A complex network and chaos-based method, based on the visibility graph algorithm, is applied to study particle fluctuations in $\pi^{−}$–AgBr interactions at 350 GeV with respect to the shower multiplicity dependence. The fractal structure of the fluctuations is studied by using the power of scale freeness of visibility graph (PSVG). The selection of visibility graph as the type of complex network for our analysis is justified as this algorithm gives the most precise result with finite number of data points and this experiment has finite number of events. The topological parameters along with PSVG values are extracted and analysed. The analysis shows that the fractality character is weaker for the lowest multiplicity bin and is stronger for the highest multiplicity bin.