topology
Connectivity
Construct an adjacency dictionary from a set of edges. 
Combinatorics
Color the vertices of a network such that no two colors are adjacent. 

Identify the vertices of connected components. 
Orientation
Construct an adjacency dictionary of the given faces, assuming that the faces have arbitrary orientation. 

Construct an adjacency dictionary of the given faces, assuming that the faces have arbitrary orientation. 

Unify the cycle directions of the given faces such that adjacent faces share opposite halfedges. 

Unify the cycle directions of the given faces such that adjacent faces share opposite halfedges. 
Traversal
Find the path of least weight between two vertices of a graph using the A* search algorithm. 

Find the shortest path between two vertices of a network or mesh using the A* search algorithm. 

Return a breadthfirst ordering of all vertices in an adjacency dictionary reachable from a chosen root vertex. 

Traverse an adjacency dict in “breadthfirst” order. 

Return all paths from root to goal. 

Compute depthfirst ordering of connected vertices. 

Compute Dijkstra distances from all vertices in a connected set to one target vertex. 

Find the shortest path between two vertices if the edge weights are not all the same. 

Find the shortest path between two vertices of a network. 