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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 interplay between disease dynamics on a network and the dynamics of the structure of that network characterizes many real-world systems of contacts. A continuous-time adaptive susceptible-infectious-susceptible (ASIS) model is introduced in order to investigate this interaction, where a susceptible node avoids infections by breaking its links to its(More)
Defining an optimal protection strategy against viruses, spam propagation, or any other kind of contamination process is an important feature for designing new networks and architectures. In this paper, we consider decentralized optimal protection strategies when a virus is propagating over a network through an SIS epidemic process. We assume that each node(More)
— Defining an optimal protection strategy against viruses, spam propagation or any other kind of contamination process is an important feature for designing new networks and architectures. In this work, we consider decentralized optimal protection strategies when a virus is propagating over a network through a Susceptible Infected Susceptible (SIS) epidemic(More)
Due to their importance to society, communication networks should be built and operated to withstand failures. However, cost considerations make network providers less inclined to take robustness measures against failures that are unlikely to manifest, like several failures coinciding simultaneously in different geographic regions of their network.(More)
It is important that our vital networks (e.g., infrastructures) are robust to more than single-link failures. Failures might for instance affect a part of the network that resides in a certain geographical region. In this paper, considering networks embedded in a two-dimensional plane, we study the problem of finding a critical region - that is, a part of(More)
Modularity is a quantitative measure for characterizing the existence of a community structure in a network. A network's modularity depends on the chosen partitioning of the network into communities, which makes finding the specific partition that leads to the maximum modularity a hard problem. In this paper, we prove that deciding whether a graph with a(More)
In data-communication networks, network reliability is of great concern to both network operators and customers. On the one hand, the customers care about receiving reliable services and, on the other hand, for the network operators it is vital to determine the most vulnerable parts of their network. In this paper, we first study the problem of establishing(More)
Modularity has been explored as an important quantitative metric for community and cluster detection in networks. Finding the maximum modularity of a given graph has been proven to be NPcomplete and therefore, several heuristic algorithms have been proposed. We investigate the problem of finding the maximum modularity of classes of graphs that have the same(More)