Katz centrality

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

A random projection approach for estimation of the betweenness centrality measure

Abstract: There are several potent measures for mining the relationships among actors in social network analysis. Betweenness centrality measure is extensively utilized in network analysis. However, it is quite time-consuming to compute exactly the betweenness centrality in high dimensional social networks. Applying random projection approach, an approximation algorithm for computing betweenness centrality of a given node, is proposed in this paper, for both weighted and unweighted graphs. It is proved that the proposed method works better than the existing methods to approximate the betweenness centrality measure. The proposed algorithm significantly reduces the number of single-source shortest path computations. We test the method on real-world networks and a synthetic benchmark and observe that the proposed algorithm shows very promising results based on statistical evaluation measure.

The Degree Measure as Utility Function over Positions in Networks

Abstract: In this paper, we connect the social network theory on centrality measures to the economic theory of preferences and utility. Using the fact that networks form a special class of cooperative TU-games, we provide a foundation for the degree measure as a von Neumann-Morgenstern expected utility function reflecting preferences over being in different positions in different networks. The famous degree measure assigns to every position in a weighted network the sum of the weights of all links with its neighbours. A crucial property of a preference relation over network positions is neutrality to ordinary risk. If an expected utility function over network positions satisfies this property and some regularity properties, then it must be represented by a utility function that is a multiple of the degree centrality measure. We show this in three steps. First, we characterize the degree measure as a centrality measure for weighted networks using four natural axioms. Second, we relate these network centrality axioms to properties of preference relations over positions in networks. Third, we show that the expected utility function is equal to a multiple of the degree measure if and only if it represents a regular preference relation that is neutral to ordinary risk. Similarly, we characterize a class of affine combinations of the outdegree and indegree measure in weighted directed networks and deliver its interpretation as a von Neumann-Morgenstern expected utility function.

Centrality Measures Based on Matrix Functions

Abstract: Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.

FVBM: A Filter-Verification-Based Method for Finding Top-k Closeness Centrality on Dynamic Social Networks

Abstract: Closeness centrality is often used to identify the top-k most prominent nodes in a network. Real networks, however, are rapidly evolving all the time, which results in the previous methods hard to adapt. A more scalable method that can immediately react to the dynamic network is demanding. In this paper, we endeavour to propose a filter and verification framework to handle such new trends in the large-scale network. We adopt several pruning methods to generate a much smaller candidate set so that bring down the number of necessary time-consuming calculations. Then we do verification on the subset; which is a much time efficient manner. To further speed up the filter procedure, we incremental update the influenced part of the data structure. Extensive experiments using real networks demonstrate its high scalability and efficiency.

Matrix growth models based on centrality measures: a first analysis

Abstract: A general growth model of random networks based on centrality measures is introduced. This formalism extends the well-known models of prefer- ential attachment. We propose to set the preferential attachment using a linear function of some centrality measures ranging from local to global scale. The aim is to include spectral measures, such as PageRank and Bonacich, and geodesic measures, such as betweenness and closeness. In this paper we present a first analysis using degree and Personalized PageRank.