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Multilayer networks have been widely used to represent and analyze systems of interconnected entities where both the entities and their connections can be of different types. However, real multilayer networks can be difficult to analyze…

Complex network theory is being widely used to study many real-life systems. One of the fields that can benefit from complex network theory approach is transportation network. In this paper, we briefly review the complex network theory…

Networks are pervasive in the real world. Nature, society, economy, and technology are supported by ostensibly different networks that in fact share an amazing number of interesting structural properties. Network thinking exploded in the…

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…

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…

The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the…

In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…

This work explores entropy analysis as a tool for probing information distribution within Transformer-based architectures. By quantifying token-level uncertainty and examining entropy patterns across different stages of processing, we aim…

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…

In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…

Measure the similarity of the nodes in the complex networks have interested many researchers to explore it. In this paper, a new method which is based on the degree centrality and the Relative-entropy is proposed to measure the similarity…

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…

The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…

In this article the problem of reconstructing the pattern of connection between agents from partial empirical data in a macro-economic model is addressed, given a set of behavioral equations. This systemic point of view puts the focus on…

We propose a multi-phase approach to explore network structures. In this method, structure analysis is not carried out on the observed network directly. Instead, certain similarity measures of the nodes are derived from the network firstly,…

This article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. The network entropy of a bipartite graph with random links is calculated both numerically and theoretically. As an application…

A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…

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…

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…

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…