An approach to explore exotic hadronic states in $$^{24}$$Mg-Ag/Br interactions at 4.5 A GeV/c in framework of complex network analysis

The visibility graph (VG) and horizontal visibility graph (HVG) have been recently introduced as a mapping between the time series and the complex networks. Here, the relativistic nucleus–nucleus interaction data, $$^{24}$$ Mg-Ag/Br at 4.5 A GeV/c are analyzed and used to characterizing the multifractal properties by extending VG, HVG and the sandbox algorithm (SB). In this work, the HVG–SB techniques have been applied to confirm the scale-freeness and the presence of fractal properties in the process of multiplicity fluctuation. We try to find deterministic information by means of precise determination of topological parameter from a complex network perspective. We have analyzed the degree distributions which are associated with event-wise pseudorapidity distributions, typical of any multifractality measurement, different patterns of symmetry scaling, scale-freeness, correlation and clustering among the produced particles. We try to find deterministic information by means of precise determination of topological parameter from a complex network perspective. It has been also observed that the multifractal variables were derived by SB algorithm for the experimental data sets to some extent distinct from the respective Monte Carlo simulated results.