This paper contains a description of a general class of city formation models. Individual economic agents have preferences for locations that depend on the population distribution. A location's attractiveness depends upon some combination of its population and its average distance to other...

This paper considers both structural and strategic influences on collective action. Each person in a group wants to participate only if the total number participating is at least her threshold; people use a social network to communicate their thresholds. Results include: cliques form the common...

We study percolation on small-world networks, which has been proposed as a simple model of the propagation of disease. The occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively. We give an...

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the 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...

Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical lenth about six. This phenomenon, colloquially referred to as the "six degrees of separation", has been the subject of a...

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...

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 network vertices that are within a given distance...

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physical and mathematical literature. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/recovered...

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of...