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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Predicted edge weight and degree distributions for Twitter reply networks.(Top) The predicted edge weight distribution. (Bottom, left) Predicted Pr(kin) and (Bottom, right) Pr(kout) for Twitter reply networks.
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pone-0108471-g010: Predicted edge weight and degree distributions for Twitter reply networks.(Top) The predicted edge weight distribution. (Bottom, left) Predicted Pr(kin) and (Bottom, right) Pr(kout) for Twitter reply networks.

Mentions: The number of edges can be predicted using Equations 31 and 32. We present our results in Figure 9. In all cases, the number of edges increases throughout the period of the study. Figure 10 depicts the predicted edge weight and degree distributions. The edge weight distribution shows that very few (<.001%) edges have weight greater than 102. The degree distribution of the observed subnetwork can be rescaled by reassigning nodes of degree k, to nodes of degree . Figure 10 demonstrates a slightly heavier tail in the in-degree distribution as compared to the out-degree distribution. The degree distribution reveals that fewer than .01% of the nodes have more than 102 distinct neighbors. This value is approximately Dunbar's number, a value suggested to be the upper limit on the number of active social contacts for humans [49].


Estimation of global network statistics from incomplete data.

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

Predicted edge weight and degree distributions for Twitter reply networks.(Top) The predicted edge weight distribution. (Bottom, left) Predicted Pr(kin) and (Bottom, right) Pr(kout) for Twitter reply networks.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0108471-g010: Predicted edge weight and degree distributions for Twitter reply networks.(Top) The predicted edge weight distribution. (Bottom, left) Predicted Pr(kin) and (Bottom, right) Pr(kout) for Twitter reply networks.
Mentions: The number of edges can be predicted using Equations 31 and 32. We present our results in Figure 9. In all cases, the number of edges increases throughout the period of the study. Figure 10 depicts the predicted edge weight and degree distributions. The edge weight distribution shows that very few (<.001%) edges have weight greater than 102. The degree distribution of the observed subnetwork can be rescaled by reassigning nodes of degree k, to nodes of degree . Figure 10 demonstrates a slightly heavier tail in the in-degree distribution as compared to the out-degree distribution. The degree distribution reveals that fewer than .01% of the nodes have more than 102 distinct neighbors. This value is approximately Dunbar's number, a value suggested to be the upper limit on the number of active social contacts for humans [49].

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