Assortativity and leadership emerge from anti-preferential attachment in heterogeneous networks

I. Sendiña-Nadal, M. M. Danziger, Z. Wang, S. Havlin, S. Boccaletti

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19 Scopus citations


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.

Original languageEnglish
Article number21297
JournalScientific Reports
StatePublished - 18 Feb 2016

Bibliographical note

Funding Information:
Work partly supported by the Ministerio de Economía y Competitividad of Spain under projects FIS2012-38949-C03-01 and FIS2013-41057-P. I.S.N. acknowledges support from GARECOM, Group of Research Excelence URJC-Banco de Santander. S.H. acknowledges support from MULTIPLEX (No. 317532) EU project, the Israel Science Foundation, ONR and DTRA. M.M.D. thanks the Azrieli Foundation for the award of an Azrieli Fellowship grant.


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