Various embodiments relate to a non-transitory computer readable medium and method thereof for finding a minimum hop path in a segment graph traversing the least number of links in a physical topology, the method including receiving a connection request for a connection between a source node and a destination node, computing the segment graph, the segment graph having a plurality of links, computing a bandwidth for each of the plurality of links in the segment graph, computing the number of links for a shortest path (“N(q)”) for each of the plurality of links, eliminating each of the plurality of link with a bandwidth less than the minimum bandwidth and selecting the shortest path in the physical topology between the plurality of links.