Size-estimation framework with applications to transitive closure and reachability
Journal of Computer and System Sciences
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
ANF: a fast and scalable tool for data mining in massive graphs
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
SimRank: a measure of structural-context similarity
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Reachability and Distance Queries via 2-Hop Labels
SIAM Journal on Computing
Fast Random Walk with Restart and Its Applications
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Spatially-decaying aggregation over a network
Journal of Computer and System Sciences
The link-prediction problem for social networks
Journal of the American Society for Information Science and Technology
Summarizing data using bottom-k sketches
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
A sketch-based distance oracle for web-scale graphs
Proceedings of the third ACM international conference on Web search and data mining
HyperANF: approximating the neighbourhood function of very large graphs on a budget
Proceedings of the 20th international conference on World wide web
A comparison of three algorithms for approximating the distance distribution in real-world graphs
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Robustness of social networks: comparative results based on distance distributions
SocInfo'11 Proceedings of the Third international conference on Social informatics
Sparse reliable graph backbones
Information and Computation
How user behavior is related to social affinity
Proceedings of the fifth ACM international conference on Web search and data mining
Hierarchical hub labelings for shortest paths
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
HLDB: location-based services in databases
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
Fast exact shortest-path distance queries on large networks by pruned landmark labeling
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
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Similarity estimation between nodes based on structural properties of graphs is a basic building block used in the analysis of massive networks for diverse purposes such as link prediction, product recommendations, advertisement, collaborative filtering, and community discovery. While local similarity measures, based on properties of immediate neighbors, are easy to compute, those relying on global properties have better recall. Unfortunately, this better quality comes with a computational price tag. Aiming for both accuracy and scalability, we make several contributions. First, we define closeness similarity, a natural measure that compares two nodes based on the similarity of their relations to all other nodes. Second, we show how the all-distances sketch (ADS) node labels, which are efficient to compute, can support the estimation of closeness similarity and shortest-path (SP) distances in logarithmic query time. Third, we propose the randomized edge lengths (REL) technique and define the corresponding REL distance, which captures both path length and path multiplicity and therefore improves over the SP distance as a similarity measure. The REL distance can also be the basis of closeness similarity and can be estimated using SP computation or the ADS labels. We demonstrate the effectiveness of our measures and the accuracy of our estimates through experiments on social networks with up to tens of millions of nodes.