  Bipartite graphs are rich data structures with prevalent applications and
identifier structural features. However, less is known about their growth
patterns, particularly in streaming settings. Current works study the patterns
of static or aggregated temporal graphs optimized for certain down-stream
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 known as butterflies, leading to a phenomenon that we call
"scale-invariant strength assortativity of streaming butterflies". 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, sGrow, to
pinpoint the generative origins. sGrow supports streaming paradigms, emergence
of 4-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 sGrow in realization of the
observed patterns independent of initial conditions, scale, temporal
characteristics, and model configurations. Theoretical and experimental
analysis verify the robust ability of sGrow in generating streaming graphs
based on user-specified configurations that affect the scale and burstiness of
the stream, level of strength assortativity, probability of-of-order streaming
records, generation time, and time-sensitive connections.
