Related papers: Minimal paths between communities induced by geogr…
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…
A class of centrality measures called betweenness centralities reflects degree of participation of edges or nodes in communication between different parts of the network. The original shortest-path betweenness centrality is based on…
The concept of multilayer networks has become recently integrated into complex systems modeling since it encapsulates a very general concept of complex relationships. Biological pathways are an example of complex real-world networks, where…
A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and…
Studying the topology of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are…
We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network…
In this article we investigate the topological changes undergone by trajectory networks as a consequence of progressive geographical infiltration. Trajectory networks, a type of knitted network, are obtained by establishing paths between…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Betweenness centrality (BC) is one of the most used centrality measures for network analysis, which seeks to describe the importance of nodes in a network in terms of the fraction of shortest paths that pass through them. It is key to many…
The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
Multiplex networks describe a large number of complex social, biological and transportation networks where a set of nodes is connected by links of different nature and connotation. Here we uncover the rich community structure of multiplex…
This paper surveys visualization and interaction techniques for geospatial networks from a total of 95 papers. Geospatial networks are graphs where nodes and links can be associated with geographic locations. Examples can include social…
Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Networks are fundamental for our understanding of complex systems. Interactions between individual nodes in networks generate network motifs - small recurrent patterns that can be considered the network's building-block components,…
Urban science has largely relied on universal models, rendering the heterogeneous and locally specific nature of cities effectively invisible. Here we introduce a topological framework that defines and detects localities in human mobility…
Cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. Focusing on cycle structure, this paper defines a new matrix, named cycle number matrix, to represent cycle…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…