Shortest path algorithm

I need some algorithm to find the paths between any 2 nodes in a graph and also the shortest path. The nodes denote people, the links denote relationship strength. I need the shgortest way to reach one person to another. also, the relastionship links are weighted by some strength value. I have a network of 20000 relastionhip links and a thousand nodes. Can any one give me reasonable fast / efficient algorithm / code solving this problem of finding the paths ( all paths or k smallest paths ) and the shortest path path between 2 points ? ## Deliverables 1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. 2) Deliverables must be in ready-to-run condition, as follows? (depending on the nature? of the deliverables): a)? For web sites or? other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment. b) For all others including desktop software or software the buyer intends to distribute: A software? installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request. 3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement). ## Platform Any, C#, C, C++ preferred