The number of nodes may vary upto at most of 50.How many nodes and edges are we talking about?

Basically my network would be taken from the existing features of the city or any area. So the minimum and maximum number of edges connected to a single node is all dependent on the type of network the user is going to provide. No any restriction to the connection to any node.What is the minimum and maximum number of edges connected to a single node?

I am looking for an algorithm that will yield a comparatively quickest path that would visit all the nodes.Do you require the optimum (shortest) path, regardless of computation time (usually requiring a distributed algorithm, so you can run it in reasonable time on e.g. a cluster), or are you looking for an algorithm that will yield just a very good path?