A family of algorithms for computing consensus about node state from network data.

Eleanor R Brush,Jessica C Flack,David C Krakauer,Stefano Allesina

doi:10.1371/journal.pcbi.1003109

Abstract

Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node's state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node's direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms' cognitive and computational demands. This is an important consideration in systems in which individuals use the collective opinions of others to make decisions.

Highlights

A goal of many of network studies (e.g. [1,2,3,4]) is to predict the effects of perturbations, such as extinction and predation events, on network structure
In the work cited above it was demonstrated that consensus in the group about individual i0s ability to successfully win its fights can be calculated by quantifying uniformity in the weighted in-degree distribution of signals sent to i by its senders and weighting this score by the total number of signals i received
Policing is an important social function because by controlling conflict it facilitates edge building by nodes in the signaling as well as other social networks [18,20]. These results suggest that (1) network structure can encode node function and that (2) measures that quantify agreement in node connectivity patterns can be used to decode this population coding of node function

Summary

Introduction

A goal of many of network studies (e.g. [1,2,3,4]) is to predict the effects of perturbations, such as extinction and predation events, on network structure. The data suggest that individuals use this information to determine how they are collectively perceived [14,19] Variation in this collective perception gives rise to the distribution of social power, where social power is defined operationally as the consensus opinion of group members about whether an individual can win fights [14,21]. We evaluate whether measures of consensus applied to this physics collaboration network gives a reputation index that predicts NSF grant-related success (see Section Methods for data set details and definitions). The interactions are unweighted and undirected so that Mji~Mij is 1 if there is evidence for a functional linkage between genes j and i and 0 otherwise

Objectives

Results

Conclusion