Theinterdisciplinary field of complex networks has been actively developing since1999 [1]. Many models of network growth have been proposed by theoreticalphysicists, mathematicians, and computer scientists but none of them wasvalidated against the measurements according to accepted physical standards.Our goal is to take one well-documented complex network and to establish itsgrowth mechanism through modeling and model-inspired measurements.

We focused on citationnetworks of Physics, Economics, and Mathematics papers [2]. Using modeling andmodel-based measurements we uncovered citation dynamics of these researchfields [3]. Contrary to common belief that citation dynamics is determined by thelinear preferential attachment (Markov process) we found that it followsthe nonlinear autocatalytic growth (Hawkes process). Thenonlinearity stems from a synergistic effect in propagation ofcitation cascades (a kind of social reinforcement) and is intricately related tolocal network topology and network motifs. The nonlinearity results innon-stationary citation distributions, diverging citation trajectories ofsimilar papers, and runaways or "immortal papers" [4]. Thenonlinearity is the reason why the ideas advocated in highly-cited papersundergo viral propagation in scientific community.

We present a stochastic modelof citation dynamics based on recursive search (triadic closure). The model isfully quantitative and has been validated against the measurements. This calibrated model can serveas a probabilistic predictive tool allowing forecasting of the futurecitation behavior of a paper or of a group of papers. We trace similarities between this model and Bass model of diffusionof innovations, epidemiological models, and viral marketing.

1.      A. L. Barabasi and  R. Albert,  "Emergence of scaling in random networks", Science 286, 509 (1999).

2.      S. Redner, “How popular is your paper?An empirical study of the citation distribution”, European PhysicalJournal B 4, 131 (1998).

3.     M. Golosovsky and S. Solomon “Growing complex networkof citations of scientific papers: Modeling and measurements”, PRE  95 012324(2017).

4.     M. Golosovsky, “Power-law citation distributions arenot scale-free”, PRE  96032306 (2017).