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Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by…
Viral spread on large graphs has many real-life applications such as malware propagation in computer networks and rumor (or misinformation) spread in Twitter-like online social networks. Although viral spread on large graphs has been…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
Bootstrap percolation is an often used model to study the spread of diseases, rumors, and information on sparse random graphs. The percolation process demonstrates a critical value such that the graph is either almost completely affected or…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the…
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are…
We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
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…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…