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Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in…
We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
A typical result in graph theory says that a graph $G$, satisfying certain conditions, has some property $\cal P$. Once such a theorem is established, it is natural to ask how strongly $G$ satisfies $\cal P$. Can one strengthen the result…
We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree…
Recent work in the area of interdependent networks has focused on interactions between two systems of the same type. However, an important and ubiquitous class of systems are those involving monitoring and control, an example of…
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…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
Most complex networks are not static, but evolve along time. Given a specific configuration of one such changing network, it becomes a particularly interesting issue to quantify the diversity of possible unfoldings of its topology. In this…
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…
A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…
In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most…
As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…