Identifying time dependence in network growth

Max Falkenberg, Jong Hyeok Lee, Shun Ichi Amano, Ken Ichiro Ogawa, Kazuo Yano, Yoshihiro Miyake, Tim S. Evans, Kim Christensen

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

Identifying power-law scaling in real networks - indicative of preferential attachment - has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution when looking for preferential attachment. However, many of the established methods do not account for any potential time dependence in the attachment kernels of growing networks, or methods assume that node degree is the key observable determining network evolution. In this paper, we argue that these assumptions may lead to misleading conclusions about the evolution of growing networks. We illustrate this by introducing a simple adaptation of the Barabási-Albert model, the "k2 model,"where new nodes attach to nodes in the existing network in proportion to the number of nodes one or two steps from the target node. The k2 model results in time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment, and without the need to include explicit time dependence in key network parameters (such as the average out-degree). We show that similar effects are seen in several real world networks where constant network growth rules do not describe their evolution. This implies that measurements of specific degree distributions in real networks are likely to change over time.

Original languageEnglish
Article number023352
JournalPhysical Review Research
Volume2
Issue number2
DOIs
StatePublished - 18 Jun 2020
Externally publishedYes

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