Related papers: Networks with the Smallest Average Distance and th…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…

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…

This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…

The graph theoretic properties of the clustering coefficient, characteristic (or average) path length, global and local efficiency, provide valuable information regarding the structure of a graph. These four properties have applications to…

Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive…

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely average path length, degree distribution and clustering coefficient. Although the…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

Relations between average shortest path length and average clustering coefficient, radiality, closeness and stress centralities were obtained for simple graphs.

A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large…

Even though clustering trajectory data attracted considerable attention in the last few years, most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying…

Let \( D \) be a strongly connected digraph. The average distance of a vertex \( v \) in \( D \) is defined as the arithmetic mean of the distances from \( v \) to all other vertices in \( D \). The remoteness \( \rho(D) \) of \( D \) is…

A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…

We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…

We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and…

The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…