Estimating clustering coefficients and size of social networks via random walk

Hardiman, Stephen J.; Katzir, Liran

doi:10.1145/2488388.2488436

Cited by 84 publications

(104 citation statements)

References 29 publications

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“…We estimate clustering coefficients among the male PWID populations sampled with RDS in Cebu and Mandaue using modified estimators, originally defined for internet samples [10] and recently expanded for in-person RDS studies [9]. These estimators work by defining recruiter-recruit-recruitee triplets in the RDS sample and taking a degree weighted average of the number that are closed.…”

Section: Methodsmentioning

confidence: 99%

“…An additional network measure that can be obtained from RDS surveys [9,10] and may be useful for studying the spread of infectious disease is the clustering coefficient [12,13,31]. For individuals in friendship networks, we can say that each person’s level of network clustering is the proportion of his friends who are friends with each other.…”

Section: Introductionmentioning

confidence: 99%

“…At the network level, researchers have designed several statistics to summarize a network’s tendency toward clustering [9]. Two that we focus on are known as the global clustering coefficient, which sums the number of observed closed triplets in the network and divides by the total number of triplets (closed or open), and the local clustering coefficient, which takes the average of each person’s network clustering [10]. …”

Section: Introductionmentioning

confidence: 99%

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Social Network Clustering and the Spread of HIV/AIDS Among Persons Who Inject Drugs in 2 Cities in the Philippines

Verdery

Siripong

Pence

2017

JAIDS Journal of Acquired Immune Deficiency Syndromes

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INTRODUCTION The Philippines has seen rapid increases in HIV prevalence among people who inject drugs. We study two neighboring cities where a linked HIV epidemic differed in timing of onset and levels of prevalence. In Cebu, prevalence rose rapidly from under 1% to 54% between 2009 and 2011 and remained high through 2013. In nearby Mandaue, HIV remained below 4% through 2011 then rose rapidly to 38% by 2013. OBJECTIVES We hypothesize that infection prevalence differences in these cities may owe to aspects of social network structure, specifically levels of network clustering. Building on prior research, we hypothesize that higher levels of network clustering are associated with greater epidemic potential. METHODS Data were collected with respondent-driven sampling among males who inject drugs in Cebu and Mandaue in 2013. We first examine sample composition using estimators for population means. We then apply new estimators of network clustering in respondent-driven sampling data to examine associations with HIV prevalence. RESULTS Samples in both cities were comparable in terms of composition by age, education, and injection locations. Dyadic needle sharing levels were also similar between the two cities, but network clustering in the needle sharing network differed dramatically. We found higher clustering in Cebu than Mandaue, consistent with expectations that higher clustering is associated with faster epidemic spread. CONCLUSION This paper is the first to apply estimators of network clustering to empirical respondent-driven samples, and it offers suggestive evidence that researchers should pay greater attention to network structure’s role in HIV transmission dynamics.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Social Network Clustering and the Spread of HIV/AIDS Among Persons Who Inject Drugs in 2 Cities in the Philippines

Verdery

Siripong

Pence

2017

JAIDS Journal of Acquired Immune Deficiency Syndromes

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“…We also consider collisions, but more of as a baseline since any collision-based approach requires Ω( √ n) many samples, which as we show, is an overkill for average degree estimation. Hardiman and Katzir [10] use collision among neighbors for network size estimation and show that it has a tighter confidence interval than a simple node collision estimator. They also consider the problem of estimating the clustering coefficients.…”

Section: Related Workmentioning

confidence: 99%

On estimating the average degree

Dasgupta

Kumar

Sarlós

2014

Proceedings of the 23rd International Conference on World Wide Web

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Networks are characterized by nodes and edges. While there has been a spate of recent work on estimating the number of nodes in a network, the edge-estimation question appears to be largely unaddressed. In this work we consider the problem of estimating the average degree of a large network using efficient random sampling, where the number of nodes is not known to the algorithm. We propose a new estimator for this problem that relies on access to node samples under a prescribed distribution. Next, we show how to efficiently realize this ideal estimator in a random walk setting. Our estimator has a natural and simple implementation using random walks; we bound its performance in terms of the mixing time of the underlying graph. We then show that our estimators are both provably and practically better than many natural estimators for the problem. Our work contrasts with existing theoretical work on estimating average degree, which assume that a uniform random sample of nodes is available and the number of nodes is known.

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“…Size estimation is a classic problem that has many applications, ranging from the war time problem of finding out the number of German tanks [7], to the more recent challenge of gauging the size of the Web and search engines [1,3,12,20] and online social networks [8,11]. The direct calculation of data size is often not possible or desirable for several reasons.…”

Section: Introductionmentioning

confidence: 99%

Uniform Random Sampling Not Recommended

Lü

Wang

2018

Companion of the the Web Conference 2018 on the Web Conference 2018 - WWW '18

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We show that uniform random sampling is not as effective as PPS (probability proportional to size) sampling in many estimation tasks. In the setting of (graph) size estimation, this paper demonstrates that random edge sampling outperforms random node sampling, with a performance ratio proportional to the normalized graph degree variance. This result is particularly important in the era of big data, when data are typically large and scale-free, resulting in large degree variance. We derive the result by first giving the variances of random node and random edge estimators. A simpler and more intuitive result is obtained by assuming that the data is large and degree distribution follows a power law.

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Estimating clustering coefficients and size of social networks via random walk

Cited by 84 publications

References 29 publications

Social Network Clustering and the Spread of HIV/AIDS Among Persons Who Inject Drugs in 2 Cities in the Philippines

Social Network Clustering and the Spread of HIV/AIDS Among Persons Who Inject Drugs in 2 Cities in the Philippines

On estimating the average degree

Uniform Random Sampling Not Recommended

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