Katz centrality

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

A centrality measure based on spectral optimization of modularity density

Abstract: Centrality analysis has been shown to be a valuable method for the structural analysis of complex networks. It is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting candidates. In this paper, we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel matrix. Based on the eigenvectors belonging to the largest eigenvalue of kernel matrix, we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network, called modularity density centrality. The measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data set. The statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real world. Experimental results show the significance of the proposed approach.

Local Information-based Betweenness Centrality to Identify Important Nodes in Social Networks

Abstract: In traditional social network analysis, the betweenness centrality measure has been heavily used to identify the relative importance of nodes in terms of message delivery. Since the time complexity to calculate the betweenness centrality is very high, however, it is difficult to get it of each node in large-scale social network where there are so many nodes and edges. In this paper, we define a new type of network, called the expanded ego network, which is built only with each node’s local information, i.e., neighbor information of the node’s neighbor nodes, and also define a new measure, called the expended ego betweenness centrality. Through the intensive experiment with Barabasi-Albert network model to generate the scale-free networks which most social networks have as their embedded feature, we also show that the nodes’ importance rank based on the expanded ego betweenness centrality has high similarity with that based on the traditional betweenness centrality. Keywords:Social Network Analysis, Betweenness Centrality, Local Information, Expanded Ego Network

Recommendation of shopping places based on social and geographical influences

Abstract: The project tackled in this article is a shopping recommender system that aims at providing recommendations of new interesting shopping places to users, by considering their tastes and those of their friends, since social friends are often sharing common interests. This kind of system is a Location-Based Social Network. It considers social relationships and check-ins; i.e. the action of visiting a shopping place. In order to recommend shopping places, we are proposing a method combining three separated graphs, namely the social graph, the frequentation graph and a geographic graph into one graph. Hence, in this merged graph, nodes can represent users or places, and edges can connect users to each other (social links), users with places (frequentation relations) or places to each other (geographic relations). Given that check-in behavior of users is strongly dependent on the distances, the geographic graph is constructed considering the density of probabilities that a check-in is done according to its distance to the other check-ins. The Katz centrality is then used on the merged graph to compute the scores of candidate locations to be recommended. Finally, the top-n unvisited shopping places are recommended to the target user. The proposed method is compared to methods from the literature on a real-world datatset. The results confirm the real interest of considering both social and geographic data beyond the frequentations for recommending new places. Generally, our method outperforms significantly the compared methods, but under certain conditions that we analyze, we show it gives sometimes mixed results.

An Empirical Study of Robustness of Network Centrality Scores in Various Networks and Conditions

Abstract: Network centrality score is an important measure to assess the importance and the major roles that each node plays in a network. In addition, the centrality score is also vitally important in assessing the overall structure and connectivity of a network. In a narrow sense, nearly all network mining algorithms, such as social network community detection, link predictions etc., involve certain types of centrality scores to some extent. Despite of its importance, very few researches have empirically analyzed the robustness of these measures in different network environments. Our existing works know very little about how network centrality score behaves at macro- (i.e. network) and micro- (i.e. individual node) levels. At the network level, what are the inherent connections between network topology structures and centrality scores? Will a sparse network be more (or less) robust in its centrality scores if any change is introduced to the network? At individual node levels, what types of nodes (high or low node degree) are more sensitive in their centrality scores, when changes are imposed to the network?And which centrality score is more reliable in revealing the genuine network structures? In this paper, we empirically analyze the robustness of three types of centrality scores: Betweenness centrality score, Closeness centrality score, and Eigen-vector centrality score for various types of networks. We systematically introduce biased and unbiased changes to the networks, by adding and removing different percentages of edges and nodes, through which we can compare and analyze the robustness and sensitivity of each centrality score measurement. Our empirical studies draw important findings to help understand the behaviors of centrality scores in different social networks.

Closeness Centrality on BBS Reply Network

Abstract: In this paper, a reply network was constructed with the data downloaded from SINA BBS. Based on the complex network theory, we firstly studied the node closeness centrality and graph closeness centralization of the reply network, and analyzed the influence of the central figure in reply network by studying the node closeness centrality. The leadership of the central figure was proved through experimental validation method. Then the correlation of degree and average closeness centrality was discussed. Finally, a conclusion was drawn that degree and average closeness centrality are positive correlation. Experimental results indicated that degree centrality and closeness centrality were effective measure in studying the center position and function of the nodes in BBS reply networks.