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Register a new userTopology and Geometry of Online Social Networks
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Authors
D. Zinoviev
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In this paper, we study certain geometric and topological properties of online social networks using the concept of density and geometric vector spaces. Moi Krug (My Circle), a Russian social network that promotes the principle of the six degrees of separation and is positioning itself as a vehicle for professionals and recruiters seeking each others services, is used as a test vehicle.
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Scholars, advertisers and political activists see massive online social networks as a representation of social interactions that can be used to study the propagation of ideas, social bond dynamics and viral marketing, among others. But the linked structures of social networks do not reveal actual interactions among people. Scarcity of attention and the daily rythms of life and work makes people default to interacting with those few that matter and that reciprocate their attention. A study of social interactions within Twitter reveals that the driver of usage is a sparse and hidden network of connections underlying the declared set of friends and followers.
Instant quality feedback in the form of online peer ratings is a prominent feature of modern massive online social networks (MOSNs). It allows network members to indicate their appreciation of a post, comment, photograph, etc. Some MOSNs support both positive and negative (signed) ratings. In this study, we rated 11 thousand MOSN member profiles and collected user responses to the ratings. MOSN users are very sensitive to peer ratings: 33% of the subjects visited the researchers profile in response to rating, 21% also rated the researchers profile picture, and 5% left a text comment. The grades left by the subjects are highly polarized: out of the six available grades, the most negative and the most positive are also the most popular. The grades fall into three almost equally sized categories: reciprocal, generous, and stingy. We proposed quantitative measures for generosity, reciprocity, and benevolence, and analyzed them with respect to the subjects demographics.
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.
We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents desire to maintain some uniqueness in their opinions. We derive a general analytical expression for opinion diversity, which holds for any network and depends on the networks topology through its spectral properties alone. Using this expression, we find that opinion diversity decreases as communities and clusters are broken down. We test our predictions against data describing empirical influence networks between major news outlets and find that incorporating our measure in linear models for the sentiment expressed by such sources on a variety of topics yields a notable improvement in terms of explanatory power.
In this paper, we introduce a novel, general purpose, technique for faster sampling of nodes over an online social network. Specifically, unlike traditional random walk which wait for the convergence of sampling distribution to a predetermined target distribution - a waiting process that incurs a high query cost - we develop WALK-ESTIMATE, which starts with a much shorter random walk, and then proactively estimate the sampling probability for the node taken before using acceptance-rejection sampling to adjust the sampling probability to the predetermined target distribution. We present a novel backward random walk technique which provides provably unbiased estimations for the sampling probability, and demonstrate the superiority of WALK-ESTIMATE over traditional random walks through theoretical analysis and extensive experiments over real world online social networks.
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