Emergent Network Geometry

Explore emergent network geometry in this 43-minute lecture by Ginestra Bianconi, presented as part of the Hausdorff Trimester Program on Applied and Computational Algebraic Topology. Delve into topics such as network topology, clique percolation, world association networks, and brain functional topology. Examine collaboration networks, hidden metrics of complex networks, and quantum spacetime. Investigate quantum gravity approaches to networks and simplicial complexes, scale-free networks, and the unitary cell of growing networks. Learn about fitness, energy distribution in Cayley tree networks, attachment probability, and generalized degree distributions. Conclude with insights on discrete manifolds and related processes, gaining a comprehensive understanding of the intersection between network science and geometry.

Intro
Network Topology and Geometry
Clique percolation
World association network
Topology reveal brain functional
Collaboration networks
The hidden metric of complex networks
Quantum Spacetime
Quantum gravity approaches networks and simplicial complexes
Scale-free networks
The unitary cell of growing networks Consider the following unitary cell of a network
Fitness
Energy distribution of the nodes at the bulk of the growing Cayley tree network
Attachment probability
Generalized degree distributions
Conclusions
Discrete Manifolds
Process (b)