# Choosing the number of groups in a latent stochastic block model for dynamic networks

## TL;DR

This paper introduces a Markovian extension of stochastic block models for dynamic networks, providing a scalable method to determine the optimal number of groups and track node cluster evolution over time.

## Contribution

It develops a new Markovian latent stochastic block model for dynamic networks and a scalable algorithm to estimate the number of groups and cluster memberships.

## Key findings

- Effective in real and artificial datasets
- Accurately estimates the number of groups
- Tracks cluster evolution over time

## Abstract

Latent stochastic block models are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between nodes are observed at a number of different times. In this paper we extend the original stochastic block model by using a Markovian property to describe the evolution of nodes' cluster memberships over time. We recast the problem of clustering the nodes of the network into a model-based context, and show that the integrated completed likelihood can be evaluated analytically for a number of likelihood models. Then, we propose a scalable greedy algorithm to maximise this quantity, thereby estimating both the optimal partition and the ideal number of groups in a single inferential framework. Finally we propose applications of our methodology to both real and artificial datasets.