Bias reduction in traceroute sampling: towards a more accurate map of the Internet

Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculating statistics about the internet, it can introduce bias that corrupts these estimates. This paper reports on a theoretical and experimental investigation of a new technique to reduce the bias of traceroute sampling when estimating the degree distribution. We develop a new estimator for the degree of a node in a traceroute-sampled graph; validate the estimator theoretically in Erdos-Renyi graphs and, through computer experiments, for a wider range of graphs; and apply it to produce a new picture of the degree distribution of the autonomous system graph.Comment: 12 pages, 3 figure

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Social networks and infectious disease: The Colorado Springs study

The social network paradigm provides a set of concepts and methods useful for studying the structure of a population through which infectious agents transmitted during close personal contact spread, and an opportunity to develop improved disease control programs. The research discussed was a first attempt to use a social network approach to better understand factors affecting the transmission of a variety of pathogens, including hepatitis B virus (HBV) and human immunodeficiency viruses (HIV), in population of prostitutes, injecting drug users (IDU) and their personal associates in a moderate-sized city (Colorado Springs, CO). Some of the challenges of studying large social networks in epidemiological research are described, some initial results reported and a new view of interconnections in an at risk population provided. Overall, for the first time in epidemiologic research a large number of individuals (over 600) were found connected to each other, directly or indirectly, using a network design. The average distance (along observed social relationships) between persons infected with HIV and susceptible persons was about three steps (3.1) in the core network region. All susceptibles in the core were within seven steps of HIV infection.epidemiologic models social networks HIV hepatitis B prostitutes injecting drug users contact tracing