/// <summary>
/// Compute the modularity of a partition of a graph.
/// Raises:
/// KeyNotFoundException if the partition does not partition all graph nodes
/// InvalidOperationException if the graph has no link
/// References:
/// 1. Newman, M.E.J. & Girvan, M. Finding and evaluating community structure in networks. Physical Review E 69,
/// 26113(2004).
/// </summary>
/// <param name="graph">The graph which is decomposed.</param>
/// <param name="partition">
/// The partition of the nodes in the graph (i.e., a dictionary where keys are nodes and values are
/// communities).
/// </param>
/// <returns>The modularity.</returns>
public static double Compute(Graph graph, Dictionary <int, int> partition)
{
Dictionary <int, double> inc = new Dictionary <int, double>();
Dictionary <int, double> deg = new Dictionary <int, double>();
double links = graph.TotalWeight;
if (links == 0)
{
throw new InvalidOperationException("A graph without links has undefined modularity.");
}
foreach (int node in graph.Nodes)
{
int com = partition[node];
deg[com] = deg.GetValueOrDefault(com) + graph.GetDegree(node);
foreach (var edge in graph.GetIncidentEdges(node))
{
int neighbor = edge.ToNode;
if (partition[neighbor] == com)
{
double weight;
if (neighbor == node)
{
weight = edge.Weight;
}
else
{
weight = edge.Weight / 2;
}
inc[com] = inc.GetValueOrDefault(com) + weight;
}
}
}
double res = 0;
foreach (int component in partition.Values.Distinct())
{
res += inc.GetValueOrDefault(component) / links - Math.Pow(deg.GetValueOrDefault(component) / (2 * links), 2);
}
return(res);
}
