9,528 research outputs found
Properties of weighted complex networks
We study two kinds of weighted networks, weighted small-world (WSW) and
weighted scale-free (WSF). The weight of a link between nodes and
in the network is defined as the product of endpoint node degrees; that is
. In contrast to adding weights to links during
networks being constructed, we only consider weights depending on the ``
popularity\rq\rq of the nodes represented by their connectivity. It was found
that the both weighted networks have broad distributions on characterization
the link weight, vertex strength, and average shortest path length.
Furthermore, as a survey of the model, the epidemic spreading process in both
weighted networks was studied based on the standard \emph{susceptible-infected}
(SI) model. The spreading velocity reaches a peak very quickly after the
infection outbreaks and an exponential decay was found in the long time
propagation.Comment: 14 pages, 5 figure
Optimal curing policy for epidemic spreading over a community network with heterogeneous population
The design of an efficient curing policy, able to stem an epidemic process at
an affordable cost, has to account for the structure of the population contact
network supporting the contagious process. Thus, we tackle the problem of
allocating recovery resources among the population, at the lowest cost possible
to prevent the epidemic from persisting indefinitely in the network.
Specifically, we analyze a susceptible-infected-susceptible epidemic process
spreading over a weighted graph, by means of a first-order mean-field
approximation. First, we describe the influence of the contact network on the
dynamics of the epidemics among a heterogeneous population, that is possibly
divided into communities. For the case of a community network, our
investigation relies on the graph-theoretical notion of equitable partition; we
show that the epidemic threshold, a key measure of the network robustness
against epidemic spreading, can be determined using a lower-dimensional
dynamical system. Exploiting the computation of the epidemic threshold, we
determine a cost-optimal curing policy by solving a convex minimization
problem, which possesses a reduced dimension in the case of a community
network. Lastly, we consider a two-level optimal curing problem, for which an
algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network
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