Computing Graph Descriptors on Edge Streams

Graph feature extraction is a fundamental task in graphs analytics. Using feature vectors (graph descriptors) in tandem with data mining algorithms that operate on Euclidean data, one can solve problems such as classification, clustering, and anomaly detection on graph-structured data. This idea has proved fruitful in the past, with spectral-based graph descriptors providing state-of-the-art classification accuracy on benchmark datasets. However, these algorithms do not scale to large graphs since: 1) they require storing the entire graph in memory, and 2) the end-user has no control over the algorithm's runtime. In this paper, we present single-pass streaming algorithms to approximate structural features of graphs (counts of subgraphs of order $k \geq 4$). Operating on edge streams allows us to avoid keeping the entire graph in memory, and controlling the sample size enables us to control the time taken by the algorithm. We demonstrate the efficacy of our descriptors by analyzing the approximation error, classification accuracy, and scalability to massive graphs. Our experiments showcase the effect of the sample size on approximation error and predictive accuracy. The proposed descriptors are applicable on graphs with millions of edges within minutes and outperform the state-of-the-art descriptors in classification accuracy.