Reservoir-based sampling over large graph streams to estimate triangle counts and node degrees

Reservoir sampling is widely employed to characterize large graph streams by producing edge samples. However, existing reservoir-based sampling methods mainly focus on counting triangles but perform poorly in analyzing topological characteristics reflected by node degrees. This paper proposes a new method, called triangle-induced reservoir sampling, or T-Sample, to count triangles and estimate node degrees simultaneously and efficiently. While every edge in a graph stream is processed only once by T-Sample, a dual sampling mechanism performing both uniform sampling and non-uniform sampling is carefully designed. Specifically, T-Sample's uniform sampling is used to count triangles by a newly proposed method with smaller estimation variances than existing reservoir-based sampling methods; whereas, its non-uniform sampling ensures that edge samples are connected. Experimental results driven by real datasets show that T-Sample can count triangles with smaller estimation errors and variances than the state-of-the-art reservoir-based sampling methods while obtaining much more accurate information about node degrees at smaller time and memory costs. (C) 2020 Elsevier B.V. All rights reserved.