1. Introduction
1.1. Scope and contribution
1.2. Outline
2. Topological Characterization of power systems networks
2.1 The Laplacian spectrum
2.2 The Largest eigenvalue
2.3 Algebraic connectivity
2.4 Laplacian eigenvalues and graph structure
3. Applications on power system operation and planning
3.1 Identification of subnetworks
3.2 Identification of critical nodes
3.3 Identification of islands
4. Security strategy applications
5. Applications on electricity markets
