Related papers: Localization and centrality in networks
We study the h Hirsch index as a local node centrality measure for complex networks in general. The h index is compared with the Degree centrality (a local measure), the Betweenness and Eigenvector centralities (two non-local measures) in…
Eigenvector centrality is a standard network analysis tool for determining the importance of (or ranking of) entities in a connected system that is represented by a graph. However, many complex systems and datasets have natural multi-way…
Network centralization, driven by hub nodes, impacts communication efficiency, structural integration, and dynamic processes such as diffusion and synchronization. Although numerous centralization measures exist, a major challenge lies in…
Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks, however, it is computationally costly, and its measurement for networks with millions of nodes is near impossible. By…
We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes…
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…
This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…
In various applications involving complex networks, network measures are employed to assess the relative importance of network nodes. However, the robustness of such measures in the presence of link inaccuracies has not been well…
In the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical…
The non-trivial structure of such complex systems makes the analysis of their collective behavior a challenge. The problem is even more difficult when the information is distributed across networks (e.g., communication networks in different…
Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and…
To understand a node's centrality in a multiplex network, its centrality values in all the layers of the network can be aggregated. This requires a normalization of the values, to allow their meaningful comparison and aggregation over…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
Networks significantly influence social, economic, and organizational outcomes, with centrality measures serving as crucial tools to capture the importance of individual nodes. This paper introduces Laplacian Eigenvector Centrality (LEC), a…
Given a network G, edge centrality is a metric used to evaluate the importance of edges in G, which is a key concept in analyzing networks and finds vast applications involving edge ranking. In spite of a wealth of research on devising edge…
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…
We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are…
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…
In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…