Connectivity aware path finding

A non-transitory, computer-readable medium containing instructions that, when executed by at least one processor of a system, cause the system to perform operations for configuring a communications network, the operations comprising:

• obtaining a network graph representing the communications network, the network graph including vertices corresponding to nodes in the communications network and edges corresponding to communications links in the communications network;
• obtaining a demand on the network graph, the demand specifying a source vertex of the vertices and a terminal vertex of the vertices;
• determining a valid path from the source vertex to the terminal vertex, the determination comprising:
• identifying a path length for which some valid path exists between the source vertex and the terminal vertex using a structure lacking zero divisors and a connectivity set for the network graph, wherein communicatively connected consecutive pairs of communication links in the communications network are each associated with an element of the connectivity set;
• and
• determining a valid path of the identified path length on the network graph using the connectivity set;
• and
• configuring one or more components of the communications network to implement a route that satisfies the demand using the valid path.