Utility-driven graph summarization

Abstract

A lot of the large datasets analyzed today represent graphs. In many real-world applications, summarizing large graphs is beneficial (or necessary) so as to reduce a graph's size and, thus, achieve a number of benefits, including but not limited to 1) significant speed-up for graph algorithms, 2) graph storage space reduction, 3) faster network transmission, 4) improved data privacy, 5) more effective graph visualization, etc. During the summarization process, potentially useful information is removed from the graph (nodes and edges are removed or transformed). Consequently, one important problem with graph summarization is that, although it reduces the size of the input graph, it also adversely affects and reduces its utility. The key question that we pose in this paper is, can we summarize and compress a graph while ensuring that its utility or usefulness does not drop below a certain user-specified utility threshold? We explore this question and propose a novel iterative utilitydriven graph summarization approach. During iterative summarization, we incrementally keep track of the utility of the graph summary. This enables a user to query a graph summary that is conditioned on a user-specified utility value. We present both exhaustive and scalable approaches for implementing our proposed solution. Our experimental results on real-world graph datasets show the effectiveness of our proposed approach. Finally, through multiple real-world applications we demonstrate the practicality of our notion of utility of the computed graph summary.

Graph Summarization with Controlled Utility Loss

“…In order to measure the amount of spuriousness, we also introduce the notion of importance for spurious edges and denote that by ( , ). Now in a similar way to [10] we define the utility of a summary graph G = (V, E) as follows.…”

“…instance, the web graph consists of more than a trillion websites [2] and the social graphs of Facebook, Twitter, and Weibo, have billions of users with many friend/follow connections per user [1,3,4]. Consequently, storing such graphs and answering queries, mining patterns, and visualizing them are becoming highly impractical [10,21]. Graph summarization is a fundamental task of finding a compact representation of the original graph called the summary.…”

“…The problem has been approached from different directions, such as compression to reduce the number of required bits for describing graphs [5,20], sparsification to remove less important nodes/edges in order to make the graph simpler [15,23] and grouping to merge nodes into supernodes based on some interestingness measure [8,10,11,13,16,19,21]. Grouping methods constitute the most popular approach as they allow the user to logically relate the graph summary to the original graph.…”

“…They do not incorporate measuring utility at each step of the algorithm. To the best of our knowledge the only works that present utility-aware algorithms are [21], [8], and [10]. In [21], Shin et al present SWeG, an algorithm that preserves a neighborhood similarity measure for each pair of corresponding nodes in and ′ .…”

“…In [10], Kumar and Efstathopoulos are the first to address global utility. However, their approach, UDS, requires time ( 2 ); based on our experiments, it can only handle small to moderate datasets, often requiring more than 100 hours.…”