Robustness of Structures: Role of Graph Complexity

Graphs are widely employed in many fields of Science and Humanities studies, e.g. network analysis, communications, or literature. This abstract representation serves to analyse large systems, in which each element plays a role in the overall behaviour. In this paper, this concept is applied to structural engineering. A scheme with beams (or columns) and joints can be represented, mathematically, as a set of nodes and edges. The information content of a graph, i.e. of the corresponding structure, is used as a measure of complexity by means of the so called Shannon’s entropy. The deformation work plays a fundamental role in the description of the behaviour of the loaded scheme. Further, an optimization of the complexity lets to stress the capabilities of the novel metrics in the design of robust structures.