Estimation of Graphlet Counts in Massive Networks.

Ryan A Rossi,Nesreen K Ahmed,Rong Zhou

doi:10.1109/tnnls.2018.2826529

Ryan A Rossi, Nesreen K Ahmed + Show 1 more

Open Access

https://doi.org/10.1109/tnnls.2018.2826529

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Abstract

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small graphs. Most previous work has focused on exact algorithms; however, it is often too expensive to compute graphlets exactly in massive networks with billions of edges, and finding an approximate count is usually sufficient for many applications. In this paper, we propose an unbiased graphlet estimation framework that is: (a) fast with large speedups compared to the state of the art; (b) parallel with nearly linear speedups; (c) accurate with less than 1% relative error; (d) scalable and space efficient for massive networks with billions of edges; and (e) effective for a variety of real-world settings as well as estimating global and local graphlet statistics (e.g., counts). On 300 networks from 20 domains, we obtain <1% relative error for all graphlets. This is vastly more accurate than the existing methods while using less data. Moreover, it takes a few seconds on billion edge graphs (as opposed to days/weeks). These are by far the largest graphlet computations to date.

Highlights

LOCALIZED GRAPHLET ESTIMATION FRAMEWORK we propose a new family of graphlet estimation methods based on selecting a set of localized neighborhoods
Estimating Graphlet Frequency Distributions We investigate the methods for estimating the graphlet frequency distribution (GFD) from a wide variety of networks with different structural characteristics including real-world and synthetic graphs
We investigated selecting node-centric neighborhoods and other methods based on sampling graphlets directly, though the accuracy was worse in all cases, and removed for brevity

Summary

Introduction

G RAPHLETS are small induced subgraphs and are important for many predictive and descriptive modeling and learning systems/tasks [1]–[8] such as image processing and computer vision learning systems that use neural networks [1], [9], network alignment [6], [10]–[12], classification [2], [3], visualization and sensemaking [13], [14], dynamic network analysis [15], [16], community detection [17]–[19], role discovery [20], anomaly detection [21], [22], and link prediction [8], [23], [24]. The application and general use of graphlets (especially those of size k = 4 nodes and larger) remain severely limited to networks that are small enough to avoid the scalability and performance limitations of exact algorithms [13], [25]–[28]. Shervashidze et al [3] take hours to count graphlets on small networks (i.e., a few hundreds/thousands of nodes/edges) for the graph classification [2].

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