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Katz centrality
About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.
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TL;DR: In this article, betweenness centrality of a vertex of a graph is defined as the portion of the shortest paths all pairs of vertices passing through a given vertex in a graph.
Abstract: A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.
TL;DR: In this article , causal centrality for dynamic causal models (DCM) is introduced, which is a dynamics-sensitive and causally-founded centrality measure based on the notion of intervention in graphical models.
Abstract: Network representation has been a groundbreaking concept for understanding the behavior of complex systems in social sciences, biology, neuroscience, and beyond. Network science is mathematically founded on graph theory, where nodal importance is gauged using measures of centrality. Notably, recent work suggests that the topological centrality of a node should not be over-interpreted as its dynamical or causal importance in the network. Hence, identifying the influential nodes in dynamic causal models (DCM) remains an open question. This paper introduces causal centrality for DCM, a dynamics-sensitive and causally-founded centrality measure based on the notion of intervention in graphical models. Operationally, this measure simplifies to an identifiable expression using Bayesian model reduction. As a proof of concept, the average DCM of the extended default mode network (eDMN) was computed in 74 healthy subjects. Next, causal centralities of different regions were computed for this causal graph, and compared against major graph-theoretical centralities. The results showed that the subcortical structures of the eDMN are more causally central than the cortical regions, even though the (dynamics-free) graph-theoretical centralities unanimously favor the latter. Importantly, model comparison revealed that only the pattern of causal centrality was causally relevant. These results are consistent with the crucial role of the subcortical structures in the neuromodulatory systems of the brain, and highlight their contribution to the organization of large-scale networks. Potential applications of causal centrality - to study other neurotypical and pathological functional networks – are discussed, and some future lines of research are outlined.
27 Mar 2023
TL;DR: In this paper , the authors proposed a centrality measure for spreading information, pathogens, etc. through weighted, directed networks based on the independent cascade model (ICM) and showed that the centrality measures (Viral Centrality) provided an excellent approximation to ICM results for networks in which the weighted strength of cycles is not too large.
Abstract: Abstract While many centrality measures for complex networks have been proposed, relatively few have been developed specifically for weighted, directed (WD) networks. Here we propose a centrality measure for spread (of information, pathogens, etc.) through WD networks based on the independent cascade model (ICM). While deriving exact results for the ICM requires Monte Carlo simulations, we show that our centrality measure (Viral Centrality) provides excellent approximation to ICM results for networks in which the weighted strength of cycles is not too large. We show this can be quantified with the leading eigenvalue of the weighted adjacency matrix, and we show that Viral Centrality outperforms other common centrality measures in both simulated and empirical WD networks.
01 Jan 2014
TL;DR: Wang et al. as discussed by the authors investigated the formation mechanism of dissemination force and the influence models of nodes' network centrality in the virtual social network and found that both a node's degree centrality and betweenness centrality have a positive impact on its dissemination force; closeness centrality didn't.
Abstract: This study investigates the formation mechanism of dissemination force and the influence models of nodes’ network centrality in the virtual social network. Combining the Social Network Analysis and Tobit regression, we find that: 1) both a node’s degree centrality and betweenness centrality have a positive impact on its dissemination force; 2) the closeness centrality didn’t. For theory contribution, we have a clever understand of the source of member’ dissemination force and the various influence models of different node centralities in virtual social network. For practice contribution, different kinds of opinion leaders can be distinguished according to different centralities in a more accurate way, so that we can make a more effective use of their dissemination force in network marketing.