# topology

## connectivity

 adjacency_from_edges Construct an adjacency dictionary from a set of edges.

## combinatorics

 vertex_coloring Color the vertices of a network such that no two colors are adjacent. connected_components Identify the vertices of connected components.

## orientation

 face_adjacency Construct an adjacency dictionary of the given faces, assuming that the faces have arbitrary orientation. face_adjacency_numpy Construct an adjacency dictionary of the given faces, assuming that the faces have arbitrary orientation. unify_cycles Unify the cycle directions of the given faces such that adjacent faces share opposite halfedges. unify_cycles_numpy Unify the cycle directions of the given faces such that adjacent faces share opposite halfedges.

## traversal

 astar_shortest_path Find the shortest path between two vertices of a network using the A* search algorithm. breadth_first_ordering Return a breadth-first ordering of all vertices in an adjacency dictionary reachable from a chosen root vertex. breadth_first_traverse Traverse an adjacency dict in “breadth-first” order. breadth_first_paths Return all paths from root to goal. depth_first_ordering Compute depth-first ordering of connected vertices. dijkstra_distances Compute Dijkstra distances from all vertices in a connected set to one target vertex. dijkstra_path Find the shortest path between two vertices if the edge weights are not all the same. shortest_path Find the shortest path between two vertices of a network.