Katz centrality

About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.

Analyzing complex networks through correlations in centrality measurements

Abstract: Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some centrality measures, with different centrality definitions stressing different aspects of the network. It is interesting to know to what extent these different centrality definitions are related for different networks. In this work, we study the correlation between pairs of a set of centrality measures for different real world networks and two network models. We show that the centralities are in general correlated, but with stronger correlations for network models than for real networks. We also show that the strength of the correlation of each pair of centralities varies from network to network. Taking this fact into account, we propose the use of a centrality correlation profile, consisting of the values of the correlation coefficients between all pairs of centralities of interest, as a way to characterize networks. Using the yeast protein interaction network as an example we show also that the centrality correlation profile can be used to assess the adequacy of a network model as a representation of a given real network.

Terrorist Networks, Network Energy and Node Removal: A New Measure of Centrality Based on Laplacian Energy

Abstract: In this work we propose a centrality measure for networks, which we refer to as Laplacian centrality, that provides a general framework for the centrality of a vertex based on the idea that the importance (or centrality) of a vertex is related to the ability of the network to respond to the deactivation or removal of that vertex from the network. In particular, the Laplacian centrality of a vertex is defined as the relative drop of Laplacian energy caused by the deactivation of this vertex. The Laplacian energy of network G with n vertices is defined as , where is the eigenvalue of the Laplacian matrix of G. Other dynamics based measures such as that of Masuda and Kori and PageRank compute the importance of a node by analyzing the way paths pass through a node while our measure captures this information as well as the way these paths are “redistributed” when the node is deleted. The validity and robustness of this new measure are illustrated on two different terrorist social network data sets and 84 networks in James Moody’s Add Health in school friendship nomination data, and is compared with other standard centrality measures.

Some centrality results new and old

Abstract: We prove a number of results on betweenness and closeness centrality and centralization. In particular, we prove the much used normalization expression for closeness centrality first given by Freeman (1979), correcting an error in the justification given in his paper. We explore the relationship between betweenness and the cutting number and use these results to prove and correct some centrality and centralization formulae first proposed by Borgatti and Everett (1997).

Should we simulate mental models to assess whether they agree

Abstract: Modeling approaches can support policy coherence by capturing the logistics of an intervention involving multiple individuals, or by identifying goals and preferences of each individual. An important intermediate step is to identify agreement among individuals. This may be achieved through intensive qualitative methods such as interviews, or by automatically comparing models. Current comparisons are limited as they either assess whether individuals think of the same factors, or see the same causal connections between factors. Systems science suggests that, to test whether individuals really share a paradigm, we should mobilize their whole models. Instead of comparing their whole models through multiple simulation scenarios, we suggested using network centrality. We performed experiments on mental models from 264 participants in the context of fishery management. Our results suggest that if stakeholder groups agree on the central factors (per Katz centrality), they also tend to agree on simulation outcomes and thus share a paradigm.