kk-layout-in-3-packages-zika.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kamada-Kawai layout in igraph, graphviz and networkx illustrated by Plotly plots of an unrooted tree ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tree as an instance of the igraph.Graph class ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "        <script type=\"text/javascript\">\n",
       "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
       "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
       "        if (typeof require !== 'undefined') {\n",
       "        require.undef(\"plotly\");\n",
       "        requirejs.config({\n",
       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
       "            }\n",
       "        });\n",
       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
       "        });\n",
       "        }\n",
       "        </script>\n",
       "        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.graph_objects as go\n",
    "import plotly.io as pio\n",
    "import igraph as ig\n",
    "pio.templates.default='none'\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode,  iplot\n",
    "init_notebook_mode(connected=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = ig.Graph.Read_GML('Data/zika.gml')\n",
    "V = range(len(G.vs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = [e.tuple for e in G.es]# list of edges\n",
    "labels = [v['name'] for v in G.vs]\n",
    "layt = G.layout('kk') #kamada-kawai"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define data for the Plotly plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_plotly_data(E, coords):\n",
    "    # E is the list of tuples representing the graph edges\n",
    "    # coords is the list of node coordinates \n",
    "    N = len(coords)\n",
    "    Xnodes = [coords[k][0] for k in range(N)]# x-coordinates of nodes\n",
    "    Ynodes = [coords[k][1] for k in range(N)]# y-coordnates of nodes\n",
    "\n",
    "    Xedges = []\n",
    "    Yedges = []\n",
    "    for e in E:\n",
    "        Xedges.extend([coords[e[0]][0], coords[e[1]][0], None])\n",
    "        Yedges.extend([coords[e[0]][1], coords[e[1]][1], None])\n",
    "        \n",
    "    return Xnodes, Ynodes, Xedges, Yedges \n",
    "\n",
    "def get_node_trace(x, y, labels, marker_size=5, marker_color='#6959CD', \n",
    "                   line_color='rgb(50,50,50)', line_width=0.5):\n",
    "    return go.Scatter(\n",
    "                x=x,\n",
    "                y=y,\n",
    "                mode='markers',\n",
    "                marker=dict(\n",
    "                            size=marker_size, \n",
    "                            color=marker_color,\n",
    "                            line=dict(color=line_color, width=line_width)\n",
    "                             ),\n",
    "            text=labels,\n",
    "            hoverinfo='text'\n",
    "               )\n",
    "\n",
    "def get_edge_trace(x, y, linecolor='rgb(210,210,210)', linewidth=1):\n",
    "    return go.Scatter(\n",
    "                x=x,\n",
    "                y=y,\n",
    "                mode='lines',\n",
    "                line=dict(color=linecolor, width=linewidth),\n",
    "                hoverinfo='none'\n",
    "               )\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xn, Yn, Xe, Ye = get_plotly_data(E, layt)\n",
    "trace1 = get_edge_trace(Xe, Ye)\n",
    "trace2 = get_node_trace(Xn, Yn, labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the plot layout:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "title1= \"Unrooted tree\"\n",
    "width=800\n",
    "height=800\n",
    "layout=go.Layout(title=title1,\n",
    "            font_size=12,\n",
    "            showlegend=False,\n",
    "            width=width,\n",
    "            height=height,\n",
    "            xaxis_visible=False,\n",
    "            yaxis_visible=False,          \n",
    "            hovermode='closest',\n",
    "            paper_bgcolor='#eeeeee',     \n",
    "            annotations=[dict(showarrow=False, \n",
    "                               text='igraph Kamada-Kawai layout',  \n",
    "                               xref='paper',     \n",
    "                               yref='paper',     \n",
    "                               x=0,  \n",
    "                               y=-0.1,  \n",
    "                               xanchor='left',   \n",
    "                               yanchor='bottom',  \n",
    "                               font=dict(size=14)     \n",
    "                              )\n",
    "                        ],           \n",
    "            )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "linkText": "Export to plot.ly",
        "plotlyServerURL": "https://plot.ly",
        "showLink": false
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       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1 = go.Figure(data=[trace1, trace2], layout=layout)\n",
    "iplot(fig1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the number of weak connected components in this graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(G.clusters( mode='weak'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tree as an instance of the  pygraphviz.AGraph class ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pygraphviz as pgv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = pgv.AGraph(strict=True, directed=False)\n",
    "g.add_nodes_from(V)\n",
    "g.add_edges_from(E)\n",
    "g.layout(prog='neato') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_node_coordinates(g):\n",
    "    #convert the string containing the node coordinates to a list of two floats\n",
    "    #returns the list of lists of node coordinates\n",
    "    if  not isinstance(g, pgv.AGraph):\n",
    "        raise ValueError('The graph g must be a pygraphviz AGraph')\n",
    "    N = len(g.nodes())    \n",
    "    coords=[]\n",
    "    for k in range(N):\n",
    "        s = g.get_node(k).attr['pos']\n",
    "        t = s.split(\",\")\n",
    "        coords.append([float(t[0]), float(t[1])])\n",
    "    return coords  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "pgvlayt = get_node_coordinates(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xnode, Ynode, Xedge, Yedge = get_plotly_data(E, pgvlayt)\n",
    "trace3 = get_edge_trace(Xedge, Yedge)\n",
    "trace4 = get_node_trace(Xnode, Ynode, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = go.Figure(data=[trace3, trace4], layout=layout)\n",
    "#fig2.update_layout(annotations[0]['text']='Graphviz neato layout')\n",
    "fig2['layout']['annotations'][0]['text'] = \"Graphviz neato layout\"\n",
    "iplot(fig2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Tree as an instance of the networkx.Graph class###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = nx.Graph()\n",
    "H.add_nodes_from(V)\n",
    "H.add_edges_from(E)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Get the node positions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pos = nx.kamada_kawai_layout(H) \n",
    "nodes=pos.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define data for the  Plotly plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xv = [pos[node][0] for node in nodes]\n",
    "Yv = [pos[node][1] for node in nodes]\n",
    "Xed = []\n",
    "Yed = []\n",
    "for edge in H.edges():\n",
    "    Xed.extend([pos[edge[0]][0],pos[edge[1]][0], None])\n",
    "    Yed.extend([pos[edge[0]][1],pos[edge[1]][1], None]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "trace5 = get_edge_trace(Xed, Yed)\n",
    "trace6 = get_node_trace(Xv, Yv, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "linkText": "Export to plot.ly",
        "plotlyServerURL": "https://plot.ly",
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       "                        {\"annotations\": [{\"font\": {\"size\": 14}, \"showarrow\": false, \"text\": \"Networkx Kamada-Kawai layout\", \"x\": 0, \"xanchor\": \"left\", \"xref\": \"paper\", \"y\": -0.1, \"yanchor\": \"bottom\", \"yref\": \"paper\"}], \"font\": {\"size\": 12}, \"height\": 800, \"hovermode\": \"closest\", \"paper_bgcolor\": \"#eeeeee\", \"showlegend\": false, \"template\": {\"data\": {\"scatter\": [{\"type\": \"scatter\"}]}}, \"title\": {\"text\": \"Unrooted tree\"}, \"width\": 800, \"xaxis\": {\"visible\": false}, \"yaxis\": {\"visible\": false}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
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       "            Plotly.purge(gd);\n",
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       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
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       "\n",
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       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
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      ]
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     "metadata": {},
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    }
   ],
   "source": [
    "fig3 = go.Figure(data=[trace5, trace6], layout=layout)\n",
    "fig3['layout'].update(width=800, height=800)\n",
    "fig3['layout']['annotations'][0]['text'] = \"Networkx Kamada-Kawai layout\"\n",
    "iplot(fig3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the number of connected components computed via networkx:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print (nx.number_connected_components(H))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case the graph is connected and the KK-layout implemented in the three Python packages generates similar nodes placement, up to a transformation.\n",
    "\n",
    "Comparing with the results of the experiment performed in this [Jupyter Notebook](http://nbviewer.jupyter.org/github/empet/Networks/blob/master/kk-layout-in-3-packages-netsci.ipynb) we are led to the conclusion that the `nx.kamada_kawada_layout` doesn't work with disconnected graphs. "
   ]
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