Related papers: Eigenvector centrality of nodes in multiplex netwo…
Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation,…
Identifying influential nodes in a network is a major issue due to the great deal of applications concerned, such as disease spreading and rumor dynamics. That is why, a plethora of centrality measures has emerged over the years in order to…
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…
Finding the important nodes in complex networks by topological structure is of great significance to network invulnerability. Several centrality measures have been proposed recently to evaluate the performance of nodes based on their…
Complex networks are ubiquitous to several Computer Science domains. Centrality measures are an important analysis mechanism to uncover vital elements of complex networks. However, these metrics have high computational costs and…
Networks have been widely used as the data structure for abstracting real-world systems as well as organizing the relations among entities. Network embedding models are powerful tools in mapping nodes in a network into continuous…
Centrality, in some sense, captures the extent to which a vertex controls the flow of information in a network. Here, we propose Local Detour Centrality as a novel centrality-based betweenness measure that captures the extent to which a…
This paper examines the fundamental problem of identifying the most important nodes in a network. We use an axiomatic approach to this problem. Specifically, we propose six simple properties and prove that PageRank is the only centrality…
There is great significance in evaluating a node's Influence ranking in complex networks. Over the years, many researchers have presented different measures for quantifying node interconnectedness within networks. Therefore, this paper…
We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness. We show that for low values of the decay parameter the nodes with maximum decay…
Real networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify vital nodes is thus very significant, allowing us to control the outbreak of epidemics, to conduct advertisements for…
This paper proposes a family of network centralities called fixed-point centralities. This centrality family is defined via the fixed point of permutation equivariant mappings related to the underlying network. Such a centrality notion is…
The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
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…
We introduce a methodology based on averaging similarity matrices with the aim of integrating the layers of a multiplex network into a single monoplex network. Multiplex networks are adopted for modelling a wide variety of real-world…
Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…
Multilayer network analysis has become a vital tool for understanding different relationships and their interactions in a complex system, where each layer in a multilayer network depicts the topological structure of a group of nodes…
Several expressions for the $j$-th component $\left( x_{k}\right)_{j}$ of the $k$-th eigenvector $x_{k}$ of a symmetric matrix $A$ belonging to eigenvalue $\lambda_{k}$ and normalized as $x_{k}^{T}x_{k}=1$ are presented. In particular, the…
There are several applications that benefit from a definition of centrality which is applicable to sets of vertices, rather than individual vertices. However, existing definitions might not be able to help us in answering several network…