Computation of Polarized Metrized Graph Invariants By Using Discrete   Laplacian Matrix
  Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian matrix and its pseudo inverse. Algorithms we give can be used for both symbolic and numerical computations. We present various examples to illustrate the implementation of these algorithms. 
Zubeyir Cinkir
math.NT math.CO