The "Fediverse", a federation of decentralized social media servers, has emerged after a decade in which centralized platforms like X (formerly Twitter) have dominated the landscape. The structure of a federation should affect user activity, as a user selects a server to access the Fediverse and posts are distributed along the structure. This paper reports on the differences in user activity between Twitter and Mastodon, a prominent example of decentralized social media. The target of the analysis is Japanese posts because both Twitter and Mastodon are actively used especially in Japan. Our findings include a larger number of replies on Twitter, more consistent user engagement on mstdn.jp, and different topic preferences on each server.

Analysis of social networks with limited data access is challenging for third parties. To address this challenge, a number of studies have developed algorithms that estimate properties of social networks via a simple random walk. However, most existing algorithms do not assume private nodes that do not publish their neighbors’ data when they are queried in empirical social networks. Here we propose a practical framework for estimating properties via random walk-based sampling in social networks involving private nodes. First, we develop a sampling algorithm by extending a simple random walk to the case of social networks involving private nodes. Then, we propose estimators with reduced biases induced by private nodes for the network size, average degree, and density of the node label. Our results show that the proposed estimators reduce biases induced by private nodes in the existing estimators by up to 92.6% on social network datasets involving private nodes.

Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing algorithms are limited to the estimation of local structural properties. Here we propose a method for restoring the original social graph from the small sample obtained by a random walk. The proposed method generates a graph that preserves the estimates of local structural properties and the structure of the subgraph sampled by a random walk. We compare the proposed method with subgraph sampling using a crawling method and the existing method for generating a graph that structurally resembles the original graph via a random walk. Our experimental results show that the proposed method more accurately reproduces the local and global structural properties on average and the visual representation of the original graph than the compared methods. We expect that our method will lead to exhaustive analyses of social graphs with limited data access.

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a random walk have been studied. However, existing algorithms do not consider private nodes who hide their neighbors in real social networks, leading to some practical problems. Here we design random walk-based algorithms to accurately estimate properties without any problems caused by private nodes. First, we design a random walk-based sampling algorithm that comprises the neighbor selection to obtain samples having the Markov property and the calculation of weights for each sample to correct the sampling bias. Further, for two graph property estimators, we propose the weighting methods to reduce not only the sampling bias but also estimation errors due to private nodes. The proposed algorithms improve the estimation accuracy of the existing algorithms by up to 92.6% on real-world datasets.