What Counts as a Weak Tie? A Comparison of Filtering Techniques to Analyze Co-Exposure Networks

Abstract

Co-exposure networks offer a useful tool for analyzing audience behavior. In these networks, nodes are sources of information and ties measure the strength of audience overlap. Past research has used this method to analyze exposure to content on social media and the web. However, we still lack a systematic assessment of how different choices in the construction of these networks impact the results. Here we evaluate three different filtering rules that have been used in the literature to eliminate noise in raw data and identify the strongest connections (i.e., those above a certain weight). Moreover, we also provide a mathematical heuristic to choose the optimal threshold. To illustrate our approach, we use two observed networks measuring co-exposure to news sources on the web. We then formulate the problem of filtering the networks as a trade-off between network sparsity (i.e., the need to remove the weakest ties) and connectedness (i.e., the need to preserve the observed connectivity). Our mathematical approach resolves this problem by finding the threshold that maximizes the number of edges removed while minimizing the number of nodes becoming isolates. This analytical technique is generalizable and can be applied to the analysis of any weighted structure that requires solving a similar trade-off between network measures.

Keywords: weighted graphs; co-exposure networks; news exposure; thresholding; L-curve method.