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 Ps for Twitter reply networks.(Left) The node strength distribution for in-coming interactions. (Right) The node strength distribution out-going interactions. In both cases, the distribution is heavy tailed, but falls off faster than would be expected in a scale-free distribution.
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pone-0108471-g007: Predicted Ps for Twitter reply networks.(Left) The node strength distribution for in-coming interactions. (Right) The node strength distribution out-going interactions. In both cases, the distribution is heavy tailed, but falls off faster than would be expected in a scale-free distribution.

Mentions: Figure 7 depicts a log-log plot of the predicted node strength distribution. This plot reveals that there are fewer nodes in the high strength region than would be expected in a scale-free distribution. Figure 8 reveals that low degree nodes dominate the dataset and that many of these low degree nodes often have low average edge weight (). We find a peak in the average weight per edge as a function of degree around . This peak is more pronounced for out-going edges. Beyond this value, a limiting factor may prevent increases in the weight per edge, a result also noted by Gonçalves et al. [48].


Estimation of global network statistics from incomplete data.

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

Predicted Ps for Twitter reply networks.(Left) The node strength distribution for in-coming interactions. (Right) The node strength distribution out-going interactions. In both cases, the distribution is heavy tailed, but falls off faster than would be expected in a scale-free distribution.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0108471-g007: Predicted Ps for Twitter reply networks.(Left) The node strength distribution for in-coming interactions. (Right) The node strength distribution out-going interactions. In both cases, the distribution is heavy tailed, but falls off faster than would be expected in a scale-free distribution.
Mentions: Figure 7 depicts a log-log plot of the predicted node strength distribution. This plot reveals that there are fewer nodes in the high strength region than would be expected in a scale-free distribution. Figure 8 reveals that low degree nodes dominate the dataset and that many of these low degree nodes often have low average edge weight (). We find a peak in the average weight per edge as a function of degree around . This peak is more pronounced for out-going edges. Beyond this value, a limiting factor may prevent increases in the weight per edge, a result also noted by Gonçalves et al. [48].

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