Epidemic spreading on interconnected networks

Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately, and even when the number of coupling connections is small. Our analytic results are successfully confronted against large-scale numerical simulations

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Multiplex PageRank

(15 pages, 6 figures

Percolation of interdependent networks with intersimilarity

Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al \cite{PAR10B}). For example, the coupled world wide port network and the global airport network are intersimilar since many pairs of linked nodes (neighboring cities), by direct flights and direct shipping lines exist in both networks. Nodes in both networks in the same city are regarded as interdependent. If two neighboring nodes in one network depend on neighboring nodes in the another we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results suggest that intersimilarity has considerable effect on reducing the cascading failures, however, a theoretical understanding on this effect on the cascading process is currently missing. Here, we map the cascading process with inter-similarity to a percolation of networks composed of components of common links and non common links. This transforms the percolation of inter-similar system to a regular percolation on a series of subnetworks, which can be solved analytically. We apply our analysis to the case where the network of common links is an Erd\H{o}s-R\'{e}nyi (ER) network with the average degree $K$, and the two networks of non-common links are also ER networks. We show for a fully coupled pair of ER networks, that for any $K\geq0$, although the cascade is reduced with increasing $K$, the phase transition is still discontinuous. Our analysis can be generalized to any kind of interdependent random networks system

Effect of Topological Structure and Coupling Strength in Weighted Multiplex Networks

International audienc