public Status(Graph graph, Dictionary <int, int> part)
: this()
{
int count = 0;
this.TotalWeight = graph.Size;
if (part == null)
{
foreach (int node in graph.Nodes)
{
Node2Com[node] = count;
double deg = graph.Degree(node);
if (deg < 0)
{
throw new ArgumentException("Graph has negative weights.");
}
Degrees[count] = GDegrees[node] = deg;
Internals[count] = Loops[node] = graph.EdgeWeight(node, node, 0);
count += 1;
}
}
else
{
foreach (int node in graph.Nodes)
{
int com = part[node];
Node2Com[node] = com;
double deg = graph.Degree(node);
Degrees[com] = DictGet(Degrees, com, 0) + deg;
GDegrees[node] = deg;
double inc = 0;
foreach (Graph.Edge edge in graph.IncidentEdges(node))
{
int neighbor = edge.ToNode;
if (edge.Weight <= 0)
{
throw new ArgumentException("Graph must have postive weights.");
}
if (part[neighbor] == com)
{
if (neighbor == node)
{
inc += edge.Weight;
}
else
{
inc += edge.Weight / 2;
}
}
}
Internals[com] = DictGet(Internals, com, 0) + inc;
}
}
}
/// <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 Modularity(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.Size;
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] = DictGet(deg, com, 0) + graph.Degree(node);
foreach (var edge in graph.IncidentEdges(node))
{
int neighbor = edge.ToNode;
if (partition[neighbor] == com)
{
double weight;
if (neighbor == node)
{
weight = edge.Weight;
}
else
{
weight = edge.Weight / 2;
}
inc[com] = DictGet(inc, com, 0) + weight;
}
}
}
double res = 0;
foreach (int component in partition.Values.Distinct())
{
res += DictGet(inc, component, 0) / links - Math.Pow(DictGet(deg, component, 0) / (2 * links), 2);
}
return(res);
}
