Limits...
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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Subnetwork generated from sampled links.(Left) A network is sampled by randomly selecting links shown in red. (Right) The subnetwork consists of all sampled links and only nodes which are incident with the sampled links. In this type of sampling, no nodes of degree zero are included in the network. Large degree nodes are more likely to be included in the subnetwork.
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pone-0108471-g003: Subnetwork generated from sampled links.(Left) A network is sampled by randomly selecting links shown in red. (Right) The subnetwork consists of all sampled links and only nodes which are incident with the sampled links. In this type of sampling, no nodes of degree zero are included in the network. Large degree nodes are more likely to be included in the subnetwork.

Mentions: We sample each of these simulated and empirical networks and examine the subnetwork induced on sampled nodes (Fig. 1), the subnetwork obtained by failing links (Fig. 2), and the subnetwork generated by sampled links (Fig. 3). For a given network, 100 simulated subnetworks are obtained for a given sampling strategy and subsampling percentage q, as q varies from 5% to 100% in increments of 5%.


Estimation of global network statistics from incomplete data.

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

Subnetwork generated from sampled links.(Left) A network is sampled by randomly selecting links shown in red. (Right) The subnetwork consists of all sampled links and only nodes which are incident with the sampled links. In this type of sampling, no nodes of degree zero are included in the network. Large degree nodes are more likely to be included in the subnetwork.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0108471-g003: Subnetwork generated from sampled links.(Left) A network is sampled by randomly selecting links shown in red. (Right) The subnetwork consists of all sampled links and only nodes which are incident with the sampled links. In this type of sampling, no nodes of degree zero are included in the network. Large degree nodes are more likely to be included in the subnetwork.
Mentions: We sample each of these simulated and empirical networks and examine the subnetwork induced on sampled nodes (Fig. 1), the subnetwork obtained by failing links (Fig. 2), and the subnetwork generated by sampled links (Fig. 3). For a given network, 100 simulated subnetworks are obtained for a given sampling strategy and subsampling percentage q, as q varies from 5% to 100% in increments of 5%.

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