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A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
Spread of information in crowd is analysed in terms of directed percolation in two-dimensional spatial network. We investigate the case when the information transmitted can be incomplete or damaged. The results indicate that for small or…
We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order…
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…
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…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity driven network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework…
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…
While studies of meso-scale structures in networks often focus on community structure, core--periphery structures can reveal new insights. This structure typically consists of a well-connected core and a periphery that is well connected to…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
Almost all network research has been focused on the properties of a single network that does not interact and depends on other networks. In reality, many real-world networks interact with other networks. Here we develop an analytical…
We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in…
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…
The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…
Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study…
We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.
In a quantum communication network, links represent entanglement between qubits located at different nodes. Even if two nodes are not directly linked by shared entanglement, communication channels can be established between them via quantum…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…