This chapter begins with an introduction to the Graph Theory or Network Modelling. Next, the formulation of a varied set of network modelling problems is proposed with the corresponding solution. Specifically, shortest path problemsNetwork modellingshortest path problem, maximal flow problemsNetwork modellingmaximal flow problem, minimal spanning tree problemsNetwork modellingminimal spanning tree problem and minimal cost flow problemsNetwork modellingminimal cost flow problems are contemplated. The solution is carried out usingNetwork modellingFord Ford and Bellman-KalabaNetwork modellingBellman-Kalaba algorithms for minimum spanning problems, the Ford-FulkersonNetwork modellingFord-Fulkerson algorithm for maximal flow problemsNetwork modellingmaximal flow problem and the KruskalNetwork modellingKruskal algorithm for the minimal spanning tree problemsNetwork modellingminimal spanning tree problem. Only the modelling of the minimal cost flow problemsNetwork modellingminimal cost flow problems is presented. Therefore, different formulations for the problems are presented along with their solutions related to Industrial Organisation Engineering and the management setting.