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Estimation of global network statistics from incomplete data.

Bliss CA, Danforth CM, Dodds PS - PLoS ONE (2014)

Bottom Line: A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible.Our methods are transparent and do not assume a known generating process for the network, thus enabling prediction of network statistics for a wide variety of applications.We validate analytical results on four simulated network classes and empirical data sets of various sizes.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, Vermont Complex Systems Center, The Computational Story Lab, and the Vermont Advanced Computing Core, University of Vermont, Burlington, Vermont, United States of America.

ABSTRACT
Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible. Previous work addressing the impacts of partial network data is surprisingly limited, focuses primarily on missing nodes, and suggests that network statistics derived from subsampled data are not suitable estimators for the same network statistics describing the overall network topology. We generate scaling methods to predict true network statistics, including the degree distribution, from only partial knowledge of nodes, links, or weights. Our methods are transparent and do not assume a known generating process for the network, thus enabling prediction of network statistics for a wide variety of applications. We validate analytical results on four simulated network classes and empirical data sets of various sizes. We perform subsampling experiments by varying proportions of sampled data and demonstrate that our scaling methods can provide very good estimates of true network statistics while acknowledging limits. Lastly, we apply our techniques to a set of rich and evolving large-scale social networks, Twitter reply networks. Based on 100 million tweets, we use our scaling techniques to propose a statistical characterization of the Twitter Interactome from September 2008 to November 2008. Our treatment allows us to find support for Dunbar's hypothesis in detecting an upper threshold for the number of active social contacts that individuals maintain over the course of one week.

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Weighted subnetwork generated from sampled interactions.(Left) An unsampled weighted network consists of nodes, links and weights representing the number of interactions represented by the link. (Right) Sampling by interacting produces a subsample whereby links are included in the subsample only if at least one interaction has been sampled. The subnetwork is the induced subgraph on these links with wi≥1.
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pone-0108471-g004: Weighted subnetwork generated from sampled interactions.(Left) An unsampled weighted network consists of nodes, links and weights representing the number of interactions represented by the link. (Right) Sampling by interacting produces a subsample whereby links are included in the subsample only if at least one interaction has been sampled. The subnetwork is the induced subgraph on these links with wi≥1.

Mentions: In this set of experiments, we generate Erdös-Rényi networks with N = 2000 nodes and kavg = 6. We assign each edge to have equal weight, w, where w = 1, 2, 3, 4, or 5 (corresponding to Cases I–V). We similarly generate Scale-free networks with N = 2000 nodes and kavg = 6. We then sample each of the weighted, undirected networks by randomly selecting interactions and examine the subnetwork generated by links with w(ej)>0 (Fig. 4). This procedure is repeated to generate one hundred simulated networks for each class and varying proportions of sampled interactions (q).


Estimation of global network statistics from incomplete data.

Bliss CA, Danforth CM, Dodds PS - PLoS ONE (2014)

Weighted subnetwork generated from sampled interactions.(Left) An unsampled weighted network consists of nodes, links and weights representing the number of interactions represented by the link. (Right) Sampling by interacting produces a subsample whereby links are included in the subsample only if at least one interaction has been sampled. The subnetwork is the induced subgraph on these links with wi≥1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4206292&req=5

pone-0108471-g004: Weighted subnetwork generated from sampled interactions.(Left) An unsampled weighted network consists of nodes, links and weights representing the number of interactions represented by the link. (Right) Sampling by interacting produces a subsample whereby links are included in the subsample only if at least one interaction has been sampled. The subnetwork is the induced subgraph on these links with wi≥1.
Mentions: In this set of experiments, we generate Erdös-Rényi networks with N = 2000 nodes and kavg = 6. We assign each edge to have equal weight, w, where w = 1, 2, 3, 4, or 5 (corresponding to Cases I–V). We similarly generate Scale-free networks with N = 2000 nodes and kavg = 6. We then sample each of the weighted, undirected networks by randomly selecting interactions and examine the subnetwork generated by links with w(ej)>0 (Fig. 4). This procedure is repeated to generate one hundred simulated networks for each class and varying proportions of sampled interactions (q).

Bottom Line: A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible.Our methods are transparent and do not assume a known generating process for the network, thus enabling prediction of network statistics for a wide variety of applications.We validate analytical results on four simulated network classes and empirical data sets of various sizes.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, Vermont Complex Systems Center, The Computational Story Lab, and the Vermont Advanced Computing Core, University of Vermont, Burlington, Vermont, United States of America.

ABSTRACT
Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible. Previous work addressing the impacts of partial network data is surprisingly limited, focuses primarily on missing nodes, and suggests that network statistics derived from subsampled data are not suitable estimators for the same network statistics describing the overall network topology. We generate scaling methods to predict true network statistics, including the degree distribution, from only partial knowledge of nodes, links, or weights. Our methods are transparent and do not assume a known generating process for the network, thus enabling prediction of network statistics for a wide variety of applications. We validate analytical results on four simulated network classes and empirical data sets of various sizes. We perform subsampling experiments by varying proportions of sampled data and demonstrate that our scaling methods can provide very good estimates of true network statistics while acknowledging limits. Lastly, we apply our techniques to a set of rich and evolving large-scale social networks, Twitter reply networks. Based on 100 million tweets, we use our scaling techniques to propose a statistical characterization of the Twitter Interactome from September 2008 to November 2008. Our treatment allows us to find support for Dunbar's hypothesis in detecting an upper threshold for the number of active social contacts that individuals maintain over the course of one week.

Show MeSH
Related in: MedlinePlus