Qualitative representation and reasoning on Complex Systems (CS) is important for a number of human activities on CS, mainly for the understanding of both, our perception about their structure as well as their dynamics. Formal Concept Analysis can help understanding the conceptual structure behind these qualitative representations by means of the called concept lattices (CL). In this research line the scale free conceptualization hypothesis, (SFCH) is asserted. SFCH claims that a scale-free distribution in node’s connectivity appears on the CL associated to complex systems (CLCS) only when two requirements holds: CLCS is useful both to represent qualitative and reliable attributes on the CS, and to provide a basis for (qualitatively) successfully reasoning about the CS. Experiments revealed that the topologies of CLCS are similar when the amount of information on the CS is sufficient, while it is different in other concept lattices associated to random formal contexts or to other systems in which some of the above requirements do not hold.