Damage spreading on networks: Clustering effects

The damage spreading of the Ising model on three kinds of networks is studied with Glauber dynamics. One of the networks is generated by evolving the hexagonal lattice with the star-triangle transformation. Another kind of network is constructed by connecting the midpoints of the edges of the topological hexagonal lattice. With the evolution of these structures, damage spreading transition temperature increases and a general explanation for this phenomenon is presented from the view of the network. The relationship between the transition temperature and the network measure-clustering coefficient is set up and it is shown that the increase of damage spreading transition temperature is the result of more and more clustering of the network. We construct the third kind of network-random graphs with Poisson degree distributions by changing the average degree of the network. We show that the increase in the average degree is equivalent to the clustering of nodes and this leads to the increase in damage spreading transition temperature.