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Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
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…
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 directed percolation inverse problem for diode networks: Given information about which pairs of nodes allow current to percolate from one to the other, can one find a configuration of diodes consistent with the observed…
A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
We study entanglement distribution in quantum complex networks where nodes are connected by bipartite entangled states. These networks are characterized by a complex structure, which dramatically affects how information is transmitted…
We consider percolation on interdependent locally treelike networks, recently introduced by Buldyrev et al., Nature 464, 1025 (2010), and demonstrate that the problem can be simplified conceptually by deleting all references to cascades of…
In discrete-time dynamics, it is frequently assumed that the transition probabilities (e.g., the recovery probability) are independent of the network structure. However, there is a lack of empirical evidence to support this claim in large…
Reciprocity is an important characteristic of directed networks and has been widely used in the modeling of World Wide Web, email, social, and other complex networks. In this paper, we take a statistical physics point of view and study the…
In this work, we explore the analogy between entanglement and secret classical correlations in the context of large networks, more precisely the question of percolation of secret correlations in a network. It is known that entanglement…
We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering…
We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)],…
Despite the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
Link prediction is one of the fundamental problems in network analysis. In many applications, notably in genetics, a partially observed network may not contain any negative examples of absent edges, which creates a difficulty for many…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
This paper develops a framework for identification, estimation, and inference on the causal mechanisms driving endogenous social network formation. Identification is challenging because of unobserved confounders and reverse causality;…