# Semi-Markov Graph Dynamics

@article{Raberto2011SemiMarkovGD, title={Semi-Markov Graph Dynamics}, author={Marco Raberto and Fabio Rapallo and Enrico Scalas}, journal={PLoS ONE}, year={2011}, volume={6} }

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…

## 15 Citations

### On discrete-time semi-Markov processes

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2021

In the last years many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are…

### Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution

- MathematicsFractional Calculus and Applied Analysis
- 2022

Consider a Markov chain with finite state space and suppose you wish to change time replacing the integer step index n with a random counting process N ( t ). What happens to the mixing time of the…

### Max-Plus Objects to Study the Complexity of Graphs

- Mathematics, Computer Science
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This work defines a new object HG, called the mp-chart of G, in the max-plus algebra and shows how to compute the mean and the variance of HG in terms of the adjacency matrix of G and gives a central limit theorem for HG.

### Relaxation patterns and semi-Markov dynamics

- PhysicsStochastic Processes and their Applications
- 2019

### On semi-Markov processes and their Kolmogorov's integro-differential equations

- MathematicsJournal of Functional Analysis
- 2018

### Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2020

In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov…

### Low-traffic limit and first-passage times for a simple model of the continuous double auction

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- 2017

### Generalized space–time fractional diffusion equation with composite fractional time derivative

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- 2012

### Banking Networks and Leverage Dependence: Evidence from Selected Emerging Countries

- Economics
- 2015

We use bank-level balance sheet data from 2005 to 2010 to study interactions within the banking system of five emerging countries: Argentina, Brazil, Mexico, South Africa, and Taiwan. For each…

### Banking Networks and Leverage Dependence in Emerging Countries

- EconomicsAdv. Complex Syst.
- 2015

This work constructs banking networks using bank-level balance sheet data from 2005 to 2010 from five emerging countries and simulates the banking system through a model of corporate and interbank loans with credit shocks, where links between banks arise due to insufficient liquidity.

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