Chordless cycles in networks

Using closure concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph. The chordless cycles which comprise this irreducible core effectively characterize the connectivity structure of the network as a whole. By counting the number of cycles of length 3 ≤ k ≤ max_length, we can also create a kind of signature that can be used to identify the network. Its longest chordless cycles can be used to redraw the network and visually reveal its global connectivity patterns. Performance is analyzed, and the concepts we develop are illustrated by means of a relatively small running sample network of about 400 nodes.