Semi-Markov Graph Dynamics

TL;DR

This paper introduces a novel graph dynamics model combining Markov chains with semi-Markov processes, allowing for random transition timings, with potential applications in complex network systems like interbank markets.

Contribution

It proposes a new semi-Markov graph dynamics model that integrates Markov chains with renewal processes, expanding the framework for network evolution modeling.

Findings

Model captures graph evolution with random transition epochs

Potential connections to algebraic geometry are discussed

Application example in interbank market networks

Abstract

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.