw+vCrG6uhr+/v7YuXMnIiIiWMfRmp07d2Lfvn347bffWEchPMDr4tuzZw/27t2Lffv2sY5CGKuqqkJKSopGIVZUVMDf31+jEF1cXIzymKz33nsPd+7cwfbt21lH0ari4mJ4e3ujqKiIFjuRduP1zZCMjAw66ogAADp16oTBgwdj8ODBah8vLy9XK8QjR44gOTkZtbW1ak+6aPzTu3dvgy3E1NRUbNq0CUlJSayjaJ2DgwN8fHxw6dIlo96aQQwDr4tPIpEY7BOmiWGwt7fH0KFDMXToULWPl5WVqW3KP3jwIJKTkyGTyTTKMDAwEI6OjkwLkeM4zJ07F4sXL0bPnj2Z5dCl6Oho/P3331R8pN14PdU5ZMgQfPvttxg+fDjrKIQniouLNU6pSU5OBgDVYd73/3FwcNBLrr179+Lzzz9HXFwcb1e1Xrx4ETExMYiPj2cdhRg5Xhdft27dkJqaSs+dIzrFcRwKCwubLEQrK6smR4hdu3bV2vUbF7Ts2rULI0aM0Nr7Ghq5XI4ePXpALBYb3WHbxLDwtvhKS0vh4eGB8vJyg70nQ/iN4zjcvXtXoxBTUlJga2vbZCF27ty51dd59913kZ+fj59//lkH34VheeGFFzB+/Hi8+uqrrKMQI8bb4ouNjcXcuXNx9epV1lEIUcNxnOpJF/cXYmpqKuzt7TWmTAMCAtCpU6cm3ys1NRURERFISkri7b29+23evBnHjh3DL7/8wjoKMWK8Lb7t27fj77//xq5du1hHIaRFlEolbt26pfZQYLFYjLS0NDg4OGgUop+fH5566ik89dRTmDdvHuv4enH37l0EBwejsLCQt/cyie7x9m+ORCKBj48P6xiEtJiZmRnc3d3h7u6OJ554QvVxhUKB7OxsVRkePXoUy5cvR2pqKgQCAWxsbJCfn69WiHx9hE/v3r3h7OyMq1evYsiQIazjECPF2xHfiy++iAkTJuA///kP6yiEaF1VVRX8/f3x9ddfw9raWm3K9ObNm3B2dtYYIfr6+sLKyop19HZ79913IRQK8emnn7KOQowUb4svLCwMP/74IwYOHMg6CiFat2jRIhQWFmLbtm0an5PJZKonXdxfiNnZ2XBzc9MoRB8fH6M60/P06dN47733cPnyZdZRiJHiZfFxHAc7Ozvk5ubC3t6edRxCtColJQUikQhisRiOjo4t/rr6+npIJBKNQszNzYWHh4dGIXp5eRnkfbSGhgY4ODjg5s2b6N69O+s4xAjxsvjy8/MRGhqKoqIi1lEI0SqO4zBq1Cg8/fTTmDt3rlbeUyqVqp50cX8p3r17F97e3hqF6OHhAXNzc61cu60mTpyIF198ES+99BLTHMQ4Gd6vc1ogkUjojE7CS3v27EFZWRlmzZqltfcUCoXo27cv+vbtq/bx2tpa1ZMukpOTsWHDBiQnJ6OoqAi+vr4ahejm5qa3J100Hl9GxUfagpcjvo0bN+LChQvYsmUL6yiEaE3jgpY9e/Zg2LBhTHPcX4iNU6b37t2Dn5+fRiG6urpq/RCJ7OxshIeHIz8/n1ePlSL6QSM+QozEZ599htGjRzMtPeDfJ10MGjQIgwYNUvt4RUWF6kkXycnJOHbsGJKTk1FVVYWAgACNQnRycmpzIbq7u6NLly6Ij49HWFiYNr4tYkJ4WXwZGRm0jYHwSnJyMrZu3QqxWMw6SrM6d+6MIUOGaOyvu3fvntr9w0OHDiE5ORn19fWqRz/dX4o9e/ZsUSFGR0fjyJEjVHyk1Xg51RkYGIhdu3YhNDSUdRRC2o3jOIwcORLPPvss5syZwzqO1pSUlGgsqElOToZSqVSV4P2F+OBh80ePHsXSpUtx7tw5Rt8BMVa8Kz6FQgFbW1uUlJSgY8eOrOMQ0m67d+/GN998g6tXrxrk9gJt4jgORUVFTRaihYWFWiF6eXnhmWeeoW1LpNV4V3w5OTkYPnw48vLyWEchpN0aF7T8+uuvGg/LNSUcxyE/P1+jEK9duwZbW1uEhYVpjBCpDElzeFd8x48fx7Jly3Dq1CnWUQhpt4ULF6K0tJRWKDdj5cqVuHz5Ml555RW1UkxJSYGdnZ3GlGlAQADs7OxYxyaM8a741qxZg8TERPz444+soxDSLmKxGI899hiSk5PpYcrNSE9Px+jRo3H79m21BTFKpRK3b99WK8PGRz9169ZNoxD9/f1ha2vL8Dsh+sS74luwYAFcXFzwzjvvsI5CSJtxHIfHHnsMzz//PGbPns06jsHiOA6enp74888/ERgY+MjXKxQK5OTkaEyZSiQSODo6ahSin58fbGxs9PCdEH3i3Z1yiUSCUaNGsY5BSLvs3r0blZWVePPNN1lHMWgCgUB1iktLis/c3Byenp7w9PTEhAkTVB+Xy+XIyspSleHhw4fxzTffIDMzE05OThqF6OvrC6FQqMtvjegQ70Z83t7e+PPPP+Hn58c6CiFtUllZCX9/f+zbt4+eOdcCBw8exOrVq3HixAmtv7dMJkNmZqbGCDErKwt9+vRR25AfFBQEHx8fdOjQQes5iHbxqvhkMhk6deqEyspK+stHjNY777yDe/fuYfPmzayjGIWqqir07t0b+fn5ertP19DQoPaki8Y/OTk58PDw0ChELy8vo3r0E9/xqvgkEgnGjRuHmzdvso5CSJuIxWKMHDkSYrGYFrS0wsiRI/H222+rPbmeBalUivT0dI1CzMvLg5eXl0Yhenp6Mn/ShSni1T0+iUQCHx8f1jEIaROO4zB79mx88sknVHqtNG7cOBw5coR58QmFQoSGhmqcGlVbW6v26KctW7ZALBajsLAQPj4+GvcQ3d3d6fBtHeJV8WVkZNDh1MRo7dq1C1VVVZg5cybrKEYnOjoaEydOBMdxWn8ShDbY2NggLCxM41zR6upqtSddrF+/HmKxGKWlpfDz89MYIbq6ulIhagGvik8ikbRoZRchhqayshKLFi3C/v37aeqrDYKCgiCVSpGZmWlUv/za2tpi4MCBGDhwoNrHKysr1Z50cerUKYjFYtXCpwcL0dnZ2SAL31DxqvgyMjIwceJE1jEIabVPPvkE48aNQ3h4OOsoRqlxW8ORI0eMqviaY2dnh/DwcI2/D/fu3VMrxCNHjiA5ORm1tbWqJ13cX4i9evUy+EIsqa7Hvut5SCuoRKVUDjuhBfx62uH5/s7oZmulk2vyanGLq6srzp49C3d3d9ZRCGmxpKQkjBo1CsnJyXBwcGAdx2jt3bsXW7duxV9//cU6it6VlpZqLKgRi8WQy+VqZdj4x9HRkXkhJuSWY82ZTJyVFAMA6uVK1eeEFmbgAET6OiBG5IVQF3utXps3xVdXV4euXbuiurqapoqI0eA4DiKRCC+99BJmzZrFOo5RKy8vh6urK4qKimhz+f958EkXjYVoZmbWZCHq6xevHbE5WHo4DVK5Ag9rIIEAEFqYY/F4P0wOd9Pa9Xkz1ZmZmQl3d3cqPWJUdu7ciZqaGsyYMYN1FKNnb2+PkJAQnDt3DlFRUazjGIQePXqgR48eeOyxx1Qf4zgOBQUFqiJMSEjArl27IBaLIRQKmyzErl27ai3Tv6WXijqZ8pGv5TigTqbA0sOpAKC18uPNiO/AgQPYtm0b/vjjD9ZRCGmRiooK+Pv747fffsPgwYNZx+GFL774AmVlZVi+fDnrKEaH4zjcuXNHY4SYkpICW1vbJguxc+fOrbpGQm45Jm2IRZ1MofpY5fU/UZN0Eg3FOejoL0L3J95q8mutLc2xZ0Y4Qpzt2/NtAuBR8X311VcoLS3Ft99+yzoKIS2yYMEC1NTUYMOGDayj8Ma1a9cwdepUpKSksI7CGxzHNfukiy5dumiUYUBAADp16tTke83Yfg3HUwvVpjdr0y8CAgHqsuPAyRqaLT6BABgb4Ij1kwe0+3vizVRnRkYG/dZMjEZiYiJ27dpFP6C1LCwsDCUlJbh16xb69OnDOg4vCAQC9OnTB3369MH48eNVH1cqlWpPujh9+jR++OEHpKWloUePHhqF2MPVE2clxRr39Gx8/33Acn1BJhSykmZzcBxwOr0YpdX17V7tyZvik0gkmDJlCusYhDxS4wktn332Gbp37846Dq+YmZkhKioKR48epfumOmZmZgYPDw94eHjgySefVH1coVCoPeni6NGjWL58OfI6+aPTkBcBi7afoywAsC8uDzMjPNuVnTfFR6e2EGOxY8cO1NXV4Y033mAdhZfGjRuH/fv3U/ExYm5uDm9vb3h7e6vtq56/Ow5/JOa3672lciXS8qvamRDgxdk3lZWVqK6uRu/evVlHIeShysvLsWjRIqxdu5ZWIOtIVFQUTp06hYaGBtZRyH2qGhSPflELVEpl7X4PXoz4MjIy4OXlxXxDJiGP8vHHH+PJJ5/EoEGDWEfhLQcHB3h7e+PSpUsQiUSs45g0mUyGuLg4nD17FtezLIAuvu1+Tzth+x/vxIvio6cyEGOQkJCAX375BcnJyayj8F7j8WVUfPpVX1+Pq1ev4uzZszh79ixiY2Ph7u6OiIgIDA8aheMFAjQo1Fe3cEoF0PiHU4KTNwBm5hCYac6ICC3M4Ner6RWjrcGL4qP7e8TQ0YIW/YqOjsacOXOwbNky1lF4rba2FrGxsTh37hzOnj2Lq1evws/PDyKRCLNnz8Yvv/yi2vxeUl2PE1+fAqBefBUXfkHFhd2q/1+TfBqdh70E+xH/0bgeB+C5MOd25+ZF8UkkEowZM4Z1DEKatX37dtTX1+P1119nHcUkDB48GLdu3UJ+fj569erFOg5vVFdX48KFC6qii4+PR3BwMEQiEf773/9i2LBhzW5q725rBZGPg8Y+PvsR/2my5B4kEACP+Tpo5eBqXhRfRkYGYmJiWMcgpEnl5eV49913cfDgQVrQoicWFhYYPXo0jh49ildffZV1HKNVXl6Of/75B2fPnsW5c+eQnJyMsLAwiEQifPLJJxgyZAg6duzY4vebHemF8xklaie3tJTQwhwxkV6t/rqmGP3JLRzHoWvXrsjIyKApJGKQ5s2bh/r6evz444+so5iUzZs349ixY/jll19YRzEaJSUlOH/+vKroMjIyMGjQIIhEIohEIgwaNAjW1tbtukZrzupsZG1phsXj/emszkYlJSXw9vZGWVkZreokBic+Ph5jx45FSkoKunXrxjqOSblz5w5CQkJQVFREI+1mFBQUqKYtz549i9u3b2Po0KGqohswYAA6dGj7hvPm7IjNwScHkyBXAhA0v6uOns7QjMYVnVR6xNAolUrMmTMHX3zxBZUeA05OTnBycsLVq1fpAb//Jzc3V63oioqKMGLECERERODVV19Fv379YGGh+1p4eZArPn/rDYS+8A7EZRwE+HdzeqPG5/E95uuAmEgvrRxMfT+jLz5a0UkM1fbt29HQ0IDp06ezjmKyxo0bhyNHjphk8XEch+zsbLWiq6qqQkREBCIiIhATE4Pg4GAmo+EjR46gY30p9i0Yi7KaBuyLy0NafhUqpTLYCS3h16sTngujJ7A3a/HixbCyssJHH33EOgohKuXl5fD398fBgwcxcOBA1nFM1unTp/Hee+/h8uXLrKPoHMdxkEgkqvtzZ8+ehVwuV01bRkREwN/fH2Zm7A/sGj16NF599VVMnjyZyfWNvvheeOEFPP3003jppZdYRyFEZe7cuZDJZFi/fj3rKCatoaEBDg4OuHnzJu8WvymVSqSkpKiK7ty5c7C0tFQVnUgkMsgTrRISEjB+/HhkZ2fr5P5hSxj9VCed2kIMTXx8PH799Vd65JAB6NChAyIjI3H8+HGj/+VYoVAgMTFRNW15/vx52NvbIyIiAuPHj8fXX38NNzc31jEfacWKFZg7dy6z0gOMfMTHcRw6deqEu3fvws7OjnUcQqBUKjFixAi89tprtFndQKxbtw6xsbHYtm0b6yitIpPJcOPGDVXRXbhwAT179lRNW0ZERMDZuf2nmOhTfn4+AgMDkZmZqTrRhQWjLr47d+6gf//+KCgoYB2FEADA1q1bsW7dOly6dMkg7qUQIDs7G0OGDMHdu3cN+t9JfX09rl27piq6S5cuwc3NTa3oHB0dWcdslyVLlqC8vBw//PAD0xxGPdVJKzqJIbl37x7ee+89HDp0yKB/wJoad3d32NvbIz4+HmFhYazjqNTV1Wmcc+nj4wORSISYmBjs2rWLV9tgamtr8eOPP+LixYusoxh38dH9PWJIPvzwQzz99NMYMGAA6yjkAY1Pa2BZfNXV1bh48aKq6G7cuIGgoCCIRCIsXLjwoedc8sHPP/+MYcOGGcRgxaiLj0Z8xFDExcVh7969SE1NZR2FNCE6OhpffvklPvjgA71ds6KiQu2cS7FYjH79+kEkEuGjjz7CkCFDYGtrq7c8LCmVSqxYsQIbNmxgHQWAkRefRCLBK6+8wjoGMXFKpRKzZ8/Gl19+yfSGPWmeSCTCCy+8gIqKCp2NqkpLS9XOuZRIJBg0aBAiIiLw1VdfYfDgwe0+59JYHT58GJ06dcKIESNYRwFg5MVHIz5iCLZt2waO4/Daa6+xjkKaYW1tjWHDhuHkyZN45plntPKehYWFaqei3Lp1C0OHDkVERARWr16NgQMHMl2yb0iWL1+Ot99+22D2FBrtqk6FQgFbW1uUlZWZ7G9RhL179+7B398ff/31F/r37886DnmIVatWQSwWt3m6LS8vT63oCgsLMXz4cNWqy7CwML2cc2lsbty4gQkTJiArKwuWlpas4wAw4uLLzs6GSCTC7du3WUchJmz27NngOA5r165lHYU8Qnp6OkaPHo3bt28/cuTBcRxycnLUiq6iogIRERGqogsJCaGnPrTA1KlTERQUhEWLFrGOomK0v57Qik7C2vXr17F//346ocVI+Pj4wMLCAikpKQgMDFT7HMdxyMjIUDvnsqGhQXX01zvvvGMw51wakzt37uDQoUNYtWoV6yhqjLb46P4eYYkWtBgfgUCg2tYQEBCgds7l2bNnYWFhoSq6Dz/8EN7e3gZzT8pYrVmzBpMnT0aXLl1YR1FjtMVHIz7C0tatWyEQCPDqq6+yjkJaQKFQICkpCXK5HF9//TW++uor2NnZQSQSITo6GsuWLYObmxsVnRbV1NRgw4YNiI2NZR1Fg9EWX0ZGBqKioljHICaorKwMH3zwAQ4fPkxTXwZKLpernXP5zz//wNHREUOHDkVlZSUSExPpF2cd27ZtG0aMGAFPT0/WUTQYbfHRiI+wsmTJEjz77LMGdfyVqWtoaNA459LV1RUikQhTp07Fhg0b0LNnTwBATk4O/fzQscYN61u2bGEdpUlGWXwNDQ24c+cO3N3dWUchJub69es4cOAAndDCmFQqVTvn8sqVK/D29oZIJMKbb76JnTt3NnvOZeN9vieeeELPqU3HoUOH0KVLFwwbNox1lCYZZfFlZWXBxcXFYPaEENOgVCoRExODZcuWGdzNer6rqalRO+cyLi4OQUFBiIiIwNtvv41hw4bB3t6+Re8VHR2ttU3spGmGtmH9QUZZfBKJhFZ0Er3bvHkzzM3N6Zg8PaisrFQ75zIpKQn9+vVDREQElixZgqFDh7b5nMvg4GDU1dUhMzMTXl5eWk5Orl+/jqysLDz77LOsozTLKIsvIyOD5ueJXpWVlWHJkiX4+++/aUGLDpSVlamdc5meno6BAwdCJBLhyy+/RHh4uNZOaLp/W8OcOXO08p7kfxqfsG7IM3JGeXLLzJkzERISgtmzZ7OOQkzErFmzYGFhge+//551FF4oKipSOxUlJycHQ4YMUZ2KMnDgQFhZWens+nv37sXWrVvx119/6ewapigvLw8hISHIyspq8dQzC0Y74nvuuedYxyAm4tq1a/j9999pQUs73LlzR63o8vPzVedcbty4Ef369dPrCGH06NGYPn06pFIphEKh3q7Ldz/88AOmTJli0KUHGGnx0T0+oi/3L2gx9P+YDcmD51yWl5djxIgREIlEqhkbludcdunSBcHBwTh//jzGjBnDLAefVFdXY+PGjbhy5QrrKI9kdMVXU1OD0tJSuLi4sI5CTMCmTZtgaWmJqVOnso5isDiOQ2ZmptrxX/X19aoDnd966y0EBAQY3L3Rxvt8VHzasXXrVohEInh4eLCO8khGd48vISEBL7/8MpKTk1lHITxXWlqKgIAAHD16FH379mUdx2BwHIfU1FS1ojM3N1fdnxOJRPDx8THYpeyNrl27hldeeYV+lmiBQqGAr68vtm3bZrB79+5ndCM+WtFJ9GXx4sV48cUXTb70lEolkpKSVNOW58+fh62tLUQiEaKiorB06VK4u7sbfNE9KCwsDMXFxbh9+zZcXV1ZxzFqf/75J7p164ahQ4eyjtIiRld8dH+P6MPVq1fxxx9/mOSCFrlcjvj4eLVzLh0cHCASifDMM89g5cqVvLjVYGZmhqioKBw5cgQzZsxgHceoGfqG9QcZXfFlZGQYxVCaGC+FQoGYmBh89dVXJrGgpaGhAdevX1cV3cWLF+Hi4gKRSITJkyfjp59+Up1zyTfR0dE4cOAAFV87XL16Fbdu3TLoDesPMrrik0gk9CgYolObNm2ClZUVpkyZwjqKTkilUly+fFl1f+7y5cvw9vZGREQEZsyYge3bt6N79+6sY+pFVFQU5syZA5lMZtAbrg3ZihUrMG/ePFhYGE+dGN3ilh49eiAhIQG9evViHYXwUOOClmPHjiE0NJR1HK2oqanBpUuXVEV3/fp1BAYGqhaiDB8+3CRGts0ZOHAgvvvuO0RERLCOYnRyc3MRGhqK7OxsdO7cmXWcFjOq4isvL4eLiwsqKyuNZi6ZGJeZM2dCKBRi1apVrKO0WWVlJS5cuKBadZmYmIi+ffuqVl0OHToUnTp1Yh3TYHz44YeQy+VYtmwZ6yhGZ9GiRZDJZFixYgXrKK1iVMV39epVzJw5E3FxcayjEB66cuUKJk6ciJSUFKMaAd27d0/tnMvU1FTVOZcREREIDw+HjY0N65gG68KFC5gzZw5u3LjBOopRqaqqgpubG65du2Z0j4gznklZ0IpOojsKhQKzZ882igUtxcXFaqeiZGdnIzw8HCKRCCtWrND5OZd8M3jwYOTk5CA/P59uobTCli1bMHLkSKMrPcDIio/28BFd2bhxI4RCoUEuaLl7965a0d29exfDhg2DSCTCTz/9hLCwMFqY0Q4WFhYYPXo0jh07Ro+caiGFQoGVK1di586drKO0iVEVn0QiQXR0NOsYhGdKSkrw4Ycf4sSJEwZx7/jWrVtqRVdWVqY65/KNN95AaGgo03Mu+WjcuHE4cuQIFV8L/fHHH3B0dMSQIUNYR2kTo7rHN3DgQHz//fcIDw9nHYXwyIwZM2BjY4OVK1fq/docx+HmzZtqx3/V1dWpHf8VGBhocOdc8s2dO3cQEhKCoqIi+qWiBYYPH4758+fj+eefZx2lTYxmxMdxHN3jI1p3+fJlHDp0SG8ntHAch7S0NLWiEwgEqqJ7//334evraxAjT1Pi5OQEJycnXL16lX6xfoTLly8jLy8PTz/9NOsobWY0xVdcXAwLCwt069aNdRRiZEqq67Hveh7SCipRKZXDTmgBv552eKZfb8yePRvffPONzvYgKZVKiMVi1bTluXPn0LFjR4hEIowZMwaff/45PDw8qOgMQOPTGqj4Hm7FihWYP3++UW1Yf5DRTHX+888/WLhwIWJjY1lHIUYiIbcca85k4qykGABQL1eqPie0MINMrkCH0gzs/vBV9HXpopVryuVyJCQkqJ1z2b17d9W0ZUREBB2IbKBOnTqFDz74gH7GPMStW7cQFhaG7Oxs2NnZsY7TZkZTfFu2bMHp06fx888/s45CjMCO2BwsPZwGqVyBh/0NFwAQWppj8Xg/TA53a/V1ZDKZxjmXzs7OakVHS+SNQ0NDAxwcHJCVlUUzS81YuHAhOI7Dd999xzpKuxjNWJXu75GW+rf0UlEnUz7ytRyAOpkCSw//e4/vUeUnlUpx5coVtXMuPT09IRKJ8Prrr2Pbtm1wcHDQwndB9K1Dhw6IjIzE8ePHMWnSJNZxDE5lZSW2bNnCiwNEjKb4MjIyjHYFEdGfhNxyLD2c1qLSu1+dTImlh9MQ4myPEGd71cdra2vVzrm8du0aAgICIBKJMG/ePAwfPhxdumhnmpSwFx0djb///puKrwmbN2/G6NGj0adPH9ZR2s1opjpDQkKwdetWhIWFsY5CDNiM7ddwPLVQY3qz4tJeVCcchaK2AhadusM+YgpsfNUfmikQACN9uuH5nuWqhSgJCQkIDQ2FSCSCSCSicy55LisrC0OHDsXdu3dpC8l95HI5vL298csvv2Dw4MGs47SbUYz4lEolMjMzaaqTPFRJdT3OSoqbvKdn0aUXHP/zNcxtu6A27R+UHPoOvZ38YGHbVfUajgNOJOdDsuMnjBw2CJ9//jmdc2liPDw80LlzZyQkJKBfv36s4xiM33//Hb179+ZF6QFGUnx37txB586d6Tdt8lD7ruc1+7mOfsP/97/9I1BxaS8a7kpg4aO+dN1aKMTkj37AzAhPneUkhq3xFBcqvv9Zvnw53nnnHdYxtMYoio/O6CQtkVZQqbZl4X7VSSdRefV3yCuKAABcQx0UdZUar5PKlUjLr9JpTmLYoqOjsWzZMrz//vusoxiES5cuoaCgABMnTmQdRWuMovhoRSdpiUqpvMmPyyuKUHrkezhOWgorJz8IzMxxd/Nc/Lums6n3kekwJTF0IpEIzz//PCoqKozq4aq60rhhnU9HuRnF3Vsa8ZGWsBM2/XucUiYFIIC5zb8/xKoTj0NWfOsh70NPOjBl1tbWGDZsGE6ePMk6CnM5OTk4efIkpk2bxjqKVhlF8dGIj7SEX087WFlo/pXu0N0VdoOeRsH2hcj7fgoainNg5RzQ5HsILczg14vuJZu6xuPLTN3q1asxbdo03q2vMIrtDH5+fti/fz8CAwNZRyEGrKS6HkOWnUArt/CpsbIww8V3R6KbLT3I1ZSlpaUhKioKt27dMtlzVCsqKuDu7o74+HjeHbNn8CM+uVyOnJwceHrSKjvSPKlUihXLPkNd1nUImrl39ygCAfCYrwOVHoGvry/Mzc319tQOQ7Rp0yaMHTuWd6UHGEHx3bp1Cz179oRQKGQdhRioS5cuoV+/fkhLS8PP7/4HQsu2rdkSWpgjJtJLy+mIMRIIBKpTXEyRXC7HqlWr8NZbb7GOohMGX3x0f480p6amBgsWLMCzzz6Lzz//HPv378fIvp5YPN4P1pat+6ttbWmGxeP91I4rI6bNlO/zHThwAK6urhg0aBDrKDph8MVHKzpJU06ePIng4GCUlZUhKSkJzz33nOpzk8PdsHi8P6wtzfGo2zMCAWBtaY7F4/3b9HQGwl8jR45EbGwsampqWEfRq8anL7z99tuso+iMwe/joxEfuV9FRQUWLlyIo0ePYv369Rg/fnyTr5sc7oYQZ3usPZOJ0+nFEODfzemNhBZm4PDvPb2YSC8a6RENnTp1woABA3DmzBk8/vjjrOPozaVLl1BSUoIJEyawjqIzBl98GRkZzf5wI6blzz//RExMDJ544gmIxeJHPggzxNke6ycPQGl1PfbF5SEtvwqVUhnshJbw69UJz4U500IW8lCNx5eZUvEtX74cCxYs4NWG9QcZ/HYGd3d3HDt2jEZ9Jqy4uBjz58/HlStXsHHjRkRGRrKORExEYmIinnnmGWRmZrKOohdZWVkYNGgQcnJyYGtryzqOzhj0Pb76+nrk5+fDzc2NdRTCAMdx+OWXXxAcHIxevXohMTGRSo/oVXBwMGpra02m+FavXo3p06fzuvQAA5/qvHnzJlxdXWFpSUdImZq7d+9i1qxZyMzMxB9//MGbx6EQ49K4reHIkSOYM2cO6zg6VV5ejp9//hmJiYmso+icQY/4aEWn6eE4Dps3b0bfvn0RGhqKuLg4Kj3ClKlsa9i4cSPGjRsHZ2dn1lF0zqBHfLSi07Tk5ORgxowZKCsrw/HjxxEaGso6EiEYM2YMXn/9dUilUt4epCGTybB69WocOHCAdRS9oBEfYU6pVOL777/HgAEDMGrUKMTGxlLpEYPRpUsXBAcH4/z586yj6Mz+/fvh7u6OAQMGsI6iFwY/4nvhhRdYxyA6lJ6ejunTpwMALly4AF9fX8aJCNHUON05ZswY1lG0rnHD+pIlS1hH0Rsa8REm5HI5vvrqKwwbNgyTJk3CuXPnqPSIweLzfb4LFy6gvLwcTzzxBOsoemOwI77q6mrcu3fPJG60mpqEhARMmzYN3bp1w7Vr12i7CjF4/fv3R1FREW7fvs27pxWYwob1BxnsiC8zMxOenp4wMzPYiKSV6uvr8eGHH2LMmDGYM2cOjh49SqVHjIKZmRnGjh2Lo0ePso6iVTdv3sS5c+fw6quvso6iVwbbKrSik18uX76MsLAwJCUlIT4+Hq+99prJPuCTGCc+TneuWrUKb7zxBjp27Mg6il4Z7FQn3d/jh9raWixZsgS7du3CqlWr8MILL1DhEaMUFRWFOXPmQCaT8eJQjXv37mHHjh1ISkpiHUXvaMRHdOb06dMIDg5GYWEhxGIxXnzxRSo9YrR69OgBLy8vXLp0iXUUrdiwYQMef/xxODk5sY6idwZbfDTiM16VlZV48803MXXqVKxatQo7d+5E9+7dWccipN34Mt3ZuGGdr09YfxSDLT4a8Rmnw4cPIygoCEqlEmKx2KSWSBP+a3xMkbHbu3cvvL29ERYWxjoKEwb5WKKysjK4ubmhoqKCpsaMRGlpKebPn49Lly5hw4YNGDlyJOtIhGidXC5Hjx49kJKSgp49e7KO0yYcx2HAgAH45JNP8OSTT7KOw4RBjvgyMjLg7e1NpWcEOI7D3r17ERQUBAcHByQmJlLpEd6ysLDAqFGjjHpbw/nz51FVVWVSD9d9kEGu6qT7e8YhPz8fs2fPRlpaGg4cOIAhQ4awjkSIzjXe53vllVdYR2mT5cuX46233jLpPdIG+Z3T/T3DxnEctm7ditDQUAQEBCAuLo5Kj5iMsWPH4vjx41AoFKyjtFpGRgYuXLiAqVOnso7ClMGO+Ex5GG7Ibt26hZkzZ6KwsBBHjx5Fv379WEciRK+cnZ3Ru3dvXLt2zeieFblq1SrMmDHD5DasP4hGfKRFlEol1qxZg/79+0MkEuHKlStUesRkGeO2hrKyMuzcuROzZ89mHYU5gys+juOo+AyMRCJBZGQkdu7cifPnz+P999/nxckVhLRVdHQ0/v77b9YxWuWnn37ChAkT0Lt3b9ZRmDO44issLISVlRW6du3KOorJk8vl+OabbzB06FA8++yzOH/+PPz9/VnHIoS5YcOGITU1FaWlpayjtEhDQwO+//57k92w/iCDu8cnkUhoRacBSEpKwrRp09C5c2dcuXIFHh4erCMRYjCsrKwgEolw/PhxTJo0iXWcR/r111/h5+eHvn37so5iEAxuxNe4h4+w0dDQgE8++QQjR47EzJkzcfz4cSo9QppgLPf5OI7D8uXL8fbbb7OOYjAMrvhoxMfO1atX0b9/f8TFxSE+Ph6vv/46HSJASDOio6Nx9OhRKJVK1lEe6uzZs6itrcW4ceNYRzEYBld8NOLTv9raWvz3v//Fk08+iQ8++AB//PGHSZ7YTkhreHh4wM7ODgkJCayjPBRtWNdkcP8kaMSnX+fOnUNoaCjy8vKQlJSEl156iUZ5hLSQoU93SiQSxMbGYsqUKayjGBSDKj6lUombN2/Cy8uLdRTeq6ysRExMDF5++WV899132L17NxwcHFjHIsSoGHrxrVy5EjNnzoSNjQ3rKAbFoIovNzcXXbt2ha2tLesovHbkyBEEBwejvr4eYrEYEyZMYB2JEKMkEokQFxeHiooK1lE0lJaWYvfu3bRhvQkGVXx0f0+3ysrK8Morr2DWrFnYuHEjNm3aBHt7e9axCDFaNjY2GDZsGE6dOsU6ioYff/wREydONNrHJ+mSQRUf3d/Tnf379yMoKAidO3dGUlISxowZwzoSIbxgiKe41NfX44cffqAN680wqA3sNOLTvoKCAsyZMwdisRh79+7FsGHDWEcihFeio6OxfPlycBxnMAvD9uzZg8DAQISEhLCOYpBoxMdTHMfh559/RmhoKLy9vREfH0+lR4gO+Pr6wszMDKmpqayjAKAN6y1BIz4eys3NxcyZM3H37l0cPnwY/fv3Zx2JEN4SCASq1Z0BAQGs4+D06dNoaGjA2LFjWUcxWAYz4pPJZLh16xY8PT1ZRzFaSqUS69evR1hYGIYOHao6iYUQolvjxo0zmG0NtGH90QQcx3GsQwD/jvaioqKQnZ3NOopRyszMxOuvvw6pVIrNmzcbxG+ehJiKqqoq9O7dGwUFBUwf8pqWlgaRSIScnBxYW1szy2HoDOZXArq/1zYKhQLfffcdwsPDMWHCBFy4cIFKjxA969SpEwYMGIAzZ84wzbFy5Uq8+eabVHqPYDD3+Oj+XuslJydj2rRpsLGxQWxsLJ14QwhDjff5Hn/8cSbXLykpwZ49e5CWlsbk+saERnxGqKGhAZ999hkiIyMxffp0nDx5kkqPEMZYH1+2fv16PPPMM3B0dGSWwVgY1IjvySefZB3D4F27dg3Tpk2Di4sL4uLi4OLiwjoSIQRASEgIampqkJmZqfdfROvr67FmzRocP35cr9c1VjTiMxJ1dXV499138fjjj2PRokU4dOgQlR4hBqRxW8PRo0f1fu3du3cjJCQEQUFBer+2MTKI4qurq0NhYSH69OnDOopBOn/+PPr27Yvs7GwkJiZi8uTJBnNCBCHkf1gcX0Yb1lvPIIrv5s2bcHNzg4WFwcy8GoSqqirMmTMHkyZNwldffYVff/2V5u8JMWCjR4/GuXPnIJVK9XbNkydPQqFQICoqSm/XNHYGUXwZGRk0zfmAY8eOITg4GDU1NRCLxXj66adZRyKEPELXrl0RFBSEf/75R2/XbBzt0SxQyxnEEEsikdBWhv9z7949vPPOOzh16hR+/PFHOnaIECPTeIrL6NGjdX6tlJQUxMXF4cCBAzq/Fp/QiM+A/P777wgKCoKNjQ2SkpKo9AgxQvrc1rBy5UrMmjULQqFQL9fjC4MZ8b388susYzBTVFSEuXPn4saNG9i9ezciIiJYRyKEtFH//v1RWFiI3Nxcna68Li4uxt69e5Genq6za/AVjfgY4jgOO3fuRHBwMPr06YOEhAQqPUKMnJmZGaKionQ+6lu3bh2ee+459OjRQ6fX4SPmh1RXVlaiV69eqKqqMqnTxPPy8vDmm2/i9u3b2LRpEwYOHMg6EiFES7Zv347ff/8d+/fv18n7S6VSuLm54eTJkwgMDNTJNfiMedM0nnJgKqXHcRx++ukn9OvXDwMHDsS1a9eo9AjhmbFjx+LUqVOQyWQ6ef9du3ahX79+VHptxPwenymt6Lx58ybeeOMNVFdX4/Tp03TKAiE81aNHD3h6eiI2NhYjRozQ6ns3blhfsWKFVt/XlDAfZpnC/T2FQoEVK1Zg8ODBGD9+PC5evEilRwjP6eoUl+PHj0MgEOhluwRfMS8+vo/4UlJSMHz4cPz++++4dOkSFi5cSCfUEGICdLWtgTastx/z4uPriE8mk+GLL75AREQEpk6ditOnT/O64Akh6sLDw5GdnY2CggKtvadYLEZCQoJJb//SBubFx8cR340bNzBo0CBcuHABcXFxmDVrlsks3iGE/MvCwgKjRo3CsWPHtPaeK1euRExMDKysrLT2nqaI6U/j0tJSKJVKODg4sIyhNVKpFB988AGio6Px1ltv4fDhw3B1dWUdixDCSOPxZdpQVFSE/fv3480339TK+5kypsXXONrjw1z1hQsX0LdvX0gkEiQkJGDq1Km8+L4IIW03duxYHDt2DAqFot3vtW7dOrzwwgu8GSiwxHSVBR/u71VXV2Px4sX49ddf8f333+O5555jHYkQYiCcnZ3Rq1cvXLt2DYMHD27z+0ilUqxbtw6nT5/WYjrTZRAjPmN14sQJhISE4N69exCLxVR6hBAN2ljduXPnTvTv3x/+/v5aSmXamBafsY74ysvL8frrr2PatGn44Ycf8PPPP6Nbt26sYxFCDFB7i4+esK59NOJrpYMHDyIoKAiWlpYQi8UYP34860iEEAM2fPhwpKSkoLS0tE1ff+zYMVhYWGDkyJFaTma6mN3j4zgOGRkZRlN8xcXFmDdvHq5evYodO3YgMjKSdSRCiBGwsrKCSCTCiRMn8OKLL7b662nDuvYxG/Hl5+fDxsYG9vb2rCK0CMdx2L17N4KDg+Hk5ITExEQqPUJIq7T1+DKxWIykpCRMmjRJB6lMF7MRnzHc37tz5w5mzZqFrKwsHDx4EIMGDWIdiRBihKKjo/HZZ59BqVS26jCLFStWYPbs2bRhXcuYjfgM+f4ex3HYuHEj+vbti379+uH69etUeoSQNvPw8ICdnR0SExNb/DWFhYU4cOAAZs6cqcNkpolGfA/Izs7GjBkzcO/ePZw4cQKhoaGsIxFCeKDxFJe+ffu26PVr167FpEmT0L17d90GM0E04vs/CoUCq1evxsCBAzFmzBjExsZS6RFCtKY12xrq6uqwfv16LFiwQLehTBSN+ACkpaVh+vTpMDMzw8WLFw0mFyGEP0QiEV544QVUVlbCzs7uoa/dsWMHBg0aBF9fXz2lMy1MRnwKhQJZWVnw8vJicXkVmUyGZcuWYfjw4XjppZdw9uxZKj1CiE7Y2Nhg6NChOHny5ENfp1QqsWLFCtqwrkNMii83Nxfdu3eHjY0Ni8sDAOLj4zF48GCcPn0a165dw5w5c+jRQYQQnWrJdOfRo0dhZWVF26Z0iMlPepb39+rr67FkyRJERUVh7ty5OHr0KNzc3JhkIYSYlsYFLhzHNfsa2rCue0yKj9X9vdjYWPTr1w/JyclISEjAa6+9Rn+5CCF64+vrC4FAgLS0tCY/n5iYiJSUlDad8EJaziRGfDU1NXjrrbfw9NNP45NPPsGBAwfQq1cvvV2fEEIAQCAQPPQUlxUrVmDOnDno0KGDnpOZFiarOjMyMjB69Gi9XOvUqVN44403MGTIECQlJdGeGEIIU9HR0Vj90xbY9H8KaQWVqJTKYSe0QG8b4I8jJ5H53XesI/KegHvYZLOOeHl54dChQ/Dz89PZNSoqKvDf//4Xf//9N9avX4/HH39cZ9cihJCWSMgtx6oTaTiZkg+h0Ar18v/9+DWHAhwHjAnqjRiRF0Jd7NkF5Tm9T3U2NDQgLy8PHh4eOrvGoUOHEBQUBIFAALFYTKVHCGFuR2wOJm2IxemMUggsOqiVHgAoYA6lwBzHUgoxaUMsdsTmsAlqAvQ+1ZmdnQ0nJyedzGGXlJRgwYIFuHTpErZt20bPryKEGIQdsTlYejgVdTLlI1/LcUCdTIGlh1MBAJPD3XSczvTofcSnixWdHMfh119/RXBwMBwcHJCYmEilRwgxCAm55Vh6OK1FpXe/OpkSSw+nITGvXDfBTJjeR3zaXtGZn5+PmJgYpKen48CBAxgyZIjW3psQQtprzZlMSOWKNn2tVK7A2jOZWD95gJZTmTajHfFxHIctW7YgNDQUgYGBuHHjBpUeIcSglFTX46ykGE0tIZRXFqPowFLkrnoZuStfQtmxdRqv4TjgdHoxSqvr9ZDWdDAZ8U2cOLFd75GTk4OZM2eiuLgYx44da/FjPgghRJ/2Xc9r8uOcUoGivZ9C2CcU3We9A4GZGerzM5p8rQDAvrg8zIzw1GFS06L3EZ9EImnziE+pVOKHH37AgAEDEBkZicuXL1PpEUIMjkwmQ2VlJeJzilAv17y315AvgaK6DF1GToNZByEEFh0gdAls8r2kciXS8qt0Hdmk6HXEV1tbi+LiYri6urb6ayUSCaZPnw6lUol//vlHp3sACSH8wXEcZDIZ6urqNP7U1tY2+fG2vO7+1wCAtbU1Ok94DxaufTUyyStLYNG5BwRm5i36HiqlMm3+IzF5ei2+zMxMeHh4wNy8Zf+yAUAul+O7777Dt99+i48++gizZ89u1dcTQgwLx3FoaGjQWwnV1dXBzMwM1tbWzf6xsbFp9nNdu3Zt0evuf42lpSUAYMGeG/g9/q7GPwMLu+6QVxaDUypaVH52Qkut/3swZXotvoyMjFat6ExMTMS0adNgb2+PK1eu6HTTOyGmiuM41NfX662EpFIpzM3NW11A1tbW6Nixo+qRZo8qoPvfz8KCzTO3/XrawcqiQGO6s0MvH5h37ILyM1vRefh//r3HV5AJoXOAxnsILczg16uTviKbBJ0fWVZSXY991/OQVlCJuKRUQFaHl8dH4vn+zuhma9Xk19TX12Pp0qVYt24dli1bhunTp9NTFIjJ4DgOUqlUJyXUXBFZWlq2qoDa+zpTmbUpqa7HsK9PNXmfT15RhLITP6E+NxkQCNAxQISuY2ZqvM7KwgwX3x3Z7M9L0no6K76E3HKsOZOJs5JiAFD7Fy+0MAMHINLXQeNMuitXrmDatGnw8PDAunXr4OTkpIt4hLSYUqlUFZGuS6iurg719fXo0KGDXgrI2toaQqHQZIqIhRnbr+F4amGTWxoeRSAAxgY40j4+LdNJ8f17PE8apHLFQ/9lCwSA0MIci8f74ZmQHvjoo4+wY8cOrFixApMmTaJRHmmSUqnUWwnV1dWhoaEBQqFQ5wV0fxGZmTF5YhjRgYTcckzaEIs6Wes3sVtbmmPPjHCEONtrP5gJ03rxteZMukYdzADZ1V8R3q0Bq1evhoODgzYjER2Ty+UtKhZtlZVMJtNLAd1fRPRLGGmPtvxctLY0w+Lx/nRWpw5otfia+s2Gk8tQemwtpDnxUEqrYWHfC11EU2HtqT50tzTjsH/WcPrNRguaW7qtixKqq6uDQqFod7m0pqg6dOhARUSMTltmwqj0dEOrxdfUXLayQYrKy/thGzwa5p0dUHfzGkoOfove036Ahb3j/4LwdC77YXuIdFFCdXV14DhO56Og+19naWlJRURICyTmlWPtmUycTi+GAP9uTm/UuPbhMV8HxER60SBAh7RWfA9bvfSgu5vmoPOwl9DRb5jax/Wxeqm5PUS6KqG6ujoIBAK9FFDjn8Y9RIQQw1RaXY99cXlIy69CpVQGO6El/Hp1wnNhza92J9qjtc0tzZ1J9yBFzT3Iyu6gg0MTp7dwHH48loAJPjY6K6G6ujrVHqLWFoutrS0cHBxaXVSs9hARQgxTN1srOnuTIa39RE4rqHzkaI9TyFFy8P/BNngULLu5aHy+XsHhp71/YVfS/hYVi52dHRwdHVs9UqKl24QQYrq0VnyVUvlDP89xSpQc+g4wt0DXMW82+7pR0U9g0+5PtRWLEEIIUaO1zUJ2wuY7lOM4lB5eDUVNORye/gAC8+ZfS2fSEUII0SWtFd+/Z9I1/XZlR9dAVpqLHs99BDPL5m/c0pl0hBBCdE3nqzrlFUW4s24aYG6pdgp51+jZsA18TO21dCYdIYQQXdPaPb7utlYQ+Tho7OOz6NwDfd479MivFwj+3b9CpUcIIUSXtHog4OxILwgt2rZiUmhhjphIL23GIYQQQjRotfhCXeyxeLwfrC1b97b/nknnRycVEEII0Tmt76xuPFuOzqQjhBBiiHT2PD46k44QQogh0vkT2OlMOkIIIYZE58VHCCGEGBJ6zDMhhBCTQsVHCCHEpFDxEUIIMSlUfIQQQkwKFR8hhBCTQsVHCCHEpFDxEUIIMSlUfIQQQkwKFR8hhBCT8v8BRRxpnnqUk/kAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"C = nx.Graph()\n",
"\n",
"lst1 = list(range(3))\n",
"lst2 = [\"a\", \"b\", \"c\"]\n",
"\n",
"C.add_nodes_from(lst1, bipartite=0)\n",
"C.add_nodes_from(lst2, bipartite=1)\n",
"\n",
"C.add_edges_from(list(it.product(lst1, lst2)))\n",
"\n",
"nx.draw(C, with_labels = True)\n",
"plt.show()\n",
"\n",
"left, right = nx.bipartite.sets(C)\n",
"positions = {}\n",
"\n",
"positions.update((node, (1, index)) for index, node in enumerate(left))\n",
"positions.update((node, (2, index)) for index, node in enumerate(right))\n",
"\n",
"nx.draw(C, pos = positions, with_labels = True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Sayama Exercise 15.4\n",
"\n",
"Every connected tree graph made of $n$ nodes has exactly $n–1$\n",
"edges. Explain why."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A connected tree graph must not have any cycles and yet have a path for every pair of nodes in it. If we build a connected tree by adding only one additional edge for every node we insert in the graph, we can see that a minimum connected graph of $n$ nodes would have $n-1$ edges. Notice that we can only form loops if we attach more than 1 edge to a new node added to the graph.\n",
"\n",
"Because there are no cycles (i.e., no 'redundancies'), this means a connected tree will always have the minimum amount of edges necessary to allow a path to exist between any 2 nodes. We can see from small examples that for every node added, we must then add an additional edge to connect it to the rest of the graph, from 0 for a 1-node graph, to 1 for a 2-node graph, and so on. Thus, a connected tree of $n$ nodes will always have $n-1$ nodes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Sayama Exercise 15.10\n",
"\n",
"Visualize the following graphs. Look them up in NetworkX’s online documentation to learn how to generate them.\n",
"- A “hypercube graph” of four dimensions.\n",
"- A “ladder graph” of length 5.\n",
"- A “barbell graph” made of two 20-node complete graphs that are connected by a single edge.\n",
"- A “wheel graph” made of 100 nodes"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = nx.hypercube_graph(4)\n",
"nx.draw(G)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"L = nx.ladder_graph(5)\n",
"nx.draw(L)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Barb = nx.barbell_graph(20, 0)\n",
"nx.draw(Barb, with_labels = True)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Wheel = nx.wheel_graph(100)\n",
"nx.draw(Wheel)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Imagine a graph representing hockey players and hockey clubs. Each node is either a player or a club and each edge indicates that a player has played for that club at some point in the past. Explain why this graph is a bipartite graph."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The graph described has two clear levels: players and clubs. Nodes of the same level cannot have edges between them because that would violate our graphical representation of the system: we cannot have different clubs having played for other clubs, just as we cannot have players having played for other players. Thus, we can divide this graph into players and clubs without having nodes in either groups connect within those groups."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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