title: Assortativity and leadership emerge from anti-preferential attachment in heterogeneous networks.
abstract: Real-world networks have distinct topologies, with marked deviations from purely random networks. Many of them exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Though microscopic mechanisms have been suggested for the emergence of other topological features, assortativity has proven elusive. Assortativity can be artificially implanted in a network via degree-preserving link permutations, however this destroys the graph's hierarchical clustering and does not correspond to any microscopic mechanism. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties in degree and clustering distributions and tunable realistic assortativity. Two distinct populations of nodes are incrementally added to an initial network by selecting a subgraph to connect to at random. One population (the followers) follows preferential attachment, while the other population (the potential leaders) connects via anti-preferential attachment: they link to lower degree nodes when added to the network. By selecting the lower degree nodes, the potential leader nodes maintain high visibility during the growth process, eventually growing into hubs. The evolution of links in Facebook empirically validates the connection between the initial anti-preferential attachment and long term high degree. In this way, our work sheds new light on the structure and evolution of social networks.
authors.affiliation: Complex Systems Group &GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.|Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors.forename: I
authors.initials: I
authors.lastname: Sendiña-Nadal
authors.affiliation: Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.
authors.forename: M M
authors.initials: MM
authors.lastname: Danziger
authors.affiliation: School of Automation, Northwestern Polytechnical University, Xi'an 710072, China.|Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan.
authors.forename: Z
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel.
authors.forename: S
authors.initials: S
authors.lastname: Havlin
authors.affiliation: CNR- Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.|The Italian Embassy in Israel, 25 Hamered st., 68125 Tel Aviv, Israel.
authors.forename: S
authors.initials: S
authors.lastname: Boccaletti
mesh_terms: D006801:Humans; D008962:Models, Theoretical; D012944:Social Support