Proximity, Communities, and Attributes in Social Network Visualisation

The identification of groups in social networks drawn as graphs is an important task for social scientists whowish to know how a population divides with respect to relationships or attributes. Community detection algorithms identify communities (groups) in social networks by finding clusters in the graph: that is, sets of people (nodes) where the relationships (edges) between them are more numerous than their relationships with other nodes. This approach to determining communities is naturally based on the underlying structure of the network, rather than on attributes associated with nodes. In this paper, we report on an experiment that (a) compares the effectiveness of several force-directed graph layout algorithms for visually identifying communities, and (b) investigates their usefulness when group membership is based not on structure, but on attributes associated with the people in the network. We find algorithms that clearly separate communities with large distances to be most effective, while using colour to represent community membership is more successful than reliance on structural layout

Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have discrete values, but many networks exhibit assortative mixing by some continuous-valued attribute, such as age or geographical location. In such cases, no discrete communities can be identified. We consider how the notion of community structure can be generalized to networks that are based on continuous-valued attributes: in general, a network may contain discrete communities which are ordered according to their attribute values. We propose a method of generating synthetic ordered networks and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.Comment: This is an extended preprint version that includes an extra example: the college football network as an ordered (spatial) network. Further improvements, not included here, appear in the journal version. Original title changed (from "Ordered and continuous community structure in networks") to match journal versio

A statistical network analysis of the HIV/AIDS epidemics in Cuba

The Cuban contact-tracing detection system set up in 1986 allowed the reconstruction and analysis of the sexual network underlying the epidemic (5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168 edges), shedding light onto the spread of HIV and the role of contact-tracing. Clustering based on modularity optimization provides a better visualization and understanding of the network, in combination with the study of covariates. The graph has a globally low but heterogeneous density, with clusters of high intraconnectivity but low interconnectivity. Though descriptive, our results pave the way for incorporating structure when studying stochastic SIR epidemics spreading on social networks