Showing papers on "Katz centrality published in 1987"
TL;DR: In this article, the rank orderings by the four networks whose analysis forms the heart of this paper were analyzed and compared to the rank ordering by the three centrality measures, i.e., betweenness, nearness, and degree.
Abstract: 2In an influential paper, Freeman (1979) identified three aspects of centrality: betweenness, nearness, and degree. Perhaps because they are designed to apply to networks in which relations are binary valued (they exist or they do not), these types of centrality have not been used in interlocking directorate research, which has almost exclusively used formula (2) below to compute centrality. Conceptually, this measure, of which c(ot, 3) is a generalization, is closest to being a nearness measure when 3 is positive. In any case, there is no discrepancy between the measures for the four networks whose analysis forms the heart of this paper. The rank orderings by the
4,482 citations
TL;DR: The theory is a generalization of the centrality function which is applicable to the network, where weight is assigned to the point and the length and capacity are assign to the edge.
Abstract: Often, in a system with a network structure, such as the communication network, traffic network and social relationships, the centrality of a point is discussed. The centrality of a point is usually measured by its relation to other points, and the distance has been used as a measure for the relation. Recently, a method based on the capacity has also been proposed. In contrast to the past theory of centrality function, which discriminated the cases into the relation between points into the distance and the capacity, this paper presents a unified theory by introducing the concept of modification of the space with respect to a point. Based on the modification of the space, the axiomatic system concerning the centrality and semi-centrality functions are newly defined, extracting the properties shared by the past centrality functions. The characterization of the real-valued function defined on a point is made based on the proposed axiomatic system, and it is shown that the proposed theory includes the past major results concerning the centrality function. Finally, the theory is applied to the network, where the weight is assigned to the point, and the length and capacity are assigned to the edge. Thus, the theory is a generalization of the centrality function which is applicable to the network, where weight is assigned to the point and the length and capacity are assigned to the edge.
1 citations