The small-world phenomenon includes both small average distance and the clustering effect. Randomly generated graphs with a power law degree distribution are widely used to model large real-world networks, but while these graphs have small average distance, they generally do not exhibit the clustering effect. We introduce an improved hybrid model that combines a global graph (a random power law...

A very wide variety of physical, demographic, biological and man-made phenomena have been observed to exhibit powerlaw behavior, including the population of cities and villages, sizes of lakes, etc. The Internet is no exception to this. The connectivity of routers, the popularity of web sites, and the degrees of World Wide Web pages are only a few examples of measurements governed by powerlaw. ...

Randomly generated graphs with power law degree distribution are typically used to model large real-world networks. These graphs have small average distance. However, the small world phenomenon includes both small average distance and the clustering effect, which is not possessed by random graphs. Here we use a hybrid model which combines a global graph (a random power law graph) with a local g...

In the last years the physics community has devoted a strong effort to the study of social networks. The availability of large databases containing information on the collaborations between movie actors, scientists, etc. has allowed for many statistical properties of the networks to be characterized. These studies have revealed that some characteristics appear to be general for these kind of ne...

Mathematical models predict that the prevalence of infection in different communities where an infectious disease is disappearing should approach a geometric distribution. Trachoma programs offer an opportunity to test this hypothesis, as the World Health Organization (WHO) has targeted trachoma to be eliminated as a public health concern by the year 2020. We assess the distribution of the comm...

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known in social science as Exponential Random Graphs, have been proposed with the ...

Internet evolution has been recently related with some aspect of user empowerment, mostly in terms of content distribution, and this has been ultimately accelerated by the fast-paced introduction and expansion of wireless technologies. Hence, the Internet should start to be seen as a communications infrastructure able to support the integration of a myriad of embedded and personal wireless obje...

In this paper we introduce a new model of spatial network growth in which nodes are placed at randomly selected locations in space over time, forming new connections to old nodes subject to the constraint that edges do not cross. The resulting network has a power law degree distribution, high clustering and the small world property. We argue that these characteristics are a consequence of two f...

Small-world networks are a class of networks that exhibit efficient long-distance communication and tightly interconnected local neighborhoods. In recent years, functional and structural brain networks have been examined using network theory-based methods, and consistently shown to have small-world properties. Moreover, some voxel-based brain networks exhibited properties of scale-free networks...

The network of 5823 cities of Mexico with a population more than 5000 inhabitants is studied. Our analysis is focused to the spectral properties of the adjacency matrix, the small-world properties of the network, the distribution of the clustering coefficients and the degree distribution of the vertices. The connection of these features with the spread of epidemics on this network is also discu...