For a given graph G, each partition of the vertices has a modularity score, with higher values
indicating that the partition better captures community structure in G. The modularity q∗(G) of …

We introduce graph clustering quality measures based on comparisons of global, intra-and
inter-cluster densities, an accompanying statistical significance test and a step-by-step …

Numerous works have been proposed to generate random graphs preserving the same
properties as real-life large-scale networks. However, many real networks are better …

In this paper we prove new bounds on the second eigenvalue of Johnson graphs. We then
apply these bounds to obtain new results on the modularity of Johnson graphs and their …

Modularity is a graph parameter measuring how clearly the set of graph vertices may be
partitioned into subsets of high edge density. It indicates the presence of community …

Determining if a graph displays a clustered structure prior to subjecting it to any cluster
detection technique has recently gained attention in the literature. Attempts to group graph …

In this article, we study the clustering properties of the spatial preferential attachment (SPA)
model. This model naturally combines geometry and preferential attachment using the …

In this study, we compare distance measures with respect to their ability to capture vertex
community structure and the scalability of their computation. Our goal is to find a distance …

Modularity is designed to measure the strength of a division of a network into clusters. For
n∈ ℕ, consider a set S of n elements. Let V be the set of all subsets of S of size r. Consider …

We relate two important notions in graph theory: expanders which are highly connected
graphs, and modularity a parameter of a graph that is primarily used in community detection …