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| { | |
| "metadata": { | |
| "name": "", | |
| "signature": "sha256:dcc9c498f43dac3f108956486820ea5ab2b7a7990fbd15aeaeab10cffcc51f23" | |
| }, | |
| "nbformat": 3, | |
| "nbformat_minor": 0, | |
| "worksheets": [ | |
| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "%matplotlib inline\n", | |
| "import itertools\n", | |
| "import networkx\n", | |
| "import copy\n", | |
| "import matplotlib.pylab as pylab\n", | |
| "pylab.rcParams['figure.figsize'] = 10, 8\n", | |
| "\n", | |
| "vertices = [\n", | |
| " ('B', 'D'), ('B', 'E'), ('A', 'E'), \n", | |
| " ('A', 'B'), ('A', 'C'), ('B', 'F'), \n", | |
| " ('E', 'F'), ('C', 'G'), ('A', 'G'), \n", | |
| " ('A', 'H'), ('G', 'H')\n", | |
| "]\n" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 1 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Original graph" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "G = networkx.DiGraph()\n", | |
| "G.add_edges_from(vertices)\n", | |
| "networkx.draw_networkx(G, pos=networkx.random_layout(G), nodecolor='r',edge_color='b', with_labels=True, node_size=1000)\n", | |
| "pylab.plt.show()" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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AcxZwI1Dmn9fNDrSRBATpAEynUWIlIpJDnz6wZg0EBZkq35kFHMUX1K1rCol+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\n9OihpErcw7LMutFrr61OWuqVvO3GdGFKSMj/27v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yOfPmyeTrp59WHYlzMUOf1dmzQEoK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ZAAAB\nVElEQVT1FBAQoKWlpakI1zDW3Jfz589rly9f1jRN0z7//HPt+eefVxCp8Y4cOWJV8/rWrVutal7X\ntWLl5eWFWbNmoUOHDldmXoWGhl4z82rcuHHIyMi40jfj7e2NuLg4PcNwKtbck8WLF2PhwoXw9vaG\nv78/Fi1apDhqx7Pmvrgja+7LTz/9hNmzZ8PLywu+vr78fIHcl4YNG6Jjx45o2rQpypUrhz59+qBR\no0aKI3cca7+Gli5dig4dOsDHx0dluIax5r6MHj0aL774IsLCwmCxWDBx4kSXrvgC1t2Xffv24YUX\nXoCHhwcaN26M+fPnK47a8Xr27In169fj3LlzqFOnDsaOHYv8/HwAck86d+6M33//HSEhIfDz88MX\nX3xR6mtaNSCUiIiIiEqn665AIiIiInfGxIqIiIhIJ0ysiIiIiHTCxIqIiIhIJ0ysiIiIiHTy/wGN\n1uDApGCoswAAAABJRU5ErkJggg==\n", | |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x7fd684868090>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 8 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Adjacency matrix\n", | |
| "\n", | |
| "If an adjacency matrix is obtained, we can iterate over it and set to zero the positions corresponding to spare edges" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def transitive_reduction_adjacency(M):\n", | |
| " indices = range(len(M))\n", | |
| " for i, j in itertools.product(indices, indices):\n", | |
| " if M[i, j]:\n", | |
| " for k in indices:\n", | |
| " if M[j, k]:\n", | |
| " M[i, k] = 0\n", | |
| "\n", | |
| "\n", | |
| " \n", | |
| "M = networkx.to_numpy_matrix(G)\n", | |
| "transitive_reduction_adjacency(M)\n", | |
| "G2 = networkx.DiGraph(M)\n", | |
| "G2 = networkx.relabel_nodes(G2, dict(zip(range(len(G.nodes())),G.nodes())))\n", | |
| "networkx.draw_networkx(G2,pos=networkx.spectral_layout(G2), nodecolor='r',edge_color='b', with_labels=True, node_size=1000)\n", | |
| "pylab.plt.show()" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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aNaCoKMDFiPiBxXJ0s1SFLgk3Pq/UyMrKolmzZjRp0oQJEyac9Jrs7GzatWtH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\n", | |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x7fd68458b790>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 3 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Breath first search\n", | |
| "\n", | |
| "Find removable edges during the BFS" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def transitive_reduction_dfs(G):\n", | |
| " for u in G.nodes():\n", | |
| " for v in G.successors(u):\n", | |
| " for w in itertools.chain.from_iterable(networkx.dfs_successors(G, v).values()):\n", | |
| " if v != w and G.has_edge(u, w):\n", | |
| " G.remove_edge(u, w)\n", | |
| " \n", | |
| "G1 = copy.deepcopy(G)\n", | |
| "transitive_reduction_dfs(G1)\n", | |
| "networkx.draw_networkx(G1, pos=networkx.spectral_layout(G1), nodecolor='r',edge_color='b', with_labels=True, node_size=1000)\n", | |
| "pylab.plt.show()" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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aNaCoKMDFiPiBxXJ0s1SFLgk3Pq/UyMrKolmzZjRp0oQJEyac9Jrs7GzatWtH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\n", | |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x7fd6848c8fd0>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 4 | |
| } | |
| ], | |
| "metadata": {} | |
| } | |
| ] | |
| } |
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