|igraph Reference Manual|
igraph_shortest_paths— The length of the shortest paths between vertices.
igraph_get_shortest_paths— Calculates the shortest paths from/to one vertex.
igraph_get_all_shortest_paths— Finds all shortest paths (geodesics) from a vertex to all other vertices
igraph_average_path_length— Calculates the average geodesic length in a graph.
igraph_path_length_hist— Create a histogram of all shortest path lenghts
igraph_diameter— Calculates the diameter of a graph (longest geodesic).
igraph_girth— The girth of a graph is the length of the shortest circle in it.