how to fill my graph with connected nodes that represnts ways on map using osm file ?

I have osm file for my city, I am using Libosmium to read it, and I'm storing nodes of each way as Vertices of My Graph, and making edges between each 2 adjacent nodes in each way, and calculationg eucledian distance between them, the problem is that : The ways are not connected with each other ! I can't reach my destination from my target, even though there is a route, but there is no node intersect between the ways (No common nodes) so I can't reach my destenation ! What nodes should I add to my Graph, and how to bridge them correctly ? so I can reach my destination from My Node ?