title: Structural Transitions in Densifying Networks.
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 p. The networks that emerge from this copying mechanism are sparse for p<1/2 and dense (average degree increasing with number of nodes N) for p≥1/2. 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 p=2/3, 3/4, 4/5, etc., where the N 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 N→∞.
authors.affiliation: naXys, Namur Center for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium.
authors.forename: R
authors.initials: R
authors.lastname: Lambiotte
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA.|Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: U
authors.initials: U
authors.lastname: Bhat
authors.affiliation: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: S
authors.initials: S
authors.lastname: Redner