From Big Bang to Big Crunch

A graph stream, which refers to the graph with edges being updated sequentially in a form of a stream, has important applications in cyber security and social networks. Due to the sheer volume and highly dynamic nature of graph streams, the practical way of handling them is by summarization. Given a graph stream G, directed or undirected, the problem of graph stream summarization is to summarize G as S G with a much smaller (sublinear) space, linear construction time and constant maintenance cost for each edge update, such that S G allows many queries over G to be approximately conducted e ciently. The widely used practice of summarizing data streams is to treat each stream element independently by e.g., hashor sample-based methods, without maintaining the connections (or relationships) between elements. Hence, existing methods can only solve ad-hoc problems, without supporting diversified and complicated analytics over graph streams. We present TCM, a novel graph stream summary. Given an incoming edge, it summarizes both node and edge information in constant time. Consequently, the summary forms a graphical sketch where edges capture the connections inside elements, and nodes maintain relationships across elements. We discuss a wide range of supported queries and establish some error bounds. In addition, we experimentally show that TCM can e↵ectively and e ciently support analytics over graph streams beyond the power of existing sketches, which demonstrates its potential to start a new line of research and applications in graph stream management. CCS Concepts •Mathematics of computing ! Network flows; •Information systems ! Data streams; •Theory of computation ! Sketching and sampling;