Using classical graph theory to generate non-isomorphic floorplan distributions in the measurement of egress complexity

A building’s egress capability is indexed by a measure of its egress complexity. Until recently, the practical application of egress complexity was inhibited because of the very large repetitions of egress complexity values calculated purely on the basis of the number of each floorplan’s habitable compartments. To overcome this problem, it was decided to restrict the analysis to non-isomorphic floorplans thereby reducing many of the repetitions. In spite of this, as the number kk of habitable compartments increased so did the repetitions of egress complexity values for each kk, necessitating a procedure for their exhaustive generation. This paper shows how, both information theory and graph theory, have been used to develop an algorithm that produces the distributions of egress complexity values corresponding to comparable sets of non-isomorphic floorplans, each represented by a unique kk-node rooted tree.