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Expressions and bounds for Newman's modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count(More)
The study of epidemics is a crucial issue to several areas. An epidemic can have devastating economic and social consequences. A single crop disease in Kansas could destroy the yearly income of many farmers. Previous work using graph theory has determined a universal epidemic threshold found in the graph topology for a binary contact network in the(More)
With increasingly ambitious initiatives such as GENI and FIND that seek to design future internets, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper investigates the characteristics of network topologies that maintain a high level of throughput in spite of multiple(More)
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines a network's survivability in the advent of classical component failures and at the onset of cryptic(More)
The robustness of a network is depending on the type of attack we are considering. In this paper we focus on the spread of viruses on networks. It is common practice to use the epidemic threshold as a measure for robustness. Because the epidemic threshold is inversely proportional to the largest eigenvalue of the adjacency matrix, it seems easy to compare(More)
Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and results of general studies cannot be directly applied since population densities and human mobility factors are very(More)
BACKGROUND Recent study of complex networks has yielded many new insights into phenomenon such as social networks, the internet, and sexually transmitted infections. The purpose of this analysis is to examine the properties of a network created by the 'co-care' of patients within one region of the Veterans Health Affairs. METHODS Data were obtained for(More)
Horizontal transfer of mobile genetic elements (conjugation) is an important mechanism whereby resistance is spread through bacterial populations. The aim of our work is to develop a mathematical model that quantitatively describes this process, and to use this model to optimize antimicrobial dosage regimens to minimize resistance development. The bacterial(More)