Structure of networks constructed from mentioning relationships between posts in online media may be valuable for understanding how information and opinions spread in these media. We crawled Twitter to collect tweets and replies to construct a large number of so-called reply trees, each of which was rooted at a tweet and joined by replies. Consistent with the previous literature, we found that the empirical trees were characterized by some long path-like reply trees, large star-like trees, and long irregular trees, although their frequencies were not high. We tested several branching process models to explain the empirical frequency of these types of reply trees as well as more basic quantities such as the distributions of the size and depth of the reply tree. Based on our modeling results, we suggest that the in-degree of the tweet that initiates a reply tree (i.e., the number of times that the tweet is directly mentioned by other reply posts) may play an important role in forming the global shape of the reply tree.
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