Finding Statistically Significant Communities in Networks
Figure 1
A schematic representation of a subgraph , whose significance is to be assessed.
The subgraph is embedded within a random graph generated by the configuration model. The degrees of all vertices of the network are fixed, in the figure we have highlighted the degrees of
(
), of the vertex
at the center of the analysis (
) and of the rest of the graph
(
). These quantities are expressed as sums of contributions which are internal to their own set of vertices (as
) or related to subgraph
(in or out). This notation is used in the distribution of Eq. 1.