Semi-Markov graph dynamics

Raberto, Marco, Rapallo, Fabio and Scalas, Enrico (2011) Semi-Markov graph dynamics. PLoS ONE, 6 (8). e23370. ISSN 1932-6203

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: H Social Sciences > HG Finance > HG3691 Credit. Debt. Loans
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Enrico Scalas
Date Deposited: 24 Sep 2014 06:05
Last Modified: 07 Mar 2017 14:18
URI: http://sro.sussex.ac.uk/id/eprint/50242

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