{
    "info": {
        "author": "chengjun",
        "author_email": "wangchj04@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 3 - Alpha",
            "Intended Audience :: Developers",
            "License :: OSI Approved :: MIT License",
            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.3",
            "Programming Language :: Python :: 3.4",
            "Programming Language :: Python :: 3.5",
            "Programming Language :: Python :: 3.6",
            "Topic :: Software Development :: Build Tools"
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        "description": "# flownetwork\n\nA python package for flow network analysis https://pypi.python.org/pypi/flownetwork\n\n## install the most updated github version\n\n```python\npip install -U git+https://github.com/chengjun/flownetwork.git\n```\n\n## install and upgrade\n\nOpen a terminal, and input:\n\n\n```python\npip install flownetwork\n```\n\nif your want to ungrade to a new version, just input:\n\n```python\npip install --upgrade flownetwork\n```\n\nif your want to uninstall, please input:\n\n```python\npip uninstall flownetwork\n```\n\n## import\n\n```python\n# import packages\nimport flownetwork.flownetwork as fn\nimport networkx as nx\nimport matplotlib.pyplot as plt\n\nprint(fn.__version__)\n\n```\n\n    $version = 3.0.9$\n\n\n\n## flow network analysis\n\n```python\nhelp(fn.constructFlowNetwork)\n```\n\n    Help on function constructFlowNetwork in module flownetwork.flownetwork:\n\n    constructFlowNetwork(C)\n        C is an array of two dimentions, e.g.,\n        C = np.array([[user1, item1],\n                      [user1, item2],\n                      [user2, item1],\n                      [user2, item3]])\n        Return a balanced flow network\n\n\n\n\n```python\n# constructing a flow network\ndemo = fn.attention_data\ngd = fn.constructFlowNetwork(demo)\n```\n\n```python\n# drawing a demo network\nfig = plt.figure(figsize=(12, 8),facecolor='white')\npos={0: np.array([ 0.2 ,  0.8]),\n 2: np.array([ 0.2,  0.2]),\n 1: np.array([ 0.4,  0.6]),\n 6: np.array([ 0.4,  0.4]),\n 4: np.array([ 0.7,  0.8]),\n 5: np.array([ 0.7,  0.5]),\n 3: np.array([ 0.7,  0.2 ]),\n 'sink': np.array([ 1,  0.5]),\n 'source': np.array([ 0,  0.5])}\nwidth=[float(d['weight']*1.2) for (u,v,d) in gd.edges(data=True)]\nedge_labels=dict([((u,v,),d['weight']) for u,v,d in gd.edges(data=True)])\nnx.draw_networkx_edge_labels(gd,pos,edge_labels=edge_labels, font_size = 15, alpha = .5)\nnx.draw(gd, pos, node_size = 3000, node_color = 'orange',\n        alpha = 0.2, width = width, edge_color='orange',style='solid')\nnx.draw_networkx_labels(gd,pos,font_size=18)\nplt.show()\n```\n\n![](img/flownetwork_demo.png)\n\n\n```python\nnx.info(gd)\n```\n\n\n\n\n    'Name: \\nType: DiGraph\\nNumber of nodes: 9\\nNumber of edges: 15\\nAverage in degree:   1.6667\\nAverage out degree:   1.6667'\n\n\n\n\n```python\n# balancing the network\n# if it is not balanced\ngh = fn.flowBalancing(gd)\nnx.info(gh)\n```\n\n\n\n\n    'Name: \\nType: DiGraph\\nNumber of nodes: 9\\nNumber of edges: 15\\nAverage in degree:   1.6667\\nAverage out degree:   1.6667'\n\n\n\n\n\n\n```python\n# flow matrix\nm = fn.getFlowMatrix(gd)\nm\n```\n\n\n\n\n    matrix([[ 0.,  1.,  0.,  0.,  3.,  1.,  0.,  0.,  0.],\n            [ 0.,  0.,  3.,  0.,  0.,  0.,  0.,  0.,  0.],\n            [ 0.,  0.,  0.,  2.,  0.,  0.,  0.,  0.,  2.],\n            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  2.],\n            [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  2.],\n            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  2.],\n            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.],\n            [ 5.,  2.,  1.,  0.,  0.,  0.,  1.,  0.,  0.],\n            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])\n\n\n\n\n```python\nfn.getMarkovMatrix(m)\n```\n\n\n\n\n    array([[ 0.        ,  0.2       ,  0.        ,  0.        ,  0.6       ,\n             0.2       ,  0.        ,  0.        ,  0.        ],\n           [ 0.        ,  0.        ,  1.        ,  0.        ,  0.        ,\n             0.        ,  0.        ,  0.        ,  0.        ],\n           [ 0.        ,  0.        ,  0.        ,  0.5       ,  0.        ,\n             0.        ,  0.        ,  0.        ,  0.5       ],\n           [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n             0.        ,  0.        ,  0.        ,  1.        ],\n           [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n             0.33333333,  0.        ,  0.        ,  0.66666667],\n           [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n             0.        ,  0.        ,  0.        ,  1.        ],\n           [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n             0.        ,  0.        ,  0.        ,  1.        ],\n           [ 0.55555556,  0.22222222,  0.11111111,  0.        ,  0.        ,\n             0.        ,  0.11111111,  0.        ,  0.        ],\n           [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n             0.        ,  0.        ,  0.        ,  0.        ]])\n\n\n\n\n```python\nfn.getUmatrix(gd)\n```\n\n\n\n\n    matrix([[ 1.        ,  0.2       ,  0.2       ,  0.1       ,  0.6       ,\n              0.4       ,  0.        ],\n            [ 0.        ,  1.        ,  1.        ,  0.5       ,  0.        ,\n              0.        ,  0.        ],\n            [ 0.        ,  0.        ,  1.        ,  0.5       ,  0.        ,\n              0.        ,  0.        ],\n            [ 0.        ,  0.        ,  0.        ,  1.        ,  0.        ,\n              0.        ,  0.        ],\n            [ 0.        ,  0.        ,  0.        ,  0.        ,  1.        ,\n              0.33333333,  0.        ],\n            [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n              1.        ,  0.        ],\n            [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n              0.        ,  1.        ]])\n\n\n\n\n```python\n# return dissipationToSink,totalFlow,flowFromSource\n\nfn.networkDissipate(gd)\n```\n\n\n\n\n    defaultdict(<function flownetwork.flownetwork.<lambda>>,\n                {0: [0, 5, 5],\n                 1: [0, 3, 2],\n                 2: [2, 4, 1],\n                 3: [2, 2, 0],\n                 4: [2, 3, 0],\n                 5: [2, 2, 0],\n                 6: [1, 1, 1]})\n\n\n\n\n```python\n# flow distance\nfn.flowDistanceFromSource(gd)\n```\n\n\n\n\n    {0: 1.0,\n     1: 1.333333333333333,\n     2: 2.0,\n     3: 3.0,\n     4: 2.0,\n     5: 2.5,\n     6: 1.0,\n     'sink': 3.2222222222222214}\n\n\n\n\n```python\nfn.outflow(gd, 1)\n```\n\n\n\n\n    3\n\n\n\n\n```python\nfn.inflow(gd, 1)\n```\n\n\n\n\n    3\n\n\n\n\n```python\nfn.averageFlowLength(gd)\n```\n\n\n\n\n    3.2222222222222223\n\n\n\n\n```python\n# fn.getAverageTimeMatrix(gd)\n```\n\n\n## Plot\n\n```python\nfig = plt.figure(figsize=(9, 9),facecolor='white')\nax = fig.add_subplot(111)\nfn.plotTree(gd,ax)\nplt.show()\n```\n\n\n\n```python\nfrom random import random\nx = np.array(range(1, 100))\ny = (x+random()*x)**3\n\nplt.plot(x, y)\nplt.xscale('log');plt.yscale('log')\nplt.show()\n```\n\n\n![png](img/output_109_0.png)\n\n\n\n```python\nfn.alloRegressPlot(x,y,'r','s','$x$','$y$', loglog=True)\n```\n\n\n![png](img/output_110_0.png)\n\n\n\n```python\nrg = np.array([ 20.7863444 ,   9.40547933,   8.70934714,   8.62690145,\n     7.16978087,   7.02575052,   6.45280959,   6.44755478,\n     5.16630287,   5.16092884,   5.15618737,   5.05610068,\n     4.87023561,   4.66753197,   4.41807645,   4.2635671 ,\n     3.54454372,   2.7087178 ,   2.39016885,   1.9483156 ,\n     1.78393238,   1.75432688,   1.12789787,   1.02098332,\n     0.92653501,   0.32586582,   0.1514813 ,   0.09722761])\nfn.powerLawExponentialCutOffPlot(rg, '$x$', '$p(x)$')\n```\n\n\n\n\n    [-0.0099301962503268171,\n     -0.064764460567964449,\n     -0.17705123513352666,\n     0.89999847894045781]\n\n\n\n\n![png](img/output_111_1.png)\n\n\n\n```python\nfn.DGBDPlot(rg)\n```\n\n\n![png](img/output_112_0.png)\n\n\n\n```python\nfrom networkx.utils import powerlaw_sequence\npl_sequence = powerlaw_sequence(1000,exponent=2.5)\n\nfig = plt.figure(figsize=(4, 4),facecolor='white')\nax = fig.add_subplot(111)\nfn.plotPowerlaw(pl_sequence,ax,'r','$x$')\n\n```\n\n    Calculating best minimal value for power law fit\n\n\n\n![png](img/output_113_1.png)\n\n\n\n```python\nfig = plt.figure(figsize=(4, 4),facecolor='white')\nax = fig.add_subplot(111)\nfn.plotCCDF(pl_sequence,ax,'b','$x$')\n\n```\n\n    Calculating best minimal value for power law fit\n\n\n\n![png](img/output_114_1.png)\n\n\n\n```python\nbins, result, gini_val = fn.gini_coefficient(np.array(pl_sequence))\n\nplt.plot(bins, bins, '--', label=\"perfect\")\nplt.plot(bins, result, label=\"observed\")\nplt.title(\"$GINI: %.4f$\" %(gini_val))\n\nplt.legend(loc = 0, frameon = False)\nplt.show()\n```\n\n\n![png](img/output_115_0.png)",
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