Eszter Bokányi

Gamal Adel, Eszter Bokányi, Eelke M. Heemskerk et al.

Community detection is a critical tool for understanding the mesoscopic structure of large-scale networks. However, when applied to aggregated or coarse-grained social networks, disjoint community partitions cannot capture the diverse composition of community memberships within aggregated nodes. While existing mixed membership methods alleviate this issue, they may detect communities that are highly sensitive to the aggregation resolution, not reliably reflecting the community structure of the underlying individual-level network. This paper presents the Link Fraction Mixed Membership (LFMM) method, which computes the mixed memberships of nodes in aggregated networks. Unlike existing mixed membership methods, LFMM is consistent under aggregation. Specifically, we show that it conserves community membership sums at different scales. The method is utilized to study a population-scale social network of the Netherlands, aggregated at different resolutions. Experiments reveal variation in community membership across different geographical regions and evolution over the last decade. In particular, we show how our method identifies large urban hubs that act as the melting pots of diverse, spatially remote communities.

Eszter Bokányi, Dániel Kondor, Gábor Vattay

Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United States. We observe a slightly superlinear urban scaling with the city population for the total volume of the tweets and words created in a city. We then find that a certain core vocabulary follows the scaling relationship of that of the bulk text, but most words are sensitive to city size, exhibiting a super- or a sublinear urban scaling. For both regimes we can offer a plausible explanation based on the meaning of the words. We also show that the parameters for Zipf's law and Heaps law differ on Twitter from that of other texts, and that the exponent of Zipf's law changes with city size.