considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks … such as the Internet, social networks or biological networks it leaves a lot to be desired. In particular, it differs from … real networks in two crucial ways: it lacks network clustering or transitivity, and it has an unrealistic Poissonian degree …

A number of recent studies have focused on the statistical properties of networked systems such as social networks and … networks: the small-world property, power-law degree distributions, and network transitivity. In this paper, we highlight … another property which is found in many networks, the property of community structure, in which network nodes are joined …

We study percolation on small-world networks, which has been proposed as a simple model of the propagation of disease …

We study some simple models of disease transmission on small-world networks, in which either the probability of … infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior … when the infection or transmission probability rises above the threshold for site or bond percolation on the network, and …

Recent work has demonstrated that many social networks, and indeed many networks of other types also, have broad … distributions of vertex degree. Here we show that this has a substantial impact on the shape of ego-centered networks, i.e., sets of … methods based on ego-centered networks, such as snowball sampling and the Òripple effect.Ó In particular, we argue that oneÕs …

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent … wide variety of networks. Solutions are possible for cases with heterogeneous or correlated probabilities of transmission … exact solutions by comparison with computer simulations of epidemics propagating on the corresponding networks. …

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses …

for several real-world networks is 100% accurate. As a demonstration of the algorithm, we apply it to two large graphs for …