Network Sampling

Abstract

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete understanding of network sampling is critical to support the field of network science. In this paper, we outline a framework for the general problem of network sampling by highlighting the different objectives, population and units of interest, and classes of network sampling methods. In addition, we propose a spectrum of computational models for network sampling methods, ranging from the traditionally studied model based on the assumption of a static domain to a more challenging model that is appropriate for streaming domains. We design a family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs. Furthermore, we demonstrate how traditional static sampling algorithms can be modified for graph streams for each of the three main classes of sampling methods: node, edge, and topology-based sampling. Experimental results indicate that our proposed family of sampling methods more accurately preserve the underlying properties of the graph in both static and streaming domains. Finally, we study the impact of network sampling algorithms on the parameter estimation and performance evaluation of relational classification algorithms.

A Space-Efficient Streaming Algorithm for Estimating Transitivity and Triangle Counts Using the Birthday Paradox

“…Becchetti et al [2008] gave a semistreaming algorithm for counting the triangles incident to every vertex.Their algorithm uses clever methods to approximate Jaccard similarities and requires multiple passes over the data. Ahmed et al [2013] studied sampling a subgraph from a stream of edges that preserves multiple properties of the original graph. Our earlier results on triadic measures were presented in Jha et al [2013].…”

“…The network (graph) that represents the system is an accumulation of the observed edges. There are many methods to deal with such massive graphs, such as random sampling [Schank and Wagner 2005a;Tsourakakis et al 2009b;Seshadhri et al 2013a], the MapReduce paradigm [Suri and Vassilvitskii 2011;Plantenga 2013], distributed-memory parallelism [Arifuzzaman et al 2013;Chakrabarti et al 2011], adopting external memory [Chiang et al 1995;Arge et al 2010], and multithreaded parallelism [Berry et al 2007]. …”

Social network sampling using spanning trees

“…These network statistics are focused on a distribution of network characteristics like vertices, edges and sub-graphs. 48 Two well-known and mostly used network statistical properties: clustering coe±cient distribution (ccd) as a local statistical property and degree distribution (dd ) as a global statistical property are used for testing and comparing sampling algorithms. DD represents the fraction of vertices with degree k, for all k > 0.…”

Improving visual analysis of streaming networks

“…The visual analysis is a qualitative assessment of the decrease of cluttering in the layout after sampling and its impact on visual pattern identification. The quantitative evaluation uses Kolmogorov-Smirnov (KS) statistic (AHMED; NEVILLE; KOMPELLA, 2013;ZHAO et al, 2018) and two cluttered-related measurements: the number of edges involved in overlaps and the number of intersections that each overlapping edge has on average, both evaluated over the MSV layout after sampling (LINHARES et al, 2019b;LINHARES et al, 2019a). KS statistic is a popular measure that assesses the distance between two cumulative distribution functions.…”

“…Such characteristics make their application in very large temporal or streaming networks infeasible. There are streaming edge sampling methods as well NEVILLE;KOMPELLA, 2013;ETEMADI;LU, 2019;AHMED et al, 2017). Some of them are focused in triangles estimation (e.g., (ETEMADI; LU, 2019)), outlier detection (e.g., (AGGARWAL; ZHAO; YU, 2011)), feature preservation (e.g., (SIKDAR et al, 2018)), and so on, but few approaches concern network visualization 1 (SARMENTO et al, 2016).…”