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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.


Papers
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Posted ContentDOI
29 Jan 2022
TL;DR: In this paper , the authors derive a community-aware information-theoretic centrality score based on the coding principles behind the map equation, which measures how much further we can compress the network's modular description by not coding for random walker transitions to the respective node, using an adapted coding scheme.
Abstract: To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures, such as degree centrality and PageRank, neglect the community structure found in real-world networks. To study node importance based on network flows from a mesoscopic perspective, we analytically derive a community-aware information-theoretic centrality score based on the coding principles behind the map equation: map equation centrality. Map equation centrality measures how much further we can compress the network's modular description by not coding for random walker transitions to the respective node, using an adapted coding scheme. It can be determined from the local network context alone because changes to the coding scheme affect only the node's module. Applied to synthetic and real-world networks, we highlight how our approach enables a more fine-grained differentiation between nodes than node-local or network-global measures. Map equation centrality tends to outperform other community-aware centrality measures.
Journal Article
TL;DR: The finding of the implementation of algorithm indicated that introduced algorithm to compute the density of samples and to detect the number of mono-nodes while clustering has revealed more accuracy rather than the related works.
Abstract: Nowadays, we live in network area. The area through which the formation of various social network, new communicative and informing methods are introduced to the widespread social communications. A social network is a social structure which is made out of individuals and meanwhile, by the pass of time, the analyzing these social network will gain increasing primacy. In this research, one of the parameters of social network analysis called edge betweenness centrality is introduced. Edge betweenness is an edge to compute the shortest paths between pair of nodes in the network that passes through it most frequently. In this research, to detect the communities through edge betweenness centrality algorithm, a method is introduced in such a way that each edge by receiving one fuzzy membership degree in the interval [1, 0] the measure of its effect on the network will be different. One of the features of this algorithm that makes it distinguished from others is the application of fuzzy logic to detect the communities of social network. Then by introducing the density of each cluster the density measure of the communities graph is computed through considering the fuzzy detected structures. The finding of the implementation of algorithm indicated that introduced algorithm to compute the density of samples and to detect the number of mono-nodes while clustering has revealed more accuracy rather than the related works.
Posted Content
TL;DR: In this paper, the influence maximization problem is formulated as a mixed integer nonlinear programming problem and adopted derivative-free methods, and a customised direct search method is proposed for the proposed diffusion model, with local convergence.
Abstract: Information diffusion in social networks is a central theme in computational social sciences, with important theoretical and practical implications, such as the influence maximisation problem for viral marketing. Two widely adopted diffusion models are the independent cascade model where nodes adopt their behaviour from each neighbour independently, and the linear threshold model where collective effort from the whole neighbourhood is needed to influence a node. However, both models suffer from certain drawbacks, including a binary state space, where nodes are either active or not, and the absence of feedback, as nodes can not be influenced after having been activated. To address these issues, we consider a model with continuous variables that has the additional advantage of unifying the two classic models, as the extended independent cascade model and the extended linear threshold model are recovered by setting appropriate parameters. For the associated influence maximisation problem, the objective function is no longer submodular, a feature that most approximation algorithms are based on but is arguably strict in practice. Hence, we develop a framework, where we formulate the influence maximisation problem as a mixed integer nonlinear programming and adopt derivative-free methods. Furthermore, we propose a customised direct search method specifically for the proposed diffusion model, with local convergence. We also show that the problem can be exactly solved in the case of linear dynamics by selecting nodes according to their Katz centrality. We demonstrate the rich behaviour of the newly proposed diffusion model and the close-to-optimal performance of the customised direct search numerically on both synthetic and real networks.
Journal ArticleDOI
TL;DR: The simulation results show that network connectivity degree can reflect the overall connectivity of OSNs, which provide a basis for improving the OSNs performance.
Abstract: Connectivity is an important indicator of network performance. But the opportunistic sensor networks (OSNs) have temporal evolution characteristics, which are hard to modelled with traditional graphs. After analyzing the characteristics of OSNs, this paper constructs OSNs connectivity model based on time graph theory. The overall connectivity degree of the network is defined, and is used to estimate actual network connectivity. We also propose a computing method that uses the adjacency matrix of each snapshot. The simulation results show that network connectivity degree can reflect the overall connectivity of OSNs, which provide a basis for improving the OSNs performance.
Journal ArticleDOI
TL;DR: In this paper , the effect of combining the first and second neighbors of a given node in a network was considered, and a three-order tensor was constructed to represent the first-and second neighbor relation among nodes.
Abstract: Eigenvector centrality refers to the principal eigenvector of the adjacency matrix of a graph. The adjacency matrix can be regarded as the matrix describing the one-step walks on the graph, shortly, the one-walk matrix, and then eigenvector centrality can refer to the principal eigenvector of the one-walk matrix. In this paper, we consider the effect of combining the first and second neighbors of a given node in a network. Analogously to the one-walk matrix, we construct a three-order tensor, namely the two-steps tensor, to represent the first and second neighbor relation among nodes. We adopt the positive eigenvector of the two-steps tensor corresponding to its spectral radius as a new centrality measure. This new centrality measure is referred to as the two-steps eigenvector centrality, which extends the notion of eigenvector centrality. Experimental results show that the new centrality measure is effective, and in certain networks, it gives an additional insight regarding node importance.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202232
202114
202013
201919
201824