Related papers: Rich-club and page-club coefficients for directed …

For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a…

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their…

We show that the Internet topology at the Autonomous System (AS) level has a rich--club phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The rich--club is a…

The rich-club concept has been introduced in order to characterize the presence of a cohort of nodes with a large number of links (rich nodes) that tend to be well connected between each other, creating a tight group (club). Rich-clubness…

Modern scientific work, including writing papers and submitting research grant proposals, increasingly involves researchers from different institutions. In grant collaborations, it is known that institutions involved in many collaborations…

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…

Large scale hierarchies characterize complex networks in different domains. Elements at their top, usually the most central or influential, may show multipolarization or tend to club forming tightly interconnected communities. The rich-club…

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…

Rich-club ordering refers to the tendency of nodes with a high degree to be more interconnected than expected. In this paper we consider the concept of rich-club ordering when generalized to structural measures that differ from the node…

Rich-club ordering and the dyadic effect are two phenomena observed in complex networks that are based on the presence of certain substructures composed of specific nodes. Rich-club ordering represents the tendency of highly connected and…

Traditionally, there is no evidence suggesting that there are strong ties between the rich-club property and the function of complex networks. In this study, we find that whether a very small portion of rich nodes connected to each other or…

We present a link rewiring mechanism to produce surrogates of a network where both the degree distribution and the rich--club connectivity are preserved. We consider three real networks, the AS--Internet, the protein interaction and the…

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…

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…

In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density…

Many scale-free networks exhibit a rich club structure, where high degree vertices form tightly interconnected subgraphs. In this paper, we explore the emergence of rich clubs in the context of shortest path based centrality metrics. We…

The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the…

Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…

Based on observations in the web-graph, the power-law hypothesis states that PageRank has a power-law distribution with the same exponent as the in-degree. While this hypothesis has been analytically verified for many random graph models,…

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…