The work carried out in this paper first generates all edge-disjoint minimal paths between every pair of nodes of the interconnection network. Then the merging of the edge disjoint minimal paths from each source nodes to the rest of nodes occurs only if such merging of minimal paths does not result into cycle. Thus, the merging operation ensures connectivity of all nodes of interconnection network without any cycle which is equivalent to the generation of spanning trees. In this manner, a number of spanning tree rooted on each source node are generated and ranked according to their generation. The network reliability is then evaluated from these spanning trees by applying sum of disjoint product techniques on these trees. A mathematical model followed by an algorithm is proposed in this paper. The proposed method is well illustrated by taking a suitable example network. The simulated results obtained from the proposed method are validated against existing method. The validation results show a tolerable level discrepancy in estimating the network reliability of some benchmark networks while using a very less number of spanning trees in leu of all possible spanning tress. The network reliability of some important interconnection networks viz. Hypercube, crossed cube, folded hypercube, mesh and torus are evaluated and analyzed. The network reliability of fully connected network with size varying from 3 to 10 are evaluated and analysed.