Network Geometry

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the  Internet. Characterizing the geometrical properties of these networks  has become increasingly relevant for routing problems, inference and  data mining. In real growing networks, topological, structural and  geometrical properties emerge spontaneously from their dynamical rules. Here we show that a single two parameter  model of emergent network geometry, constructed by gluing triangles, can generate complex network geometries with non-trivial distribution of  curvatures, combining exponential growth and small-world properties  with finite spectral dimensionality. In one limit, the non-equilibrium  dynamical rules of these networks can generate scale-free networks  with clustering and communities, in another limit 2 dimensional manifolds with non-trivial modularity.   When manifolds of arbitrary dimension are constructed, and  energies are assigned to their nodes these networks can be mapped to quantum network states and they follows quantum statistics despite they do not obey equilibrium statistical mechanics.

Speaker : Dr. Ginestra Bianconi 

October 23rd, 2015 at 16:15

GO Jones Lecture Theatre
Refreshments will be served in the foyer after the event.