# Disentangling group and link persistence in Dynamic Stochastic Block models

## TL;DR

This paper investigates how memory effects in dynamic networks influence community detection, revealing that link and community persistence have opposite impacts on inference difficulty, and introduces a corrected algorithm for improved detection.

## Contribution

It analytically characterizes the impact of link and community persistence on community detection and proposes the Lagged Snapshot Dynamic (LSD) algorithm for better inference.

## Key findings

- Link persistence decreases detectability threshold, making community inference harder.
- Community persistence facilitates community detection, easing the inference process.
- The LSD algorithm effectively detects communities with consideration of time lag effects.

## Abstract

We study the inference of a model of dynamic networks in which both communities and links keep memory of previous network states. By considering maximum likelihood inference from single snapshot observations of the network, we show that link persistence makes the inference of communities harder, decreasing the detectability threshold, while community persistence tends to make it easier. We analytically show that communities inferred from single network snapshot can share a maximum overlap with the underlying communities of a specific previous instant in time. This leads to time-lagged inference: the identification of past communities rather than present ones. Finally we compute the time lag and propose a corrected algorithm, the Lagged Snapshot Dynamic (LSD) algorithm, for community detection in dynamic networks. We analytically and numerically characterize the detectability transitions of such algorithm as a function of the memory parameters of the model and we make a comparison with a full dynamic inference.