Skip navigation

Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation

Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation

Ubaldi, Enrico, Perra, Nicola ORCID: 0000-0002-5559-3064, Karsai, Márton, Vezzani, Alessandro, Burioni, Raffaella and Vespignani, Alessandro (2016) Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation. Scientific reports, 6 (35724). ISSN 2045-2322 (Print), 2045-2322 (Online) (doi:

PDF (Published version - Open Access)
16166_PERRA_Asymptotic_Theory_2016.pdf - Published Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview


The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals’ social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.

Item Type: Article
Additional Information: "This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit"
Uncontrolled Keywords: Time-varying networks; Applied physics; Statistical physics; Thermodynamics and nonlinear dynamics
Subjects: H Social Sciences > HM Sociology
Faculty / School / Research Centre / Research Group: Faculty of Business
Faculty of Business > Networks and Urban Systems Centre (NUSC) > Centre for Business Network Analysis (CBNA)
Faculty of Business > Department of International Business & Economics
Last Modified: 21 Oct 2020 10:05

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics