| CPC H04L 45/02 (2013.01) [G06F 16/9024 (2019.01); H04L 41/0826 (2013.01); H04L 45/22 (2013.01)] | 18 Claims |

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1. A non-transitory, computer-readable medium containing first instructions that, when executed by at least one processor of a system, cause the system to perform operations comprising:
selecting a cycle of a communication network, the communication network including network nodes configured to communicate using communication links, the cycle including a subset of the network nodes and communication links in the communication network, and identifying demands for the communication network that originate and terminate on network nodes in the subset;
generating a representation of the communication network and the demands, the representation including:
vertices corresponding to network nodes of the communication network on the cycle,
external edges corresponding to communication links of the communication network on the cycle, the external edges connecting the vertices,
internal edges, each internal edge connecting two of the vertices, and
a set of flows corresponding to the identified demands, each flow having a source vertex and a target vertex;
identifying a subset of the internal edges based on the set of flows;
determining, using a stream graph generated based on a one of the set of flows and the identified subset of the internal edges, a set of graph paths that satisfy the one of the flows, comprising:
obtaining an indication of a set of functional external edges and a set of functional internal edges; and
determining a graph path from a source vertex of the one of the flows to a target vertex of the one of the flows, the determination restricted to:
the set of functional external edges; and
an intersection of the set of functional internal edges and the identified subset of the first internal edges; and
providing second instructions for configuring the communication network to satisfy a one of the demands that corresponds to the one of the set of flows, the second instructions indicating a set of network paths that corresponds to the set of graph paths.
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