### Existence and emergence of navigability in social networks

**Speaker:** Emmanuelle Lebhar, CNRS

**Affiliation:** U. Paris VII, France

**Abstract:**
Social networks, as part of large spontaneous interactions networks,
present remarkable properties that are still widely misunderstood. One
of them is the navigability property, a.k.a "six degrees of
separation", which consists in the existence of very short paths
between any pair (e.g. polylogarithmic in the size of the network)
that can moreover be discovered locally, using only a very partial
information (e.g. the neighborhood). Since the seminal work of
Kleinberg on this subject in 2000, the explanation of this phenomenon
is investigated among specific probabilistic distributions of
additional links over particular classes of graphs. In this talk, we
will survey the development of random graph models dedicated to this
property and study how a natural dynamic process can converge to such
structures, and therefore shed light on the emergence of this natural
phenomenon in social networks.