  Understanding real-world networks has been a core research endeavor
throughout the last two decades. Network Creation Games are a promising
approach for this from a game-theoretic perspective. In these games, selfish
agents corresponding to nodes in a network strategically decide which links to
form to optimize their centrality. Many versions have been introduced and
analyzed, but none of them fits to modeling the evolution of social networks.
In real-world social networks, connections are often established by
recommendations from common acquaintances or by a chain of such
recommendations. Thus establishing and maintaining a contact with a friend of a
friend is easier than connecting to complete strangers. This explains the high
clustering, i.e., the abundance of triangles, in real-world social networks.
  We propose and analyze a network creation model inspired by real-world social
networks. Edges are formed in our model via bilateral consent of both endpoints
and the cost for establishing and maintaining an edge is proportional to the
distance of the endpoints before establishing the connection. We provide
results for generic cost functions, which essentially only must be convex
functions in the distance of the endpoints without the respective edge. For
this broad class of cost functions, we provide many structural properties of
equilibrium networks and prove (almost) tight bounds on the diameter, the Price
of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show
via experiments that the created equilibrium networks of our model indeed
closely mimics real-world social networks. We observe degree distributions that
seem to follow a power-law, high clustering, and low diameters. This can be
seen as a promising first step towards game-theoretic network creation models
that predict networks featuring all core real-world properties.
