Related papers: Robustness of Random Graphs Based on Natural Conne…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious…
Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable…
One of the intensely studied concepts of network robustness is $r$-robustness, which is a network topology property quantified by an integer $r$. It is required by mean subsequence reduced (MSR) algorithms and their variants to achieve…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
The correspondence between weighted undirected graphs and reversible Markov chains via vertex random walks is simple and well known. Leveraging this correspondence and ideas from the theory of dynamical systems, we study the structural…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general, we call it $p$-robust random graph. It means that every edge is present with probability at least $p$, regardless…
We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop…