Related papers: Higher order assortativity in complex networks

Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…

The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…

The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…

We examine two properties of complex networks, the robustness against targeted node removal (attack) and the transport efficiency in terms of degree correlation in node connection by numerical evaluation of exact analytic expressions. We…

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…

It has been observed that real-world social networks often exhibit stratification along economic or other lines, with consequences for class mobility and access to opportunities. With the rise in human interaction data and extensive use of…

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…

Many topological and dynamical properties of complex networks are defined by assuming that most of the transport on the network flows along the shortest paths. However, there are different scenarios in which non-shortest paths are used to…

Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…

Homophily -- the tendency of nodes to connect to others of the same type -- is a central issue in the study of networks. Here we take a local view of homophily, defining notions of first-order homophily of a node (its individual tendency to…

In this study we arrive at a closed form expression for measuring vector assortativity in networks motivated by our use-case which is to observe patterns of social mobility in a society. Based on existing works on social mobility within…

Higher order nets were introduced by Dick as a generalisation of classical $(t,m,s)$-nets, which are point sets frequently used in quasi-Monte Carlo integration algorithms. Essential tools in finding such point sets of high quality are…

Analysis of higher-order organizations, usually small connected subgraphs called motifs, is a fundamental task on complex networks. This paper studies a new problem of testing higher-order clusterability: given query access to an undirected…

Rich-club, assortativity and clustering coefficients are frequently-used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the…

Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…

A tight alignment between the degree vector and the leading eigenvector arises naturally in networks with neutral degree mixing and the absence of local structures. Many real-world networks, however, violate both conditions. We derive…

In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…