Size and connectivity of the k-core of a random graph
Discrete Mathematics
Journal of Algorithms
On the structural properties of massive telecom call graphs: findings and implications
CIKM '06 Proceedings of the 15th ACM international conference on Information and knowledge management
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Proceedings of the 16th international conference on World Wide Web
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AIRWeb '07 Proceedings of the 3rd international workshop on Adversarial information retrieval on the web
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WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
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Comparison of Feature-Based Criminal Network Detection Models with k-Core and n-Clique
ASONAM '10 Proceedings of the 2010 International Conference on Advances in Social Networks Analysis and Mining
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
Efficient core decomposition in massive networks
ICDE '11 Proceedings of the 2011 IEEE 27th International Conference on Data Engineering
Evaluating Cooperation in Communities with the k-Core Structure
ASONAM '11 Proceedings of the 2011 International Conference on Advances in Social Networks Analysis and Mining
D-cores: Measuring Collaboration of Directed Graphs Based on Degeneracy
ICDM '11 Proceedings of the 2011 IEEE 11th International Conference on Data Mining
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ICDE '12 Proceedings of the 2012 IEEE 28th International Conference on Data Engineering
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A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. k-core decomposition is often used in large-scale network analysis, such as community detection, protein function prediction, visualization, and solving NP-Hard problems on real networks efficiently, like maximal clique finding. In many real-world applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for streaming graph data. In this paper, we propose the first incremental k-core decomposition algorithms for streaming graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum k-core values have to be updated, and efficiently process this subgraph to update the k-core decomposition. Our results show a significant reduction in run-time compared to non-incremental alternatives. We show the efficiency of our algorithms on different types of real and synthetic graphs, at different scales. For a graph of 16 million vertices, we observe speedups reaching a million times, relative to the non-incremental algorithms.