Leon Danon

Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.

Self-similar community structure in a network of human interactions.

We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

COMMUNITY STRUCTURE IN JAZZ

Using a database of jazz recordings we study the collaboration network of jazz musicians. We define the network at two different levels. First we study the collaboration network between individuals, where two musicians are connected if they have played in the same band. Then we consider the collaboration between bands, where two bands are connected if they have a musician in common. The community structure analysis reveals that these constructions capture essential ingredients of the social interactions between jazz musicians. We observe correlations between recording locations, racial segregation and the community structure. A quantitative analysis of the community size distribution reveals a surprising similarity with an e-mail based social network recently studied.

Networks and the epidemiology of infectious disease

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues.

Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain

Using a novel interpretation of dynamic networks, we analyse the network of livestock movements in Great Britain in order to determine the risk of a large epidemic of foot-and-mouth disease (FMD). This network is exceptionally well characterized, as there are legal requirements that the date, source, destination and number of animals be recorded and held on central databases. We identify a percolation threshold in the structure of the livestock network, indicating that, while there is little possibility of a national epidemic of FMD in winter when the catastrophic 2001 epidemic began, there remains a risk in late summer or early autumn. These predictions are corroborated by a non-parametric simulation in which the movements of livestock in 2003 and 2004 are replayed as they occurred. Despite the risk, we show that the network displays small-world properties which can be exploited to target surveillance and control and drastically reduce this risk.

Community analysis in social networks

Abstract.We present an empirical study of different social networks obtained from digital repositories. Our analysis reveals the community structure and provides a useful visualising technique. We investigate the scaling properties of the community size distribution, and find that all the networks exhibit power law scaling in the community size distributions with exponent either -0.5 or -1. Finally we find that the networks’ community structure is topologically self-similar using the Horton-Strahler index.

The effect of size heterogeneity on community identification in complex networks

Identifying community structure can be a potent tool in the analysis and understanding of the structure of complex networks. Up to now, methods for evaluating the performance of identification algorithms use ad-hoc networks with communities of equal size. We show that inhomogeneities in community sizes can and do affect the performance of algorithms considerably, and propose an alternative method which takes these factors into account. Furthermore, we propose a simple modification of the algorithm proposed by Newman for community detection (Phys. Rev. E 69 066133) which treats communities of different sizes on an equal footing, and show that it outperforms the original algorithm while retaining its speed.

Individual identity and movement networks for disease metapopulations

The theory of networks has had a huge impact in both the physical and life sciences, shaping our understanding of the interaction between multiple elements in complex systems. In particular, networks have been extensively used in predicting the spread of infectious diseases where individuals, or populations of individuals, interact with a limited set of others—defining the network through which the disease can spread. Here for such disease models we consider three assumptions for capturing the network of movements between populations, and focus on two applied problems supported by detailed data from Great Britain: the commuter movement of workers between local areas (wards) and the permanent movement of cattle between farms. For such metapopulation networks, we show that the identity of individuals responsible for making network connections can have a significant impact on the infection dynamics, with clear implications for detailed public health and veterinary applications.

Mathematical modelling of infectious diseases.

INTRODUCTION Mathematical models allow us to extrapolate from current information about the state and progress of an outbreak, to predict the future and, most importantly, to quantify the uncertainty in these predictions. Here, we illustrate these principles in relation to the current H1N1 epidemic. SOURCES OF DATA Many sources of data are used in mathematical modelling, with some forms of model requiring vastly more data than others. However, a good estimation of the number of cases is vitally important. AREAS OF AGREEMENT Mathematical models, and the statistical tools that underpin them, are now a fundamental element in planning control and mitigation measures against any future epidemic of an infectious disease. Well-parameterized mathematical models allow us to test a variety of possible control strategies in computer simulations before applying them in reality. AREAS OF CONTROVERSY The interaction between modellers and public-health practitioners and the level of detail needed for models to be of use. GROWING POINTS The need for stronger statistical links between models and data. AREAS TIMELY FOR DEVELOPING RESEARCH Greater appreciation by the medical community of the uses and limitations of models and a greater appreciation by modellers of the constraints on public-health resources.

Social encounter networks: collective properties and disease transmission

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of −2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.