Efficient aggregation for graph summarization

Abstract

Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mostly statistical (studying statistics such as degree distributions, hop-plots and clustering coefficients). These statistical methods are very useful, but the resolutions of the summaries are hard to control.In this paper, we introduce two database-style operations to summarize graphs. Like the OLAP-style aggregation methods that allow users to drill-down or roll-up to control the resolution of summarization, our methods provide an analogous functionality for large graph datasets. The first operation, called SNAP, produces a summary graph by grouping nodes based on user-selected node attributes and relationships. The second operation, called k-SNAP, further allows users to control the resolutions of summaries and provides the "drill-down" and "roll-up" abilities to navigate through summaries with different resolutions. We propose an efficient algorithm to evaluate the SNAP operation. In addition, we prove that the k-SNAP computation is NPcomplete. We propose two heuristic methods to approximate the k-SNAP results. Through extensive experiments on a variety of real and synthetic datasets, we demonstrate the effectiveness and efficiency of the proposed methods.

Graph OLAP: a multi-dimensional framework for graph data analysis

“…With regard to summarizing attributed networks that incorporates OLAP-style functionalities, Tian et al [27] is the closet to ours in spirit. It introduces an operation called SNAP (Summarization by grouping Nodes on Attributes and Pairwise relationships), which merges nodes with identical labels (actually, it might not be necessary to require exactly the same label for real applications, e.g., Lu et al [18] introduces a way to find similar group of entities in a network, and this can be taken as the basis to guide node merges), combines corresponding edges, and aggregates a summary graph that displays relationships for such "generalized" node groups.…”

Scalable graph exploration and visualization: Sensemaking challenges and opportunities

“…Filtering [1], [2], [3] Sampling [4], [5], [6] Partitioning [7], [8], [9], [10] Clustering [11], [12], [13], [3], [14], [15] Local View Free Discovery Exploration [16], [17], [14], [18], [3], [15], [19], [20], [21] Network Motifs [22], [23], [24], [25], [26] Targeted Discovery Pattern Matching [27], [28], [29], [30], [31] Navigation [32], [33], [34], [35], [36], [19], [37] Fig. 1.…”

“…In [11], Tian et al demonstrate SNAP; which creates a summary graph by allowing user-specified attributes to determine nodenode similarity; and k-SNAP which automatically generated subgroups allowing a user to drill-down or roll-up levels of summarization. The k-SNAP system works by using OLAPstyle aggregation to roll-up multiple nodes by a given attribute, which can be done or undone multiple times, allowing a user to roll-up or drill-down their summary graph.…”

OLAP on Information Networks: A New Framework for Dealing with Bibliographic Data

“…However, he did not propose new models or operations. Tian et al introduced an operation called SNAP [16]. It can produce a summary graph by grouping nodes.…”