Ideological biases in social sharing of online information about climate change

this process is how user shares are encoded into unipartite edge weight; different weighting schemes significantly impact the performance of community detection algorithms. User con- tributions to unipartite edge weights are scaled by the factor 1/(ki − 1), where ki is the total number of article shares by user i (including repeated links), such that the total unipartite edge weight contribution by each user is ki/2 (as proposed in Newman [43]). This hyperbolic weighting scheme was found to allow robust recovery of community structures after projec- tion [44]. Without this weighting factor, a user’s edge weight contribution to the projected net- work is quadratic in the number of URLs shared, since each user creates ki(ki − 1)/2 edges in the projection, causing users who share many articles to quickly dominate the network and subsequent analysis. Computing the projection requires knowledge of the biadjacency matrix B of the giant component, where the rows represent users and the columns represent URLs; and a diagonal matrix D such that Dii = 1/(ki − 1). Given these matrices, the adjacency matrix for the weighted user projection P = BT DB and hence the weight of an edge between URLs i and j in the projec- tion wði; jÞ ¼ X u2Users wðu; iÞwðu; jÞ degðuÞ 1 : ð1Þ Fig 1. Schematic diagram of the bipartite network construction and unipartite projection. Each user is connected to the URLs they share in the study week. The unipartite projection creates edges between two URLs whenever they are shared by the same person. Multiple edges in the

projection indicate that multiple users have shared the pair of URLs, and this information is tracked by edge weights. A user’s edge contribution to the projection increases quadratically with the number of URLs they share, potentially leading to a dominance of highly active users in the unipartite projection, for example User 3 (red) in the projection; this is handled by a hyperbolic weighting scheme (see Section Network construction). https://doi.org/10.1371/journal.pone.0250656.g001 PLOS ONE Ideological biases in social sharing of online information about climate change PLOS ONE | https://doi.org/10.1371/journal.pone.0250656 April 23, 2021 7 / 25