Physical networks as network-of-networks.

Physical networks are made of nodes and links that are physical objects embedded in a geometric space. Understanding how the mutual volume exclusion between these elements affects the structure and function of physical networks calls for a suitable generalization of network theory. Here, we introduce a network-of-networks framework where we describe the shape of each extended physical node as a network embedded in space and these networks are bound together by physical links.

Controllability, Matching Ratio and Graph Convergence.

There is an important parameter in control theory which is closely related to the directed matching ratio of the network, as shown in the paper of Liu et al. (Nature 473:167-173, 2011). We give proofs of two main statements of Liu et al.