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253 lines
28 KiB
253 lines
28 KiB
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 57,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"#libraries\n",
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"\n",
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"import random\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 77,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"#Creation of the directed random regular graph according to Configuration model (Bollobas paper), with kout fixed\n",
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"#Think to a different kin, kout (kin is function of kout someway)\n",
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"\n",
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"def RRG_direct(k,N):\n",
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" bool_graph = 0\n",
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" while bool_graph == 0:\n",
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" #print('ok')\n",
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" bool_graph = 1\n",
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" buckets = [[] for i in range(N)]\n",
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" edges_out = []\n",
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" edges_in = []\n",
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" edge_list_out = [[] for i in range(N)]\n",
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" edge_list_in = [[] for i in range(N)]\n",
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" pool_out = [i for i in range(N*k)]\n",
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"\n",
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" i=0\n",
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" j=0\n",
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" while i<N:\n",
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" if(len(buckets[i]) != k):\n",
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" buckets[i].append(j)\n",
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" j += 1\n",
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" else:\n",
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" i += 1\n",
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" \n",
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" pool_out = [i for i in range(N*k)]\n",
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" pool_out_mod = list(pool_out)\n",
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" \n",
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" for i in range(int(N*k)): #outgoing edges\n",
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" j = int(random.uniform(0, 1)*(N*k-i))\n",
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" l = j\n",
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" while l == j:\n",
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" l = int(random.uniform(0, 1)*(N*k))\n",
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" \n",
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" edges_out.append(pool_out_mod[j])\n",
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" edges_in.append(pool_out[l])\n",
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" del pool_out_mod[j]\n",
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" \n",
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" \n",
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" for i in range(len(edges_out)): #We store the graph in two sorts of compressed-row pythonic formats (list of list)\n",
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" edge_list_out[int(edges_out[i]/k)].append(int(edges_in[i]/k))\n",
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" for i in range(len(edges_in)):\n",
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" edge_list_in[int(edges_in[i]/k)].append(int(edges_out[i]/k))\n",
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" \n",
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" #print(edge_list)\n",
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"\n",
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" #I check if the graph I built is good (no multiedges/no loops) for both edge_lists, \n",
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" #but in the limit of big N and low k,\n",
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" #we could neglect this since the probability of finding such a wrong graph is .... (check paper Bollobas)\n",
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"\n",
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" for i in range(len(edge_list_out)):\n",
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" for j in range(len(edge_list_out[i])):\n",
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" temp = edge_list_out[i][j]\n",
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" if i == edge_list_out[i][j]: #checking for loops\n",
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" #print('ok0')\n",
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" bool_graph = 0\n",
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" break\n",
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" no_element = list(edge_list_out[i])\n",
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" del no_element[j]\n",
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" for l in range(len(no_element)):\n",
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" if no_element[l] == temp: #checking for multiedges\n",
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" #print('ok1')\n",
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" bool_graph = 0\n",
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" break\n",
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" del no_element\n",
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" if bool_graph == 0:\n",
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" break\n",
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" if bool_graph == 0:\n",
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" break\n",
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" \n",
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" if(bool_graph==0):\n",
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" #print('ok')\n",
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" del buckets, edges_out, edges_in, edge_list_out, edge_list_in, pool_out, pool_out_mod\n",
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" \n",
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" return edge_list_out, edge_list_in"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 85,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"#Computing numerically the reciprocated arcs\n",
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"\n",
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"def r_numerical(edge_list_out, edge_list_in, k, N):\n",
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" r = 0\n",
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" for i in range(len(edge_list_out)):\n",
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" for j in range(len(edge_list_out[i])):\n",
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" if(edge_list_out[i][j] in edge_list_in[i]):\n",
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" r += 0.5\n",
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" return 2*r/(k*N)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 89,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"#Main\n",
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"\n",
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"def Compare_formula_vs_algo(k,N_ens):\n",
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" dim_arr = [10, 50, 100, 500, 1000, 5000]\n",
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" r_num = [[] for i in range(len(dim_arr))]\n",
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" r_num_mean = []\n",
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" r_num_err = []\n",
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" r_th = []\n",
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" for N in dim_arr:\n",
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" print(N)\n",
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" for n in range(N_ens):\n",
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" \n",
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" #Graph creation from ERG\n",
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" #edge_list = ERG(p,N)\n",
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" \n",
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" #Graph creation from RRG\n",
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" edge_list = RRG_direct(k,N)\n",
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" n+=1\n",
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" \n",
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" #Computing the number of reciprocated arcs (algorithm)\n",
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" r_num[dim_arr.index(N)].append(r_numerical(edge_list[0],edge_list[1],k,N))\n",
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" \n",
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" #Calculating the average over the ensemble\n",
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" r_num_mean.append(sum(r_num[dim_arr.index(N)])/N_ens)\n",
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" \n",
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" #Calculating the error for each value\n",
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" r_num_err.append(np.std(r_num[dim_arr.index(N)]))\n",
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" \n",
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" #Calculating the clustering coefficient for RRG (formula)\n",
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" r_th.append(k/(N-1))\n",
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" \n",
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" #Calculating the clustering coefficient for ERG (formula)\n",
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" #C_th.append(k/(N))\n",
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" \n",
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" return (r_num_mean, r_num_err, r_th)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 90,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"50\n",
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"100\n",
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"500\n",
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"1000\n",
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"5000\n"
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]
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}
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],
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"source": [
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"r_try = Compare_formula_vs_algo(3,100)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 94,
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"metadata": {},
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"outputs": [
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{
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"data": {
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WJo3sHOpwjDGmwpR0SWqy+z4A527mD9zu3xBY20c1VmJcJP+58UzaJtYJdSjG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\n",
|
|
"text/plain": [
|
|
"<matplotlib.figure.Figure at 0x234243d9e10>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"#Plots for random regular graphs\n",
|
|
"#Remember to specify the kout of the graph and get results for many different kout\n",
|
|
"\n",
|
|
"dim_arr = [10, 50, 100, 500, 1000, 5000]\n",
|
|
"log_dim_arr = np.log10(np.asarray(dim_arr))\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.errorbar(log_dim_arr, r_try[0], yerr=r_try[1], fmt='--o', label='C from numerics')\n",
|
|
"plt.plot(log_dim_arr, r_try[2], 'x', label='C from theory')\n",
|
|
"plt.xlabel('Net size')\n",
|
|
"plt.ylabel('# reciprocated arcs')\n",
|
|
"plt.title('Comparison reciprocated arcs numerics vs theory')\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
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"display_name": "Python [default]",
|
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"language": "python",
|
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"name": "python3"
|
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},
|
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"language_info": {
|
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"codemirror_mode": {
|
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"name": "ipython",
|
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"version": 3
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},
|
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"file_extension": ".py",
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"mimetype": "text/x-python",
|
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"name": "python",
|
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
|
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"version": "3.6.2"
|
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|
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|
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"nbformat_minor": 2
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|
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