Detecting the number of clusters in a network

Budel, G.J.A.; Van Mieghem, P.F.A.

Detecting the number of clusters in a network

Journal article (2021)

Authors

G.J.A. Budel Network Architectures and Services -

P.F.A. Van Mieghem Network Architectures and Services -

Research Group

Network Architectures and Services () (TU Delft)

Complex Networks Spectral Clustering Community Detection Non-backtracking Matrix Number of Clusters

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

Abstract

Many clustering algorithms for complex networks depend on the choice for the number of clusters and it is often unclear how to make this choice. The number of eigenvalues located outside a circle in the spectrum of the non-backtracking matrix was conjectured to be an estimator of the number of clusters in a graph. We compare the estimate of the number of clusters obtained from the spectrum of the non-backtracking matrix with three estimators based on the concept of modularity and evaluate the methods on several benchmark graphs. We find that the non-backtracking method detects the number of clusters better than the modularity-based methods for the graphs in our simulation study, especially when the clusters have slightly different sizes. The estimates of the non-backtracking method are narrowly distributed around the true number of clusters for all benchmark graphs considered. Additionally, for graphs without a clustering structure, the non-backtracking method detects exactly one cluster, which is a convenient property of an estimator of the number of clusters. However, the lack of a well-defined concept of a cluster prevents sharp conclusions.