Relaxation dynamics of maximally clustered networks

A control measure for epidemic spread based on the susceptible-infectious-susceptible (SIS) model

When an epidemic occurs in a network, finding the important links and cutting them off is an effective measure for preventing the spread of the epidemic. Traditional methods that remove important links easily lead to a disconnected network, inevitably incurring high costs arising from quarantining individuals or communities in a real-world network. In this study, we combine the clustering coefficient and the eigenvector to identify the important links using the susceptible-infectious-susceptible (SIS) model. The results show that our approach can improve the epidemic threshold while maintaining the connectivity of the network to control the spread of the epidemic. Experiments on multiple real-world and synthetic networks of varying sizes, demonstrate the effectiveness and scalability of our approach.

Self-avoiding walks and connective constants in clustered scale-free networks

Various types of walks on complex networks have been used in recent years to model search and navigation in several kinds of systems, with particular emphasis on random walks. This gives valuable information on network properties, but self-avoiding walks (SAWs) may be more suitable than unrestricted random walks to study long-distance characteristics of complex systems. Here we study SAWs in clustered scale-free networks, characterized by a degree distribution of the form P(k)∼k^{-γ} for large k. Clustering is introduced in these networks by inserting three-node loops (triangles). The long-distance behavior of SAWs gives us information on asymptotic characteristics of such networks. The number of self-avoiding walks, a_{n}, has been obtained by direct enumeration, allowing us to determine the connective constant μ of these networks as the large-n limit of the ratio a_{n}/a_{n-1}. An analytical approach is presented to account for the results derived from walk enumeration, and both methods give results agreeing with each other. In general, the average number of SAWs a_{n} is larger for clustered networks than for unclustered ones with the same degree distribution. The asymptotic limit of the connective constant for large system size N depends on the exponent γ of the degree distribution: For γ>3, μ converges to a finite value as N→∞; for γ=3, the size-dependent μ_{N} diverges as lnN, and for γ<3 we have μ_{N}∼N^{(3-γ)/2}.