Abstract
The stochastic block model is able to generate random graphs with different types of network partitions, ranging from the traditional assortative structures to the disassortative structures. Since the stochastic block model does not specify which mixing pattern is desired, the inference algorithms discover the locally most likely nodes’ partition, regardless of its type. Here we introduce a new model constraining nodes’ internal degree ratios in the objective function to guide the inference algorithms to converge to the desired type of structure in the observed network data. We show experimentally that given the regularized model, the inference algorithms, such as Markov chain Monte Carlo, reliably and quickly find the assortative or disassortative structure as directed by the value of a single parameter. In contrast, when the sought-after assortative community structure is not strong in the observed network, the traditional inference algorithms using the degree-corrected stochastic block model tend to converge to undesired disassortative partitions.
Highlights
The study of modular structure in networks has a long history in the literature[1,2,3,4]
A simple function {f(k)} satisfying this requirement is of the form f (k) = α + (1 − α), k where α is the only extra parameter we introduce to the regularized stochastic block model (RSBM)
We generate the synthetic networks with the assortative communities using the degree-corrected stochastic block model
Summary
The study of modular structure in networks has a long history in the literature[1,2,3,4]. The inference of network partition from the stochastic block model can be considered a more general approach to network clustering than the traditional modularity-based community detection algorithms. The former can discover a variety of network structures, different from the traditional assortative community structures, such as the disassortative core-periphery structures[5]. Unlike the modularity maximization algorithm which always attempts to find traditional assortative communities, the inference using this regularized stochastic block model controls with a single parameter the mixing patterns discovered in the given network
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