# MS-5 Distances on networks and its applications (Distances on Networks)

### Organizers: Angeles Carmona (Universitat Politécnica de Catalunya), Andres M. Encinas (Universitat Politécnica de Catalunya), and Margarida Mitjana (Universitat Politécnica de Catalunya)

In contrast with the geodesic distance, the resistance distance takes into account all paths between vertices. The standard method to compute the resistance distance of a network is via the Moore-Penrose inverse of the combinatorial Laplacian of the network. From the matrix point of view, this is equivalent to defining the effective resistance associated with an irreducible, symmetric and diagonally dominant M-matrix. Since the matrix associated with a positive semidefinite Schrödinger operator L_q is an irreducible, symmetric M-matrix, we can assign an effective resistance with respect to a non-negative parameter and a weight to any irreducible, symmetric M-matrix. The mini-symposium aims to provide an overview the latest developments in the area and its applications, present current research and stimulate new ideas and collaboration.

### Speakers

**Angeles Carmona**, *Matrix Tree Theorem for Schrödinger operators on networks*

**Andrés M. Encinas**,* The effective resistance of extended or contracted networks*

**Douglas J. Klein**,* Intrinsic Metrics on Graphs and Applications*

**Enric Monsó**, *Green's kernel of Schrödinger operators on generalized subdivision networks*

**Milan Randic**, *Graphical Bioinformatics: The Exact Solution to the Protein Alignment Problem*

**Yujun Yang**, *A recursion formula for resistance distances and its applications*

**Jiang Zhou**, *Resistance distance and resistance matrix of graphs*