Recent theoretical work on complex networks provides strong evidence for the existence of hidden geometries underlying many technological and social networks. Scale-free statistics in the number of connections per node as well as strong self-similar clustering observed in many complex networks allows for mapping a network to a hyperbolic space, and facilitates efficient communication without global knowledge of the networks topology. Mapping the Internet to its hyperbolic space enables optimal geometric routing in the Internet.
The Network Geometry workshop focused on the following topics:
- Modeling the evolution of complex networks using hyperbolic geometry.
- Discovering hidden metric spaces in bipartite networks.
- Hidden metric spaces in biological and social networks.
- Construction of time-efficient algorithms for embedding large networks into metric spaces.
Organizing and program committee:
- Dmitri Krioukov (CAIDA, UCSD)
- Fragkiskos Papadopoulos (UCY)
The agenda included short presentations by participants as well as extensive time for discussions and interactions among participant
- Several evolution models using hidden geometries were proposed and discussed. The proposed evolution models were juxtaposed against existing network growth models such as preferential attachment.
- Hidden variable formalism was generalized to bipartite networks, and a model for bipartite networks in hidden metric spaces was analyzed.
- Participants discussed the role of hidden metric spaces in structure and function of a number of biological and social systems, including gene regulatory, neural, and recommendation networks.
- An efficient algorithm was devised for embedding complex networks into their metric spaces. The running time of the algorithm was shown to scale optimally with the network size. The algorithm was generalized to bipartite networks.