Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Connectivity, graph minors, and subgraph multiplicity
Journal of Graph Theory
Arboricity and bipartite subgraph listing algorithms
Information Processing Letters
A Fast Approximation Algorithm for Computing theFrequencies of Subgraphs in a Given Graph
SIAM Journal on Computing
Finding and counting small induced subgraphs efficiently
Information Processing Letters
Dynamic Graph Algorithms with Applications
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
On the complexity of fixed parameter clique and dominating set
Theoretical Computer Science
Finding and counting cliques and independent sets in r-uniform hypergraphs
Information Processing Letters
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Extended dynamic subgraph statistics using h-index parameterized data structures
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Triangle listing in massive networks and its applications
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Arboricity, h-index, and dynamic algorithms
Theoretical Computer Science
Extended dynamic subgraph statistics using h-index parameterized data structures
Theoretical Computer Science
New races in parameterized algorithmics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Triangle listing in massive networks
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on the Best of SIGKDD 2011
Finding dense subgraphs of sparse graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Classifying Wikipedia articles using network motif counts and ratios
Proceedings of the Eighth Annual International Symposium on Wikis and Open Collaboration
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Simmelian backbones: amplifying hidden homophily in Facebook networks
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
A dynamic data structure for counting subgraphs in sparse graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of each possible three-vertex subgraph in time O (h ) per update, where h is the h-index of the graph, the maximum number such that the graph contains h vertices of degree at least h . We also show how to maintain the h -index itself, and a collection of h high-degree vertices in the graph, in constant time per update. Our data structure has applications in social network analysis using the exponential random graph model (ERGM); its bound of O (h ) time per edge is never worse than the $\Theta(\sqrt m)$ time per edge necessary to list all triangles in a static graph, and is strictly better for graphs obeying a power law degree distribution. In order to better understand the behavior of the h -index statistic and its implications for the performance of our algorithms, we also study the behavior of the h -index on a set of 136 real-world networks.