The Union of Shortest Path Trees of Functional Brain Networks

Communication between brain regions is still insufficiently understood. Applying concepts from network science has shown to be successful in gaining insight in the functioning of the brain. Recent work has implicated that especially shortest paths in the structural brain network seem to play a major role in the communication within the brain. So...

Kemeny's constant and the effective graph resistance

Kemeny's constant and its relation to the effective graph resistance has been established for regular graphs by Palacios et al. [1]. Based on the Moore–Penrose pseudo-inverse of the Laplacian matrix, we derive a new closed-form formula and deduce upper and lower bounds for the Kemeny constant. Furthermore, we generalize the relation between...

Topological Approach to Measure Network Recoverability

Network recoverability refers to the ability of a network to return to a desired performance level after suffering malicious attacks or random failures. This paper proposes a general topological approach and recoverability indicators to measure the network recoverability in two scenarios: 1) recovery of damaged connections and 2) any...

Topological Approach to Measure the Recoverability of Optical Networks

Optical networks are vulnerable to failures due to targeted attacks or large-scale disasters. The recoverability of optical networks refers to the ability of an optical network to return to a desired performance level after suffering topological perturbations such as link failures. This paper proposes a general topological approach and...