Related papers: Phase transitions in optimally robust network stru…
The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to $s$. We find theoretically and via simulation that in complex networks with random…
Many real world complex systems such as infrastructure, communication and transportation networks are embedded in space, where entities of one system may depend on entities of other systems. These systems are subject to geographically…
We study the joint components in a random `double graph' that is obtained by superposing red and blue binomial random graphs on $n$~vertices. A joint component is a maximal set of vertices, which contains both a red and a blue spanning…
We model the robustness against random failure or intentional attack of networks with arbitrary large-scale structure. We construct a block-based model which incorporates --- in a general fashion --- both connectivity and interdependence…
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
Living organisms, ecosystems, and social systems are examples of complex systems in which robustness against inclusion of new elements is an essential feature. A recently proposed simple model has revealed a general mechanism by which such…
Engineering networks fall into the category of large-scale networks with heterogeneous nodes such as sources and sinks. The survivability analysis of such networks requires the analysis of the connectivity of the network components for…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…
We study the component structure in random intersection graphs with tunable clustering, and show that the average degree works as a threshold for a phase transition for the size of the largest component. That is, if the expected degree is…
We study the emerging large-scale structures in networks subject to selective pressures that simultaneously drive towards higher modularity and robustness against random failures. We construct maximum-entropy null models that isolate the…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
A detailed analysis of three species-rich ecosystem food webs has shown that they display scale-free distributions of connections. Such graphs of interaction are in fact shared by a number of biological and technological networks, which…
We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a…