This paper demonstrates how a building, expressed as a well-defined st
ructure of nodes and edges, can be shown to possess a latent complexit
y measure with respect to egress. The mathematical formulation, based
on the notion of Shannon entropy, is underpinned by results from graph
theory. The method of calculating egress complexity, its use in compa
ring buildings, and its application to the positioning of additional e
xits is discussed.