Related papers: Unevenness of Loop Location in Complex Networks

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…

Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…

Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…

Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…

In complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if…

Recent work on deep neural network pruning has shown there exist sparse subnetworks that achieve equal or improved accuracy, training time, and loss using fewer network parameters when compared to their dense counterparts. Orthogonal to…

The problem of finding a resource residing in a network node (the \emph{resource location problem}) is a challenge in complex networks due to aspects as network size, unknown network topology, and network dynamics. The problem is especially…

In social network, a person located at the periphery region (marginal node) is likely to be treated unfairly when compared with the persons at the center. While existing fairness works on graphs mainly focus on protecting sensitive…

We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized…

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing…

The so-called rich-club phenomenon in a complex network is characterized when nodes of higher degree (hubs) are better connected among themselves than are nodes with smaller degree. The presence of the rich-club phenomenon may be an…

We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…

Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…

Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Unfortunately, our maps of most large networks are…

We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow…

In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…

Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…

We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…