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Many real-world networks such as Twitter and YouTube are given as fullydynamic graph streams represented as sequences of edge insertions anddeletions. (e.g., users can subscribe and unsubscribe to channels on YouTube).Existing similarity estimation methods such as MinHash and OPH are customizedto static graphs. We observe that they are indeed sampling methods and exhibita sampling bias when applied to fully dynamic graph streams, which results inlarge estimation errors. To solve this challenge, we develop a fast andaccurate sketch method VOS. VOS processes each edge in the graph stream ofinterest with small time complexity O(1) and uses small memory space to build acompact sketch of the dynamic graph stream over time. Based on the sketch builton-the-fly, we develop a method to estimate user similarities over time. Weconduct extensive experiments and the experimental results demonstrate theefficiency and efficacy of our method.

A Fast Sketch Method for Mining User Similarities over Fully Dynamic Graph Streams