Ideological biases in social sharing of online information about climate change

Community detection Community detection was used to find clusters of densely interconnected nodes in the net- work, which in this context represent sets of URLs which were seen by a group of similar Twit- ter users. Community detection [45] is a means of algorithmically identifying such clusters in a given unipartite network. This study used a greedy algorithm proposed by Clauset et al. [46] that partitions nodes into communities such that the modularity of the partition is optimised; modularity measures the proportion of edges within communities relative to the proportion of edges between communities. If a community assignment is significantly better than random, a modularity score between 0.3 and 0.7 is typically observed [45]. Modularity scores for each network are given in S1 Table in S1 File. Content analysis Page content was collected for each validated URL using Diffbot [47], an online service for extracting the constituent parts of an HTML document and presenting them in an easily ana- lysed format. In some cases, Diffbot only identifies the title and cannot automatically detect the content of a webpage. To mitigate the impact of this, the title is used as the page content for such URLs. This substitution affected less than 5% of the URLs in each week, except Week 4 which required substitution in 5.9% of the URLs. Additionally, a small number of domains were incompatible with the Diffbot API. This accounts for around 4% of all URLs in the giant components of any week and mostly arise due to page formatting or timeout issues.

Online content was analysed quantitatively by calculating term frequency-inverse docu- ment frequency (TF-IDF) scores, treating each URL as a document and the set of all URLs in the whole network as the corpus. TF-IDF analyses aim to identify distinctive or important tokens (usually words) in a document, based on their frequency in the document relative to their frequency across the corpus. Three kinds of token were studied in this way, in three sepa- rate analyses: web domains, page content unigrams, and page content bigrams. Web domains were extracted for each URL to permit analysis of the sources of content shared on Twitter. Words and bigrams (two-word phrases) were extracted from the web pages associated with each URL to allow large-scale analysis of the topics within the content. Before calculating the TF-IDF vectors for page content, the Snowball stemmer [48] was applied to each content token. Each stemmed token is mapped back to the most common token that maps to it for ease of reading, e.g. if fisher, fished and fishing all appear once and fishes appears twice then the final representation of these tokens is fishes. TF-IDF score vectors for each URL are calculated and represent the frequency of tokens in a document relative to their frequency across the corpus. For token t in document d we have TF-IDFðt; dÞ ¼ tf ðt; dÞ log 1 þ n 1 þ df ðtÞ � � þ 1 � � ; ð2Þ where n is the number of documents in the corpus, tf(t, d) counts the frequency of t in d and df(t) counts the number of documents in the corpus which contain t. To characterise each

community found in the sharing network, the TF-IDF vectors for each URL in a community were summed to obtain aggregate scores. In these community-level comparisons, a high TF-IDF score for a community means that the given token appears more frequently in the URLs in this community, when compared to other communities. In each case, tokens which occur in fewer than 50 URLs, or more than 50% of all URLs in a given week are rejected, such that very common or very rare tokens are omitted. We also removed a set of common stop- words including trump, paris and agreement. In principle, n-grams can be studied with any value of n, but beyond n = 2 token frequency is generally too low to be useful. 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 8 / 25