title: Correlated edge overlaps in multiplex networks.
abstract: We develop the theory of sparse multiplex networks with partially overlapping links based on their local treelikeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find that correlations between the overlapping and nonoverlapping links markedly change the phase diagram of the system, leading to multiple hybrid phase transitions. For assortative correlations we observe recurrent hybrid phase transitions.
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: Gareth J
authors: GJ
authors: Baxter
authors: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
authors: Ginestra
authors: G
authors: Bianconi
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: Rui A
authors: RA
authors: da Costa
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.|A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.
authors: Sergey N
authors: SN
authors: Dorogovtsev
authors: Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: José F F
authors: JF
authors: Mendes