Applied combinatorics
Optimal attack and reinforcement of a network
Journal of the ACM (JACM)
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Computing the strength of a graph
SIAM Journal on Computing
A matroid approach to finding edge connectivity and packing arborescences
Selected papers of the 23rd annual ACM symposium on Theory of computing
Mathematics of Operations Research
Algorithms for graphic polymatroids and parametric &smacr;-sets
Journal of Algorithms
Accelerating exact k-means algorithms with geometric reasoning
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Algorithms for graphic polymatroids and parametric s-Sets
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
ACM Computing Surveys (CSUR)
Data mining: concepts and techniques
Data mining: concepts and techniques
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Clustering Algorithms
Refining Initial Points for K-Means Clustering
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Proceedings of the 2004 ACM symposium on Applied computing
Flows and parity subgraphs of graphs with large odd-edge-connectivity
Journal of Combinatorial Theory Series B
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Clustering method is one of the most important tools in statistics. In a graph theory model, clustering is the process of finding all dense subgraphs. A mathematically well-defined measure for graph density is introduced in this article as follows. Let G = (V, E) be a graph (or multi-graph) and H be a subgraph of G. The dynamic density of H is the greatest integer k such that min∀P {|E(H/P)|/|V(H/P)| − 1} k where the minimum is taken over all possible partitions P of the vertex set of H, and H/P is the graph obtained from H by contracting each part of P into a single vertex. A subgraph H of G is a level-k community if H is a maximal subgraph of G with dynamic density at least k. An algorithm is designed in this paper to detect all level-h communities of an input multi-graph G. The worst-case complexity of this algorithm is upper bounded by O(|V(G)|2h2). This new method is one of few available clustering methods that are mathematically well-defined, supported by rigorous mathematical proof and able to achieve the optimization goal with polynomial complexity. As a byproduct, this algorithm also can be applied for finding edge-disjoint spanning trees of a multi-graph. The worst-case complexity is lower than all known algorithms for multi-graphs.