Using rate equation for modeling triad dynamics on Instagram

Abstract

Triadic analysis is a convenient way to assess structure and stability of a graph. This paper verifies stability of one triad type that is commonly perceived as transient and unstable, on Instagram subgraph, reconstructed by a specific crawling algorithm. Dynamics of that triad transition has been examined, wrt. degrees of that triad nodes and other basic structural properties of the triad neighborhood. Results show that the triad transition can be modeled as rate equation of order 2, and that it is fairly independent of any of the considered factors. A complete model of dynamics of triads can be further used in graph evolution forecasting, including phenomena like opinion spread or group forming, which may, in turn, affect real-life situations.