Different degrees of complexity in multiparticle production at the LHC energies with the transition from soft to hard processes

We apply a complex network-based method of visibility graph to explore the degree of complexity and fractal nature in the multiparticle production process at the LHC energy regime. For the investigation, we have used proton-proton (pp) collision events at $\sqrt{s}$ = 7 and 13 TeV and proton-nucleus (p-A) collision events at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, generated using a hybrid Monte-Carlo model, EPOS3 with hydrodynamical evolution. Particle production in high energy collisions becomes gradually harder with the increase of the produced particle's transverse momentum. We have presented for the first time a detailed analysis of the change of fractal behaviour as the process becomes gradually harder than the soft ones for the above mentioned colliding systems. The study reveals that the degree of complexity depends on the hardness of the particle production process. System size dependency, as well as energy dependency of fractal nature, are also exhibited by the present analysis.