Katz centrality

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

Identifying Node Importance by Combining Betweenness Centrality and Katz Centrality

Abstract: The assessment of node importance has been a fundamental issue in the research of complex networks, which is of overreaching importance to improve the robustness of actual system and design efficient system structure. Most researchers use the betweenness centrality (BC) or Katz centrality (KC) to measure node importance. However, the betweenness only takes into account the shortest path, regardless of the non-shortest path. The Katz centrality gives different weights to all the paths in the network, but the ranking result is close to the result of local path index. Therefore, a new algorithm combines betweenness centrality and Katz centrality(BKC) is proposed, which considers both the local node importance and the global node importance comprehensively, and overcomes the limitations that the node importance evaluation only depending on the adjacent nodes. Experimental results on the kite network and the APRP network illustrate that BKC is more effective to find out important nodes in different types of complex networks than the algorithms compared. Moreover, the cascading failures on the author collaboration network also illustrate that the networks are more vulnerable when continuously removing the important nodes identified by BKC, which further proves the effectiveness of our method.

Ranking the key nodes with temporal degree deviation centrality on complex networks

Abstract: Records of time-stamped social interactions between pairs of individuals (e.g. the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market) constitute a so-called temporal network. A remarkable difference between temporal networks and conventional static networks is that time-stamped events rather than links are the unit elements generating the collective behavior of nodes. While we have good centralities to measure the importance of the nodes in static networks, so far these have been lacking for temporal cases. In this paper we propose a simple but powerful centrality, the degree deviation centrality, which calculates the deviation of temporal degree centrality. This enables us to extend network properties vertex degree centrality metrics in a very natural way to the temporal case. We then demonstrate how our centrality applies to identify the vital nodes in temporal networks by epidemic spreading dynamics based on SI (susceptible-infected) model. The numerical experiments on several real networks indicate that the temporal degree deviation centrality method outperforms some other indicators, and the results with different time window size show that the improvement is also robust.

Two Centrality Models

Abstract: 1 Christaller differentiated clearly between "absolute importance" (called Nodality here) and "relative importance" or Centrality. Nevertheless, scholars have consistently evaluated central places by measures of absolute importance, associated the term Centrality with their derived values, and then related their findings to classical central place theory as if such measurements met the re quirements of Centrality as originally defined. This point can be abundantly demonstrated by comparing "absolute importance" and Centrality as defined in W. Christaller, Central Places in Southern Germany, translated by C. W. Baskin, (Englewood Cliffs, N. J.: Prentice-Hall, 1966), pp. 17-18, and the variety of measures associated with Centrality reviewed in M. Palomaki, "The Func tional Centers and Areas of South Bothnia, Finland," Fennia, Vol. 88 (1964), pp. 10-19; S. Godlund, "The Function and Growth of Bus Traffic within the Sphere of Urban Influence," Lund Studies in Geography, Series B, No. 18 (1956), pp. 11-37; and R. Klopper, "Methoden zur Bestimmung der Zentralitat von Siedlungen," Geographisches Taschenbuch, (1953), pp. 512-519. It would be remiss, however, to imply that either the distinctions between Nodality and Centrality or the significance of the concept of Centrality in ap plied central place research has gone totally unnoticed; for example, see E. L. Ullman, "A Theory of Location for Cities," American Journal of Sociology, Vol. 46 (1941), pp. 858-859; A. Losch, Die raumliche Ordnung der Wirtschaft (Jena 1941), translated by W. H. Woglom and W. F. Stolper as, The Economies of Location (New Haven: Yale University Press, 1954), pp. 431-438; R. E.

Centrality and power in social networks: A game theoretic approach

Abstract: In this paper, a social network is modelized as a communication graph, which shows the possible direct communications between individuals. To reflect the interests that motivate the interactions, a cooperative game in characteristic function form is considered. From the graph and the game, the graph-restricted game is obtained. Shapley value in a game is considered as actor's power. The difference between actor's power in the new game and his/her power in the original one is proposed as a centrality measure. Conditions are given to obtain desirable properties for this measure. Finally, a decomposition of this measure is proposed.

An Axiomatization of the Eigenvector and Katz Centralities

Abstract: Feedback centralities are one of the key classes of centrality measures. They assess the importance of a vertex recursively, based on the importance of its neighbours. Feedback centralities includes the Eigenvector Centrality, as well as its variants, such as the Katz Centrality or the PageRank, and are used in various AI applications, such as ranking the importance of websites on the Internet and most influential users in the Twitter social network. In this paper, we study the theoretical underpinning of the feedback centralities. Specifically, we propose a novel axiomatization of the Eigenvector Centrality and the Katz Centrality based on six simple requirements. Our approach highlights the similarities and differences between both centralities which may help in choosing the right centrality for a specific application.