Katz centrality

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

Concept of space modification and a theory of function measuring the centrality (or mediality) of a point in a network

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.

Centrality, gossip, and diffusion of information in networks

Abstract: How can we identify the most influential nodes in a network for initiating diffusion? Are people able to easily identify those people in their communities who are best at spreading information, and if so How? Using theory and recent data, we will examine these questions and see how the structure of social networks affects information transmission ranging from gossip to the diffusion of new products. In particular, the concept of diffusion centrality from Banerjee, Chandrasekhar, Duflo, and Jackson (2013) will be considered and shown to nest degree centrality, eigenvector centrality, and other measures of centrality as extreme special cases. Then it will be shown that by tracking gossip within a network, nodes can easily learn to rank the centrality of other nodes without knowing anything about the network itself. Finally, the theoretical predictions will be tested with data. The results are presented in Banerjee, Chandrasekhar, Duflo, and Jackson (2014).

Gromov centrality: A multiscale measure of network centrality using triangle inequality excess

Abstract: Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and it recovers as limits well-known concepts such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks.

Discovery of central community based on centrality

Abstract: By using combined method of degree centrality and flow-between centrality,the degree centrality and flow-between centrality of the nodes were computed first and then,the geometric center of the network and the node with the most routing through it in course of transmission of information and substances or energies on the network would be obtainedTaking these two indices as a whole into consideration,the nodes with these two indices of comparatively large magnitude were obtainedTherefore,the central community on the network could be discovered from among these and neighboring nodes by using CPM discovery algorithm of central communityBy using this method,the relatively "important" community of the network could be found and this would have certain significance for analysis of the spreading mechanism on the complex network,and successive failureFinally,the structure of central community of urban public traffic network of Lanzhou was analyzed with this method and its result indicated that the central community would play a central role in the whole network