Abstarct: In this thesis the (k,l)-core problem on a network is considered. A polynomial algorithm for solving this problem on a tree with positive and negative weight is presented. This problem on the general network is NP-hard. So for finding the (k,l)-core of a network, three genetic algorithms are designed. Also, computational results of these algorithms are compared together in terms of speed and efficiency. Then the problem of finding the 2-(k,l)-core of a tree is investigated and an algorithm that is a generalization of the (k,l)-core of a tree algorithm is introduced for solving 2-(k,l)-core problem. In addition, the problem of finding core of a network is considered on the weighted interval graphs and a new method is presented for solving this problem.