Abstract
Motifs are a fundamental building block and distinguishing feature of
networks. While characteristic motif distribution have been found in many
networks, very little is known today about the evolution of network motifs.
This paper studies the most important motifs in social networks, triangles, and
how directed triangle motifs change over time. Our chosen subject is one of the
largest Online Social Networks, Google+. Google+ has two distinguishing
features that make it particularly interesting: (1) it is a directed network,
which yields a rich set of triangle motifs, and (2) it is a young and fast
evolving network, whose role in the OSN space is still not fully understood.
For the purpose of this study, we crawled the network over a time period of six
weeks, collecting several snapshots. We find that some triangle types display
significant dynamics, e.g., for some specific initial types, up to 20% of the
instances evolve to other types. Due to the fast growth of the OSN in the
observed time period, many new triangles emerge. We also observe that many
triangles evolve into less-connected motifs (with less edges), suggesting that
growth also comes with pruning. We complement the topological study by also
considering publicly available user profile data (mostly geographic locations).
The corresponding results shed some light on the semantics of the triangle
motifs. Indeed, we find that users in more symmetric triangle motifs live
closer together, indicating more personal relationships. In contrast,
asymmetric links in motifs often point to faraway users with a high in-degree
(celebrities).
