Katz centrality

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

Centrality measures for graphons

Abstract: Graphs provide a natural mathematical abstraction for systems with pairwise interactions, and thus have become a prevalent tool for the representation of systems across various scientific domains. However, as the size of relational datasets continues to grow, traditional graph-based approaches are increasingly replaced by other modeling paradigms, which enable a more flexible treatment of such datasets. A promising framework in this context is provided by graphons, which have been formally introduced as the natural limiting objects for graphs of increasing sizes. However, while the theory of graphons is already well developed, some prominent tools in network analysis still have no counterpart within the realm of graphons. In particular, node centrality measures, which have been successfully employed in various applications to reveal important nodes in a network, have so far not been defined for graphons. In this work we introduce formal definitions of centrality measures for graphons and establish their connections to centrality measures defined on finite graphs. In particular, we build on the theory of linear integral operators to define degree, eigenvector, and Katz centrality functions for graphons. We further establish concentration inequalities showing that these centrality functions are natural limits of their analogous counterparts defined on sequences of random graphs of increasing size. We discuss several strategies for computing these centrality measures, and illustrate them through a set of numerical examples.

An Approximate Flow Betweenness Centrality Measure for Complex Network

Abstract: In complex network analysis, there are various measures to characterize the centrality of each node within a graph, which determines the relative importance of each node. The more centrality a node has in a network, the more significance it has in the spread of infection. As one of the important extensions to shortest-path based betweenness centrality, the flow betweenness centrality is defined as the degree to which each node contributes to the sum of maximum flows between all pairs of nodes. One of the drawbacks of the flow betweenness centrality is that its time complexity is somewhat high. This Letter proposes an approximate method to calculate the flow betweenness centrality and provides experimental results as evidence. key words: complex network, centrality, flow betweenness centrality, approximate flow betweenness centrality

Finding k-highest betweenness centrality vertices in graphs

Abstract: The betweenness centrality is a measure for the relative participation of the vertex in the shortest paths in the graph. In many cases, we are interested in the k-highest betweenness centrality vertices only rather than all the vertices in a graph. In this paper, we study an efficient algorithm for finding the exact k-highest betweenness centrality vertices.

Fingerprinting networks: Correlations of local and global network properties

Abstract: In complex networks a common task is to identify the most important or “central” nodes There are several definitions, often called centrality measures, which often lead to different results Here, we introduce fingerprints of networks, which we define as correlation plots of local and global network properties We show that these fingerprints are suitable tools for characterizing networks beyond single-quantity distributions In particular, we study the correlations between four local and global measures, namely the degree, the shortest-path betweenness, the random-walk betweenness and the subgraph centrality on different random-network models like Erdős–Renyi, small-world and Barabasi–Albert as well as on different real networks like metabolic pathways, social collaborations and computer networks and compare those fingerprints to determine the quality of those basic models The correlation fingerprints are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world

Correlation coefficient analysis: centrality vs. maximal clique size for complex real-world network graphs

Abstract: The high-level contribution of this paper is correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. The maximal clique size for a node is the size of the largest clique (in terms of the number of constituent nodes) the node is part of. We observe the degree-based centrality metrics such as the degree centrality and eigenvector centrality to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics such as the closeness centrality and betweenness centrality. As the real-world networks get increasingly scale-free, we observe the correlation between the centrality value and the maximal clique size to increase.