Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
Fully Dynamic All Pairs Shortest Paths with Real Edge Weights
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Parallel Algorithms for Evaluating Centrality Indices in Real-world Networks
ICPP '06 Proceedings of the 2006 International Conference on Parallel Processing
Ranking of Closeness Centrality for Large-Scale Social Networks
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Fast centrality approximation in modular networks
Proceedings of the 1st ACM international workshop on Complex networks meet information & knowledge management
Patterns of temporal variation in online media
Proceedings of the fourth ACM international conference on Web search and data mining
Algorithms
Deconstructing centrality: thinking locally and ranking globally in networks
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
DACCER: Distributed Assessment of the Closeness CEntrality Ranking in complex networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Fast approximation of betweenness centrality through sampling
Proceedings of the 7th ACM international conference on Web search and data mining
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A lot of centrality measures have been developed to analyze different aspects of importance. Some of the most popular centrality measures (e.g. betweenness centrality, closeness centrality) are based on the calculation of shortest paths. This characteristic limits the applicability of these measures for larger networks. In this article we elaborate on the idea of bounded-distance shortest paths calculations. We claim criteria for k-centrality measures and we introduce one algorithm for calculating both betweenness and closeness based centralities. We also present normalizations for these measures. We show that k-centrality measures are good approximations for the corresponding centrality measures by achieving a tremendous gain of calculation time and also having linear calculation complexity O(n) for networks with constant average degree. This allows researchers to approximate centrality measures based on shortest paths for networks with millions of nodes or with high frequency in dynamically changing networks.