A Hamiltoniancycle is a path that passes through allverticesexactlyonce
Eularian Graph = A graph which contains a trail that includes every edge and starts + finishes at the same vertex. Every node has an evendegree
Semi-Eularian Graph = A Graph which only 2 nodes have odd valencies, trail that includes every edge but starts and finishes at different vertices
All even degree = Weight of network is the weight of the shortest route
2 odd degree = Total weight plus shortest path between 2 odd nodes
More than 2 odd nodes = Consider pairings of the 4 vertices to find the ones with the shortest extra weight. Cannot do the route inspection algorithm with morethan4 oddnodes