Statistical properties of sampled networks

Lee, Sang Hoon; Kim, Pan-Jun; Jeong, Hawoong

doi:10.1103/physreve.73.016102

Cited by 358 publications

(333 citation statements)

References 40 publications

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“…where p(k) is the degree distribution of the original network and α is the sampled coverage [6,[30][31][32]. Equation (1) also describes the incoming and outgoing degree distribution of randomly sampled directed networks, where k and k 0 are replaced with k in and k 0,in (or k out and k 0,out respectively).…”

Section: Sampling Resultsmentioning

confidence: 99%

“…4, BFS sampling does not obey these simple mathematical relationships. Since BFS follows outgoing links and reaches hub nodes at early times [32,42], one could have an argument that the average degree of BFS-sampled networks overestimates the average degree. However, this can only be true when the networks contain loops.…”

Section: Fig 5 (Color Online) For Bfs Sampling Of Wiki2007 Data (Amentioning

confidence: 99%

“…Stumpf et al [30,31] studied the degree distribution of two random networks -one that had been sampled "uniformly" by picking nodes at random, and one that was subject to connectivity-dependent sampling -both analytically and numerically. Lee et al [32] also studied, numerically, the effects of random sampling and snowball sampling [33], on statistical properties of real scale-free networks -including degree distribution exponents, betweenness centrality exponents, assortativity, and clustering coefficient -demonstrating that these quantities could be either overestimated or underestimated, depending on the fraction of the network sampled and the type of sampling method used. Kurant et al [34,35] provided a detailed analytic treatment of measurement bias due to random sampling and breadth-first search (BFS) sampling [36], showing that, for example, BFS sampling can lead to overestimation of average degree, and random sampling to underestimation.…”

Section: Introductionmentioning

confidence: 99%

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Sampling properties of directed networks

Son

Christensen²,

Bizhani³

et al. 2012

Phys. Rev. E

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For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.

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Section: Sampling Resultsmentioning

confidence: 99%

Section: Fig 5 (Color Online) For Bfs Sampling Of Wiki2007 Data (Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sampling properties of directed networks

Son

Christensen²,

Bizhani³

et al. 2012

Phys. Rev. E

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“…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.…”

Section: Graph Sensemaking Global Viewmentioning

confidence: 99%

“…Lee et al investigated statistical properties of various sampling techniques and found that the method for sampling could heavily bias topological properties like betweeness centrality, assortativity and clustering coefficient [5]. Their work provides important criteria for avoiding biased estimates given different input topologies.…”

Section: A Visualization and Exploration Techniquesmentioning

confidence: 99%

Scalable graph exploration and visualization: Sensemaking challenges and opportunities

Pienta

Abello

Kahng

et al. 2015

2015 International Conference on Big Data and Smart Computing (BIGCOMP)

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Abstract-Making sense of large graph datasets is a fundamental and challenging process that advances science, education and technology. We survey research on graph exploration and visualization approaches aimed at addressing this challenge. Different from existing surveys, our investigation highlights approaches that have strong potential in handling large graphs, algorithmically, visually, or interactively; we also explicitly connect relevant works from multiple research fields -data mining, machine learning, human-computer ineraction, information visualization, information retrieval, and recommender systems -to underline their parallel and complementary contributions to graph sensemaking.We ground our discussion in sensemaking research; we propose a new graph sensemaking hierarchy that categorizes tools and techniques based on how they operate on the graph data (e.g., local vs global). We summarize and compare their strengths and weaknesses, and highlight open challenges. We conclude with future research directions for graph sensemaking.

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Optimization of Stratified Sampling with the R Package SamplingStrata: Applications to Network Data

Ballin

Barcaroli

2016

Computational Network Analysis With R

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Statistical properties of sampled networks

Cited by 358 publications

References 40 publications

Sampling properties of directed networks

Sampling properties of directed networks

Scalable graph exploration and visualization: Sensemaking challenges and opportunities

Optimization of Stratified Sampling with the R Package SamplingStrata: Applications to Network Data

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