Related papers: Complexity Threshold for Functioning Directed Netw…
This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show…
Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…
In this brief report, we present a disordered version of recursive networks. Depending on the structural parameters $u$ and $v$, the networks are either fractals with a finite fractal dimension $d_{f}$ or transfinite fractals (transfractal)…
Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary…
This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…
In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and…
Our society nowadays is governed by complex networks, examples being the power grids, telecommunication networks, biological networks, and social networks. It has become of paramount importance to understand and characterize the dynamic…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
Extensive researches have been dedicated to investigating the performance of real networks and synthetic networks against random failures or intentional attack guided by degree (degree attack). Degree is one of straightforward measures to…
We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…
We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…
Segment Routing is a recent network technology that helps optimizing network throughput by providing finer control over the routing paths. Instead of routing directly from a source to a target, packets are routed via intermediate waypoints.…
Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…
We study cascading failures in smart grids, where an attacker selectively compromises the nodes with probabilities proportional to their degrees, betweenness, or clustering coefficient. This implies that nodes with high degrees,…
From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers.…