Graph Summarization

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie

Incremental Lossless Graph Summarization

Given a fully dynamic graph, represented as a stream of edge insertions and deletions, how can we obtain and incrementally update a lossless summary of its current snapshot? As large-scale graphs are prevalent, concisely representing them is inevitable for efficient storage and analysis. Lossless graph summarization is an effective graph-compression technique with many desirable properties. It aims to compactly represent the input graph as (a) a summary graph consisting of supernodes (i.e., sets of nodes) and superedges (i.e., edges between supernodes), which provide a rough description, and (b) edge corrections which fix errors induced by the rough description. While a number of batch algorithms, suited for static graphs, have been developed for rapid and compact graph summarization, they are highly inefficient in terms of time and space for dynamic graphs, which are common in practice. In this work, we propose MoSSo, the first incremental algorithm for lossless summarization of fully dynamic graphs. In response to each change in the input graph, MoSSo updates the output representation by repeatedly moving nodes among supernodes. MoSSo decides nodes to be moved and their destinations carefully but rapidly based on several novel ideas. Through extensive experiments on 10 real graphs, we show MoSSo is (a) Fast and 'any time': processing each change in near-constant time (less than 0.1 millisecond), up to 7 orders of magnitude faster than running state-of-the-art batch methods, (b) Scalable: summarizing graphs with hundreds of millions of edges, requiring sub-linear memory during the process, and (c) Effective: achieving comparable compression ratios even to state-of-the-art batch methods.Comment: to appear at the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '20

Play like a Vertex: A Stackelberg Game Approach for Streaming Graph Partitioning

In the realm of distributed systems tasked with managing and processing large-scale graph-structured data, optimizing graph partitioning stands as a pivotal challenge. The primary goal is to minimize communication overhead and runtime cost. However, alongside the computational complexity associated with optimal graph partitioning, a critical factor to consider is memory overhead. Real-world graphs often reach colossal sizes, making it impractical and economically unviable to load the entire graph into memory for partitioning. This is also a fundamental premise in distributed graph processing, where accommodating a graph with non-distributed systems is unattainable. Currently, existing streaming partitioning algorithms exhibit a skew-oblivious nature, yielding satisfactory partitioning results exclusively for specific graph types. In this paper, we propose a novel streaming partitioning algorithm, the Skewness-aware Vertex-cut Partitioner S5P, designed to leverage the skewness characteristics of real graphs for achieving high-quality partitioning. S5P offers high partitioning quality by segregating the graph's edge set into two subsets, head and tail sets. Following processing by a skewness-aware clustering algorithm, these two subsets subsequently undergo a Stackelberg graph game. Our extensive evaluations conducted on substantial real-world and synthetic graphs demonstrate that, in all instances, the partitioning quality of S5P surpasses that of existing streaming partitioning algorithms, operating within the same load balance constraints. For example, S5P can bring up to a 51% improvement in partitioning quality compared to the top partitioner among the baselines. Lastly, we showcase that the implementation of S5P results in up to an 81% reduction in communication cost and a 130% increase in runtime efficiency for distributed graph processing tasks on PowerGraph.Comment: This paper has been accepted by SIGMOD 202