Related papers: Exponential Generalised Network Descriptors
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
A very interesting matter of Network Science is assessing how complex a given network is. In other words, by how much does such a network departs from any general patterns which could be evoked for its description. Among other choices,…
Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…
The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
With the increasing availability of behavioral data from diverse digital sources, such as social media sites and cell phones, it is now possible to obtain detailed information about the structure, strength, and directionality of social…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on 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…
Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…
Betweenness centrality is a metric that seeks to quantify a sense of the importance of a vertex in a network graph in terms of its "control" on the distribution of information along geodesic paths throughout that network. This quantity…
Crosstalk is defined as the set of unwanted interactions among the different entities of a network. Crosstalk is present in various degrees in every system where information is transmitted through a means that is accessible by all the…
Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the…
In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as…
While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
In order to take the weight of connection into consideration and to find a natural measurement of weight, we have collected papers in Econophysics and constructed a network of scientific communication to integrate idea transportation among…
In this paper we quantify our limited information horizon, by measuring the information necessary to locate specific nodes in a network. To investigate different ways to overcome this horizon, and the interplay between communication and…