Katz centrality

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

Performance Analysis of an Estimated Closeness Centrality Ranking Algorithm in Large-Scale Workflow-supported Social Networks

Abstract: This paper implements an estimated closeness centrality ranking algorithm in large-scale workflow-supported social networks and performance analyzes of the algorithm. Existing algorithm has a time complexity problem which is increasing performance time by network size. This problem also causes ranking process in large -scale workflow-supported social networks. To solve such problems, this paper conducts comparison analysis on the existing algorithm and estimated results by applying estimated-driven RankCCWSSN(Rank Closeness Centrality Workflow-supported Social Network). The RankCCWSSN algorithm proved its time-efficiency in a procedure about 50% decrease.

Measuring centrality by a generalization of degree

Abstract: Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.

Competitive Dynamics on Complex

Abstract: Ministry of Education of China, Shanghai 200240, China. We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors’ states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.

Mittag-Leffler functions and their applications in network science

Abstract: We describe a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions. This overarching theory includes as special cases well-known centrality measures like subgraph centrality and Katz centrality. The indices we introduce are parametrized by two numbers; by letting these vary, we show that Mittag-Leffler centralities interpolate between degree and eigenvector centrality, as well as between resolvent-based and exponential-based indices. We further discuss modeling and computational issues, and provide guidelines on parameter selection. The theory is then extended to the case of networks that evolve over time. Numerical experiments on synthetic and real-world networks are provided.

In)Sensitivity of Centrality Measurements in Social Networks

Abstract: In a survey a (complete) social network can be measured in manydifferent ways: different types of questions can be formu- lated, different methods for naming related actors can be used . In this process measurement errors are present . Different measurement instruments can produce more or less different measured social networks . Some studies (Holland and Leinhardt 1973 ; Sudman 1985, 1988 ; Hlebec 1993) has shown that the recognition produces a richer network than the recall . The effect of question wording and methods of naming related actors on the results should be studied more systematically also in the field of social network analysis as measurement errors can effect the structure of a network significantly . In the paper the communication flow in a small homogeneous network of twelve members and advisers of the Student Government of the University of Ljubljana in May 1992 was measured by two similar questions and each of them by two methods : recall and recognition . The effect of four types of measurement instruments on estimation of prominence or influence of actors in the network is studied . Actor prominence was measured by sixcentrality indices : in-degree point centrality indices, in-closeness global centrality indices (Sabidussi 1966), and Freeman's betweenness index (1979) . These indices are based on geodesic paths . The most interesting findings of this study are: The more complex centrality indices (e.g.,betweenness indices) are more effected by measurement errors than the simpler centrality indices (e.g.,degree indices) . The more central or prominent the actors are in the network, with less errors they are listed by the other actors