Abstract
We introduce a minimal generative model for densifying networks in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability . The networks that emerge from this copying mechanism are sparse for and dense (average degree increasing with number of nodes ) for . The behavior in the dense regime is especially rich; for example, individual network realizations that are built by copying are disparate and not self-averaging. Further, there is an infinite sequence of structural anomalies at , , , etc., where the dependences of the number of triangles (3-cliques), 4-cliques, undergo phase transitions. When linking to second neighbors of the target can occur, the probability that the resulting graph is complete—all nodes are connected—is nonzero as .
- Received 14 July 2016
DOI:https://doi.org/10.1103/PhysRevLett.117.218301
© 2016 American Physical Society