Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired. As a remedy, we propose an alternative centrality measure based on the nonbacktracking matrix, which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved, but avoids localization and gives useful results in regimes where the standard centrality fails.

Many networks can be usefully decomposed into a dense core plus an outlying, loosely connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our method fits a generative model of core-periphery structure to observed data using a combination of an expectation-maximization algorithm for calculating the parameters of the model and a belief propagation algorithm for calculating the decomposition itself. We find the method to be efficient, scaling easily to networks with a million or more nodes, and we test it on a range of networks, including real-world examples as well as computer-generated benchmarks, for which it successfully identifies known core-periphery structure with low error rate. We also demonstrate that the method is immune to the detectability transition observed in the related community detection problem, which prevents the detection of community structure when that structure is too weak. There is no such transition for core-periphery structure, which is detectable, albeit with some statistical error, no matter how weak it is.

How predictable is success in complex social systems? In spite of a recent profusion of prediction studies that exploit online social and information network data, this question remains unanswered, in part because it has not been adequately specified. In this paper we attempt to clarify the question by presenting a simple stylized model of success that attributes prediction error to one of two generic sources: insufficiency of available data and/or models on the one hand; and inherent unpredictability of complex social systems on the other. We then use this model to motivate an illustrative empirical study of information cascade size prediction on Twitter. Despite an unprecedented volume of information about users, content, and past performance, our best performing models can explain less than half of the variance in cascade sizes. In turn, this result suggests that even with unlimited data predictive performance would be bounded well below deterministic accuracy. Finally, we explore this potential bound theoretically using simulations of a diffusion process on a random scale free network similar to Twitter. We show that although higher predictive power is possible in theory, such performance requires a homogeneous system and perfect ex-ante knowledge of it: even a small degree of uncertainty in estimating product quality or slight variation in quality across products leads to substantially more restrictive bounds on predictability. We conclude that realistic bounds on predictive accuracy are not dissimilar from those we have obtained empirically, and that such bounds for other complex social systems for which data is more difficult to obtain are likely even lower.

A large number of published studies have examined the properties of either networks of citation among scientific papers or networks of coauthorship among scientists. Here we study an extensive data set covering more than a century of physics papers published in the Physical Review, which allows us to construct both citation and coauthorship networks for the same set of papers. We analyze these networks to gain insight into temporal changes in citation and collaboration over the long time period of the data, as well as correlations and interactions between the two. Among other things, we investigate the change over time in the number of publishing authors, the number of papers they publish, and the number of others with whom they collaborate, changes in the typical number of citations made and received, the extent to which individuals tend to cite themselves or their collaborators more than others, the extent to which they cite themselves or their collaborators more quickly after publication, and the extent to which they tend to return the favor of a citation from another scientist.

In the study of networked systems such as biological, technological, and social networks the available data are often uncertain. Rather than knowing the structure of a network exactly, we know the connections between nodes only with a certain probability. In this paper we develop methods for the analysis of such uncertain data, focusing particularly on the problem of community detection. We give a principled maximum-likelihood method for inferring community structure and demonstrate how the results can be used to make improved estimates of the true structure of the network. Using computer-generated benchmark networks we demonstrate that our methods are able to reconstruct known communities more accurately than previous approaches based on data thresholding. We also give an example application to the detection of communities in a protein-protein interaction network.