On Summarizing Graph Streams

TL;DR

This paper introduces gLava, a probabilistic graph model for summarizing dynamic graph streams efficiently, supporting complex queries with theoretical error bounds, by focusing on nodes rather than edges.

Contribution

The paper proposes a novel graph summarization method, gLava, that captures internal connections within stream elements and maintains relationships across elements, enabling efficient query processing.

Findings

Supports a wide range of graph queries.

Establishes theoretical error bounds for query accuracy.

Achieves sublinear space and constant update time.

Abstract

Graph streams, which refer to the graph with edges being updated sequentially in a form of a stream, have wide applications such as cyber security, social networks and transportation networks. This paper studies the problem of summarizing graph streams. Specifically, given a graph stream G, directed or undirected, the objective is to summarize G as S with much smaller (sublinear) space, linear construction time and constant maintenance cost for each edge update, such that S allows many queries over G to be approximately conducted efficiently. Due to the sheer volume and highly dynamic nature of graph streams, summarizing them remains a notoriously hard, if not impossible, problem. The widely used practice of summarizing data streams is to treat each element independently by e.g., hash- or sampling-based method, without keeping track of the connections between elements in a data stream, which gives these summaries limited power in supporting complicated queries over graph streams. This paper discusses a fundamentally different philosophy for summarizing graph streams. We present gLava, a probabilistic graph model that, instead of treating an edge (a stream element) as the operating unit, uses the finer grained node in an element. This will naturally form a new graph sketch where edges capture the connections inside elements, and nodes maintain relationships across elements. We discuss a wide range of supported graph queries and establish theoretical error bounds for basic queries.