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Current works study the patterns of static or aggregated temporal graphs optimized for certain downstream analytics or ignoring multipartite\/non-stationary data distributions, emergence patterns of subgraphs, and streaming paradigms. To address these, we perform statistical network analysis over web log streams and identify the governing patterns underlying the bursty emergence of mesoscopic building blocks, 2, 2-bicliques, leading to a phenomenon that we call<jats:italic>scale-invariant strength assortativity of streaming butterflies<\/jats:italic>. We provide the graph-theoretic explanation of this phenomenon. We further introduce a set of micro-mechanics in the body of a streaming growth algorithm,<jats:italic>sGrow<\/jats:italic>, to pinpoint the generative origins.<jats:italic>sGrow<\/jats:italic>supports streaming paradigms, emergence of four-vertex graphlets, and provides user-specified configurations for the scale, burstiness, level of strength assortativity, probability of out-of-order records, generation time, and time-sensitive connections. Comprehensive evaluations on pattern reproducing and stress testing validate the effectiveness, efficiency, and robustness of<jats:italic>sGrow<\/jats:italic>in realization of the observed patterns independent of initial conditions, scale, temporal characteristics, and model configurations. Theoretical and experimental analysis verify<jats:italic>sGrow<\/jats:italic>\u2019s robustness in generating streaming graphs based on user-specified configurations that affect the scale and burstiness of the stream, level of strength assortativity, probability of out-of-order streaming records, generation time, and time-sensitive connections.<\/jats:p>","DOI":"10.1145\/3572408","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T12:19:56Z","timestamp":1671020396000},"page":"1-46","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["sGrow: Explaining the Scale-Invariant Strength Assortativity of Streaming Butterflies"],"prefix":"10.1145","volume":"17","author":[{"given":"Aida","family":"Sheshbolouki","sequence":"first","affiliation":[{"name":"University of Waterloo"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. 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