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Networks - Graphs 4
Raw
readme.md

Graph Example 4 for How to Create Effective Network Data Visualization

This example relies on the jLouvain library to calculate community structure of the network using the Louvain method.

A second smaller network is created from the communities and their connections to each other to provide a mini-map of the network.

This also includes a simple legend of the module numbers utilizing d3.legend.

Raw
d3.legend.min.js
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d=[];if(b.length>1)d=b;else for(var e=a.domain(),f=(e[e.length-1]-e[0])/(b-1),g=0;b>g;g++)d.push(c(e[0]+g*f));return{data:d,labels:d,feature:function(b){return a(b)}}},d3_quantLegend:function(a,b,c){var d=a.range().map(function(d){var e=a.invertExtent(d);b(e[0]),b(e[1]);return b(e[0])+" "+c+" "+b(e[1])});return{data:a.range(),labels:d,feature:this.d3_identity}},d3_ordinalLegend:function(a){return{data:a.domain(),labels:a.domain(),feature:function(b){return a(b)}}},d3_drawShapes:function(a,b,c,d,e,f){"rect"===a?b.attr("height",c).attr("width",d):"circle"===a?b.attr("r",e):"line"===a?b.attr("x1",0).attr("x2",d).attr("y1",0).attr("y2",0):"path"===a&&b.attr("d",f)},d3_addText:function(a,b,c){b.append("text").attr("class","label"),a.selectAll("g.cell text").data(c).text(this.d3_identity)},d3_calcType:function(a,b,c,d,e){var f=a.ticks?this.d3_linearLegend(a,b,d):a.invertExtent?this.d3_quantLegend(a,d,e):this.d3_ordinalLegend(a);return f.labels=this.d3_mergeLabels(f.labels,c),f},d3_placement:function(a,b,c,d,e,f){b.attr("transform",c),d.attr("transform",e),"horizontal"===a&&d.style("text-anchor",f)}}},{}],3:[function(a,b,c){var d=a("./legend");b.exports=function(){function a(a){var o=d.d3_calcType(c,h,i,j,m),p=a.selectAll(".cell").data(o.data),q=p.enter().append("g",".cell").attr("class","cell").style("opacity",1e-6);shapeEnter=q.append(e).attr("class","swatch"),shapes=p.select("g.cell "+e),p.exit().transition().style("opacity",0).remove(),"line"===e?(d.d3_drawShapes(e,shapes,0,f),shapes.attr("stroke-width",o.feature)):d.d3_drawShapes(e,shapes,o.feature,o.feature,o.feature,b),d.d3_addText(a,q,o.labels);var r,s,t=p.select("text"),u=shapes[0].map(function(a,b){var d=a.getBBox(),f=c(o.data[b]);return"line"===e&&"horizontal"===n?d.height=d.height+f:"line"===e&&"vertical"===n&&(d.width=d.width),d}),v=d3.max(u,function(a){return a.height+a.y}),w=d3.max(u,function(a){return 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Raw
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Raw
index.html
<html>
<head>
<title>Modularity Minimap</title>
<meta charset="utf-8" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min.js"></script>
<script src="jsLouvain.js" type="text/JavaScript"></script>
<script src="d3.legend.min.js" type="text/JavaScript"></script>
</head>
<style>
svg {
height: 500px;
width: 500px;
border: 1px solid gray;
}
</style>
<body>
<div id="viz">
<svg class="main">
</svg>
</div>
</body>
<footer>
<script>
d3.csv("firm.csv",function(error,data) {createNetwork(data)});
function onlyUnique(value, index, self) {
return self.indexOf(value) === index;
}
function createNetwork(edgelist) {
var nodeHash = {};
var nodes = [];
var edges = [];
edgelist.forEach(function (edge) {
if (!nodeHash[edge.source]) {
nodeHash[edge.source] = {id: edge.source, label: edge.source};
nodes.push(nodeHash[edge.source]);
}
if (!nodeHash[edge.target]) {
nodeHash[edge.target] = {id: edge.target, label: edge.target};
nodes.push(nodeHash[edge.target]);
}
if (edge.weight >= 5) {
edges.push({id: nodeHash[edge.source].id + "-" + nodeHash[edge.target].id, source: nodeHash[edge.source], target: nodeHash[edge.target], weight: edge.weight});
}
});
createForceNetwork(nodes, edges);
}
function modularityCensus(nodes, edges, moduleHash) {
edges.forEach(function (edge) {
if (edge.source.module !== edge.target.module) {
edge.border = true;
}
else {
edge.border = false;
}
});
nodes.forEach(function (node) {
var theseEdges = edges.filter(function(d) {return d.source === node || d.target === node});
var theseSourceModules = theseEdges.map(function (d) {return d.source.module}).filter(onlyUnique);
var theseTargetModules = theseEdges.map(function (d) {return d.target.module}).filter(onlyUnique);
if (theseSourceModules.length > 1 || theseTargetModules.length > 1) {
node.border = true;
}
else {
node.border = false;
}
});
var modules = nodes.map(function (d) {return d.module})
.filter(onlyUnique)
.map(function (d) {return {id: d, members: []}});
var moduleEdges = [];
var singletons = {id: "singletons", members: []};
var moduleNodeHash = {};
modules.forEach(function (module) {
module.members = nodes.filter(function (d) {return d.module === module.id});
moduleNodeHash[module.id] = module;
console.log(module);
if (module.members.length === 1) {
console.log("length1");
singletons.members.push(module.members[0]);
}
});
modules.push(singletons);
var moduleEdgeHash = {};
edges.forEach(function (edge) {
if (!moduleEdgeHash[moduleNodeHash[edge.source.module].id + "-" + moduleNodeHash[edge.target.module].id]) {
var moduleEdge = {source: moduleNodeHash[edge.source.module], target: moduleNodeHash[edge.target.module], weight: 1};
moduleEdgeHash[moduleNodeHash[edge.source.module].id + "-" + moduleNodeHash[edge.target.module].id] = moduleEdge;
moduleEdges.push(moduleEdge);
}
else {
moduleEdgeHash[moduleNodeHash[edge.source.module].id + "-" + moduleNodeHash[edge.target.module].id].weight += 1;
}
})
return {nodes: modules, edges: moduleEdges}
}
function createForceNetwork(nodes, edges) {
//create a network from an edgelist
var colors = d3.scale.ordinal().domain([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]).range(["#996666", "#66CCCC", "#FFFF99", "#CC9999", "#666633", "#993300", "#999966", "#660000", "#996699", "#cc6633", "#ff9966", "#339999", "#6699cc", "#ffcc66", "#ff6600", "#00cccc"]);
var node_data = nodes.map(function (d) {return d.id});
var edge_data = edges.map(function (d) {return {source: d.source.id, target: d.target.id, weight: 1}; });
var community = jLouvain().nodes(node_data).edges(edge_data);
var result = community();
nodes.forEach(function (node) {
node.module = result[node.id]
});
var modularityGraph = modularityCensus(nodes, edges, result);
var modularityForce = d3.layout.force()
.nodes(modularityGraph.nodes)
.links(modularityGraph.edges)
.size([125,125])
.charge(function (d) {return d.members.length * -25})
.gravity(0.75)
.on("tick", updateModularityNetwork);
var mSVG = d3.select("#viz").append("svg")
.attr("class", "modularity")
.attr("height", 100)
.attr("width", 100)
.style("height", 100)
.style("width", 100)
.style("position", "absolute")
.style("left", 375)
.style("top", 375)
.style("background", "white");
mSVG.selectAll("line")
.data(modularityGraph.edges)
.enter()
.append("line")
.attr("class", "modularity")
.style("stroke-width", function (d) {return d.weight * 2})
.style("stroke", "black");
mSVG.selectAll("circle")
.data(modularityGraph.nodes.filter(function(d) {return d.members.length > 1}))
.enter()
.append("circle")
.attr("class", "modularity")
.attr("r", function (d) {return d.members.length})
.style("stroke", "black")
.style("stroke-width", "1px")
.style("fill", function (d) {return d.id == "singletons" ? "lightgray" : colors(d.id)})
modularityForce.start();
var modLegend = d3.legend.color().scale(colors);
d3.select("svg.main").append("g").call(modLegend);
var force = d3.layout.force().nodes(nodes).links(edges)
.size([500,500])
.charge(-300)
.gravity(0.2)
.on("tick", updateNetwork);
var edgeEnter = d3.select("svg.main").selectAll("g.edge")
.data(edges, function (d) {return d.id})
.enter()
.append("g")
.attr("class", "edge");
edgeEnter
.append("line")
.style("stroke-width", function (d) {return d.border ? "3px" : "1px"})
.style("stroke", "black")
.style("pointer-events", "none");
var nodeEnter = d3.select("svg.main").selectAll("g.node")
.data(nodes, function (d) {return d.id})
.enter()
.append("g")
.attr("class", "node")
.call(force.drag());
nodeEnter.append("circle")
.attr("r", 8)
.style("fill", function (d) {return colors(d.module)})
.style("stroke", "black")
.style("stroke-width", function (d) {return d.border ? "3px" : "1px"})
nodeEnter.append("text")
.style("text-anchor", "middle")
.attr("y", 3)
.style("stroke-width", "1px")
.style("stroke-opacity", 0.75)
.style("stroke", "white")
.style("font-size", "8px")
.text(function (d) {return d.id})
.style("pointer-events", "none")
nodeEnter.append("text")
.style("text-anchor", "middle")
.attr("y", 3)
.style("font-size", "8px")
.text(function (d) {return d.id})
.style("pointer-events", "none")
force.start();
function updateNetwork() {
d3.select("svg.main").selectAll("line")
.attr("x1", function (d) {return d.source.x})
.attr("y1", function (d) {return d.source.y})
.attr("x2", function (d) {return d.target.x})
.attr("y2", function (d) {return d.target.y});
d3.select("svg.main").selectAll("g.node")
.attr("transform", function (d) {return "translate(" + d.x + "," + d.y + ")"});
}
function updateModularityNetwork() {
d3.select("svg.modularity").selectAll("line")
.attr("x1", function (d) {return d.source.x})
.attr("y1", function (d) {return d.source.y})
.attr("x2", function (d) {return d.target.x})
.attr("y2", function (d) {return d.target.y});
d3.select("svg.modularity").selectAll("circle")
.attr("transform", function (d) {return "translate(" + d.x + "," + d.y + ")"});
}
}
</script>
</footer>
</html>
Raw
jsLouvain.js
/*
Author: Corneliu S. (github.com/upphiminn)
This is a javascript implementation of the Louvain
community detection algorithm (http://arxiv.org/abs/0803.0476)
Based on https://bitbucket.org/taynaud/python-louvain/overview
*/
(function(){
jLouvain = function(){
//Constants
var __PASS_MAX = -1
var __MIN = 0.0000001
//Local vars
var original_graph_nodes;
var original_graph_edges;
var original_graph = {};
var partition_init;
//Helpers
function make_set(array){
var set = {};
array.forEach(function(d,i){
set[d] = true;
});
return Object.keys(set);
};
function obj_values(obj){
var vals = [];
for( var key in obj ) {
if ( obj.hasOwnProperty(key) ) {
vals.push(obj[key]);
}
}
return vals;
};
function get_degree_for_node(graph, node){
var neighbours = graph._assoc_mat[node] ? Object.keys(graph._assoc_mat[node]) : [];
var weight = 0;
neighbours.forEach(function(neighbour,i){
var value = graph._assoc_mat[node][neighbour] || 1;
if(node == neighbour)
value *= 2;
weight += value;
});
return weight;
};
function get_neighbours_of_node(graph, node){
if(typeof graph._assoc_mat[node] == 'undefined')
return [];
var neighbours = Object.keys(graph._assoc_mat[node]);
return neighbours;
}
function get_edge_weight(graph, node1, node2){
return graph._assoc_mat[node1] ? graph._assoc_mat[node1][node2] : undefined;
}
function get_graph_size(graph){
var size = 0;
graph.edges.forEach(function(edge){
size += edge.weight;
});
return size;
}
function add_edge_to_graph(graph, edge){
update_assoc_mat(graph, edge);
var edge_index = graph.edges.map(function(d){
return d.source+'_'+d.target;
}).indexOf(edge.source+'_'+edge.target);
if(edge_index != -1)
graph.edges[edge_index].weight = edge.weight;
else
graph.edges.push(edge);
}
function make_assoc_mat(edge_list){
var mat = {};
edge_list.forEach(function(edge, i){
mat[edge.source] = mat[edge.source] || {};
mat[edge.source][edge.target] = edge.weight;
mat[edge.target] = mat[edge.target] || {};
mat[edge.target][edge.source] = edge.weight;
});
return mat;
}
function update_assoc_mat(graph, edge){
graph._assoc_mat[edge.source] = graph._assoc_mat[edge.source] || {};
graph._assoc_mat[edge.source][edge.target] = edge.weight;
graph._assoc_mat[edge.target] = graph._assoc_mat[edge.target] || {};
graph._assoc_mat[edge.target][edge.source] = edge.weight;
}
function clone(obj){
if(obj == null || typeof(obj) != 'object')
return obj;
var temp = obj.constructor();
for(var key in obj)
temp[key] = clone(obj[key]);
return temp;
}
//Core-Algorithm Related
function init_status(graph, status, part){
status['nodes_to_com'] = {};
status['total_weight'] = 0;
status['internals'] = {};
status['degrees'] = {};
status['gdegrees'] = {};
status['loops'] = {};
status['total_weight'] = get_graph_size(graph);
if(typeof part == 'undefined'){
graph.nodes.forEach(function(node,i){
status.nodes_to_com[node] = i;
var deg = get_degree_for_node(graph, node);
if (deg < 0)
throw 'Bad graph type, use positive weights!';
status.degrees[i] = deg;
status.gdegrees[node] = deg;
status.loops[node] = get_edge_weight(graph, node, node) || 0;
status.internals[i] = status.loops[node];
});
}else{
graph.nodes.forEach(function(node,i){
var com = part[node];
status.nodes_to_com[node] = com;
var deg = get_degree_for_node(graph, node);
status.degrees[com] = (status.degrees[com] || 0) + deg;
status.gdegrees[node] = deg;
var inc = 0.0;
var neighbours = get_neighbours_of_node(graph, node);
neighbours.forEach(function(neighbour, i){
var weight = graph._assoc_mat[node][neighbour];
if (weight <= 0){
throw "Bad graph type, use positive weights";
}
if(part[neighbour] == com){
if (neighbour == node){
inc += weight;
}else{
inc += weight/2.0;
}
}
});
status.internals[com] = (status.internals[com] || 0) + inc;
});
}
}
function __modularity(status){
var links = status.total_weight;
var result = 0.0;
var communities = make_set(obj_values(status.nodes_to_com));
communities.forEach(function(com,i){
var in_degree = status.internals[com] || 0 ;
var degree = status.degrees[com] || 0 ;
if(links > 0){
result = result + in_degree / links - Math.pow((degree / (2.0*links)), 2);
}
});
return result;
}
function __neighcom(node, graph, status){
// compute the communities in the neighb. of the node, with the graph given by
// node_to_com
var weights = {};
var neighboorhood = get_neighbours_of_node(graph, node);//make iterable;
neighboorhood.forEach(function(neighbour, i){
if(neighbour != node){
var weight = graph._assoc_mat[node][neighbour] || 1;
var neighbourcom = status.nodes_to_com[neighbour];
weights[neighbourcom] = (weights[neighbourcom] || 0) + weight;
}
});
return weights;
}
function __insert(node, com, weight, status){
//insert node into com and modify status
status.nodes_to_com[node] = +com;
status.degrees[com] = (status.degrees[com] || 0) + (status.gdegrees[node]||0);
status.internals[com] = (status.internals[com] || 0) + weight + (status.loops[node]||0);
}
function __remove(node, com, weight, status){
//remove node from com and modify status
status.degrees[com] = ((status.degrees[com] || 0) - (status.gdegrees[node] || 0));
status.internals[com] = ((status.internals[com] || 0) - weight -(status.loops[node] ||0));
status.nodes_to_com[node] = -1;
}
function __renumber(dict){
var count = 0;
var ret = clone(dict); //deep copy :)
var new_values = {};
var dict_keys = Object.keys(dict);
dict_keys.forEach(function(key){
var value = dict[key];
var new_value = typeof new_values[value] =='undefined' ? -1 : new_values[value];
if(new_value == -1){
new_values[value] = count;
new_value = count;
count = count + 1;
}
ret[key] = new_value;
});
return ret;
}
function __one_level(graph, status){
//Compute one level of the Communities Dendogram.
var modif = true,
nb_pass_done = 0,
cur_mod = __modularity(status),
new_mod = cur_mod;
while (modif && nb_pass_done != __PASS_MAX){
cur_mod = new_mod;
modif = false;
nb_pass_done += 1
graph.nodes.forEach(function(node,i){
var com_node = status.nodes_to_com[node];
var degc_totw = (status.gdegrees[node] || 0) / (status.total_weight * 2.0);
var neigh_communities = __neighcom(node, graph, status);
__remove(node, com_node, (neigh_communities[com_node] || 0.0), status);
var best_com = com_node;
var best_increase = 0;
var neigh_communities_entries = Object.keys(neigh_communities);//make iterable;
neigh_communities_entries.forEach(function(com,i){
var incr = neigh_communities[com] - (status.degrees[com] || 0.0) * degc_totw;
if (incr > best_increase){
best_increase = incr;
best_com = com;
}
});
__insert(node, best_com, neigh_communities[best_com] || 0, status);
if(best_com != com_node)
modif = true;
});
new_mod = __modularity(status);
if(new_mod - cur_mod < __MIN)
break;
}
}
function induced_graph(partition, graph){
var ret = {nodes:[], edges:[], _assoc_mat: {}};
var w_prec, weight;
//add nodes from partition values
var partition_values = obj_values(partition);
ret.nodes = ret.nodes.concat(make_set(partition_values)); //make set
graph.edges.forEach(function(edge,i){
weight = edge.weight || 1;
var com1 = partition[edge.source];
var com2 = partition[edge.target];
w_prec = (get_edge_weight(ret, com1, com2) || 0);
var new_weight = (w_prec + weight);
add_edge_to_graph(ret, {'source': com1, 'target': com2, 'weight': new_weight});
});
return ret;
}
function partition_at_level(dendogram, level){
var partition = clone(dendogram[0]);
for(var i = 1; i < level + 1; i++ )
Object.keys(partition).forEach(function(key,j){
var node = key;
var com = partition[key];
partition[node] = dendogram[i][com];
});
return partition;
}
function generate_dendogram(graph, part_init){
if(graph.edges.length == 0){
var part = {};
graph.nodes.forEach(function(node,i){
part[node] = node;
});
return part;
}
var status = {};
init_status(original_graph, status, part_init);
var mod = __modularity(status);
var status_list = [];
__one_level(original_graph, status);
var new_mod = __modularity(status);
var partition = __renumber(status.nodes_to_com);
status_list.push(partition);
mod = new_mod;
var current_graph = induced_graph(partition, original_graph);
init_status(current_graph, status);
while (true){
__one_level(current_graph, status);
new_mod = __modularity(status);
if(new_mod - mod < __MIN)
break;
partition = __renumber(status.nodes_to_com);
status_list.push(partition);
mod = new_mod;
current_graph = induced_graph(partition, current_graph);
init_status(current_graph, status);
}
return status_list;
}
var core = function(){
var status = {};
var dendogram = generate_dendogram(original_graph, partition_init);
return partition_at_level(dendogram, dendogram.length - 1);
};
core.nodes = function(nds){
if(arguments.length > 0){
original_graph_nodes = nds;
}
return core;
};
core.edges = function(edgs){
if(typeof original_graph_nodes == 'undefined')
throw 'Please provide the graph nodes first!';
if(arguments.length > 0){
original_graph_edges = edgs;
var assoc_mat = make_assoc_mat(edgs);
original_graph = { 'nodes': original_graph_nodes,
'edges': original_graph_edges,
'_assoc_mat': assoc_mat };
}
return core;
};
core.partition_init = function(prttn){
if(arguments.length > 0){
partition_init = prttn;
}
return core;
};
return core;
}
})();
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