Using closure and neighborhood concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph which we call its "spine". The chordless cycles which comprise this irreducible core effectively characterize the connectivity structure of the network as a whole. In particular, it is shown that the center of the network, whether defined by distance or betweenness centrality, is effectively contained in this spine. By counting the number of cycles of length 3 ≤ k ≤ max⊥ength, we can also create a kind of signature that can be used to identify the network. Performance is analyzed, and the concepts we develop are illustrated by means of a relatively small running sample network of 379 nodes, although they have been applied to networks of 4,764 and 5,242 nodes as well.
展开▼
