Brendan Meeder

Predicting Reciprocity in Social Networks

In social media settings where users send messages to one another, the issue of reciprocity naturally arises: does the communication between two users take place only in one direction, or is it reciprocated? In this paper we study the problem of reciprocity prediction: given the characteristics of two users, we wish to determine whether the communication between them is reciprocated or not. We approach this problem using decision trees and regression models to determine good indicators of reciprocity. We extract a network based on directed@-messages sent between users on Twitter, and identify measures based on the attributes of nodes and their network neighborhoods that can be used to construct good predictors of reciprocity. Moreover, we find that reciprocity prediction forms interesting contrasts with earlier network prediction tasks, including link prediction, as well as the inference of strengths and signs of network links.

We know who you followed last summer: inferring social link creation times in twitter

Understanding a networks temporal evolution appears to require multiple observations of the graph over time. These often expensive repeated crawls are only able to answer questions about what happened from observation to observation, and not what happened before or between network snapshots. Contrary to this picture, we propose a method for Twitters social network that takes a single static snapshot of network edges and user account creation times to accurately infer when these edges were formed. This method can be exact in theory, and we demonstrate empirically for a large subset of Twitter relationships that it is accurate to within a few hours in practice. We study users who have a very large number of edges or who are recommended by Twitter. We examine the graph formed by these nearly 1,800 Twitter celebrities and their 862 million edges in detail, showing that a single static snapshot can give novel insights about Twitters evolution. We conclude from this analysis that real-world events and changes to Twitters interface for recommending users strongly influence network growth.

HEigen: Spectral Analysis for Billion-Scale Graphs

Given a graph with billions of nodes and edges, how can we find patterns and anomalies? Are there nodes that participate in too many or too few triangles? Are there close-knit near-cliques? These questions are expensive to answer unless we have the first several eigenvalues and eigenvectors of the graph adjacency matrix. However, eigensolvers suffer from subtle problems (e.g., convergence) for large sparse matrices, let alone for billion-scale ones. We address this problem with the proposed HEIGEN algorithm, which we carefully design to be accurate, efficient, and able to run on the highly scalable MAPREDUCE (HADOOP) environment. This enables HEIGEN to handle matrices more than 1;000 × larger than those which can be analyzed by existing algorithms. We implement HEIGEN and run it on the M45 cluster, one of the top 50 supercomputers in the world. We report important discoveries about nearcliques and triangles on several real-world graphs, including a snapshot of the Twitter social network (56 Gb, 2 billion edges) and the “YahooWeb” data set, one of the largest publicly available graphs (120 Gb, 1.4 billion nodes, 6.6 billion edges).

Game-Theoretic Models of Information Overload in Social Networks

We study the effect of information overload on user engagement in an asymmetric social network like Twitter. We introduce simple game-theoretic models that capture rate competition between celebrities producing updates in such networks where users non-strategically choose a subset of celebrities to follow based on the utility derived from high quality updates as well as disutility derived from having to wade through too many updates. Our two variants model the two behaviors of users dropping some potential connections (followership model) or leaving the network altogether (engagement model). We show that under a simple formulation of celebrity rate competition, there is no pure strategy Nash equilibrium under the first model. We then identify special cases in both models when pure rate equilibria exist for the celebrities: For the followership model, we show existence of a pure rate equilibrium when there is a global ranking of the celebrities in terms of the quality of their updates to users. This result also generalizes to the case when there is a partial order consistent with all the linear orders of the celebrities based on their qualities to the users. Furthermore, these equilibria can be computed in polynomial time. For the engagement model, pure rate equilibria exist when all users are interested in the same number of celebrities, or when they are interested in at most two. Finally, we also give a finite though inefficient procedure to determine if pure equilibria exist in the general case of the followership model.