How do i find the eulers path with an adjacency matrix

Hi all, I have a 11x11 adjacency matrix for a graph(COST239) network with different weights on each vertices. Please help me regarding this. I tried matgraph, but that doesnt give eulers path with adjacency matrix, moreover this file inturn calls a lots of .m files.

Answer 1

[Walter Roberson]

http://en.wikipedia.org/wiki/Eulerian_path#Hierholzer.27s_algorithm

The weights are irrelevant because every vertex must be visited a fixed number of times (half of the number of edges incident on it), and every edge must be visited once. There is nothing to optimize on a Eulear's path.

(Is COST239 "Ultra-High Capacity Optical Transmission Networks" ?)

[Ajay Gautham]

Thanks for you reply. Yes you are right. its ultra high capacity networks. My application demands visiting all nodes atleast once for a weighted graph, given an adjacency matrix. I guess i was wrong on eulers path, where they dont consider the weights. Is there a matlab function or routine which could help??.

[Walter Roberson]

Without weights, visiting all nodes exactly once would be a Hamiltonian Path. With weights, visiting all nodes exactly once would be a Weighted Hamiltonian Path. With weights, visiting all nodes at least once would be Traveling Salesman Problem.

There is no polynomial-time solution to Hamiltonian Path or Traveling Salesman.