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Register a new userFriendship Paradox Biases Perceptions in Directed Networks
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How popular a topic or an opinion appears to be in a network can be very different from its actual popularity. For example, in an online network of a social media platform, the number of people who mention a topic in their posts---i.e., its global popularity---can be dramatically different from how people see it in their social feeds---i.e., its perceived popularity---where the feeds aggregate their friends posts. We trace the origin of this discrepancy to the friendship paradox in directed networks, which states that people are less popular than their friends (or followers) are, on average. We identify conditions on network structure that give rise to this perception bias, and validate the findings empirically using data from Twitter. Within messages posted by Twitter users in our sample, we identify topics that appear more frequently within the users social feeds, than they do globally, i.e., among all posts. In addition, we present a polling algorithm that leverages the friendship paradox to obtain a statistically efficient estimate of a topics global prevalence from biased perceptions of individuals. We characterize the bias of the polling estimate, provide an upper bound for its variance, and validate the algorithms efficiency through synthetic polling experiments on our Twitter data. Our paper elucidates the non-intuitive ways in which the structure of directed networks can distort social perceptions and resulting behaviors.
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In the past decade, blogging web sites have become more sophisticated and influential than ever. Much of this sophistication and influence follows from their network organization. Blogging social networks (BSNs) allow individual bloggers to form contact lists, subscribe to other blogs, comment on blog posts, declare interests, and participate in collective blogs. Thus, a BSN is a bimodal venue, where users can engage in publishing (post) as well as in social (make friends) activities. In this paper, we study the co-evolution of both activities. We observed a significant positive correlation between blogging and socializing. In addition, we identified a number of user archetypes that correspond to mainly bloggers, mainly socializers, etc. We analyzed a BSN at the level of individual posts and changes in contact lists and at the level of trajectories in the friendship-publishing space. Both approaches produced consistent results: the majority of BSN users are passive readers; publishing is the dominant active behavior in a BSN; and social activities complement blogging, rather than compete with it.
Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.
In a graph, a community may be loosely defined as a group of nodes that are more closely connected to one another than to the rest of the graph. While there are a variety of metrics that can be used to specify the quality of a given community, one common theme is that flows tend to stay within communities. Hence, we expect cycles to play an important role in community detection. For undirected graphs, the importance of triangles -- an undirected 3-cycle -- has been known for a long time and can be used to improve community detection. In directed graphs, the situation is more nuanced. The smallest cycle is simply two nodes with a reciprocal connection, and using information about reciprocation has proven to improve community detection. Our new idea is based on the four types of directed triangles that contain cycles. To identify communities in directed networks, then, we propose an undirected edge-weighting scheme based on the type of the directed triangles in which edges are involved. We also propose a new metric on quality of the communities that is based on the number of 3-cycles that are split across communities. To demonstrate the impact of our new weighting, we use the standard METIS graph partitioning tool to determine communities and show experimentally that the resulting communities result in fewer 3-cycles being cut. The magnitude of the effect varies between a 10 and 50% reduction, and we also find evidence that this weighting scheme improves a task where plausible ground-truth communities are known.
Estimating distributions of node characteristics (labels) such as number of connections or citizenship of users in a social network via edge and node sampling is a vital part of the study of complex networks. Due to its low cost, sampling via a random walk (RW) has been proposed as an attractive solution to this task. Most RW methods assume either that the network is undirected or that walkers can traverse edges regardless of their direction. Some RW methods have been designed for directed networks where edges coming into a node are not directly observable. In this work, we propose Directed Unbiased Frontier Sampling (DUFS), a sampling method based on a large number of coordinated walkers, each starting from a node chosen uniformly at random. It is applicable to directed networks with invisible incoming edges because it constructs, in real-time, an undirected graph consistent with the walkers trajectories, and due to the use of random jumps which prevent walkers from being trapped. DUFS generalizes previous RW methods and is suited for undirected networks and to directed networks regardless of in-edges visibility. We also propose an improved estimator of node label distributions that combines information from the initial walker locations with subsequent RW observations. We evaluate DUFS, compare it to other RW methods, investigate the impact of its parameters on estimation accuracy and provide practical guidelines for choosing them. In estimating out-degree distributions, DUFS yields significantly better estimates of the head of the distribution than other methods, while matching or exceeding estimation accuracy of the tail. Last, we show that DUFS outperforms uniform node sampling when estimating distributions of node labels of the top 10% largest degree nodes, even when sampling a node uniformly has the same cost as RW steps.
Users of social media sites like Facebook and Twitter rely on crowdsourced content recommendation systems (e.g., Trending Topics) to retrieve important and useful information. Contents selected for recommendation indirectly give the initial users who promoted (by liking or posting) the content an opportunity to propagate their messages to a wider audience. Hence, it is important to understand the demographics of people who make a content worthy of recommendation, and explore whether they are representative of the media sites overall population. In this work, using extensive data collected from Twitter, we make the first attempt to quantify and explore the demographic biases in the crowdsourced recommendations. Our analysis, focusing on the selection of trending topics, finds that a large fraction of trends are promoted by crowds whose demographics are significantly different from the overall Twitter population. More worryingly, we find that certain demographic groups are systematically under-represented among the promoters of the trending topics. To make the demographic biases in Twitter trends more transparent, we developed and deployed a Web-based service Who-Makes-Trends at twitter-app.mpi-sws.org/who-makes-trends.
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