# The effect of graph structure on epidemic spread in a class of modified cycle graphs

A. Szabó-Solticzky, L. P. Simon

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

In this paper, an SIS (susceptible-infected-susceptible)-type epidemic propagation is studied on a special class of 3-regular graphs, called modified cycle graphs. The modified cycle graph is constructed from a cycle graph with N nodes by connecting node i to the node i + d in a way that every node has exactly three links. Monte-Carlo simulations show that the propagation process depends on the value of d in a non-monotone way. A new theoretical model is developed to explain this phenomenon. This reveals a new relation between the spreading process and the average path length in the graph.

Original language English 89-107 19 Mathematical Modelling of Natural Phenomena 9 2 https://doi.org/10.1051/mmnp/20149206 Published - 2014

### Fingerprint

Cycle
Graph in graph theory
Vertex of a graph
Propagation
Path Length
Regular Graph
Theoretical Model
Monte Carlo Simulation
Class
Monte Carlo simulation

### Keywords

• Network process
• SIS epidemic
• Theoretical approximation

### ASJC Scopus subject areas

• Modelling and Simulation

### Cite this

In: Mathematical Modelling of Natural Phenomena, Vol. 9, No. 2, 2014, p. 89-107.

Research output: Contribution to journalArticle

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