Population-Area Relationship for Medieval European Cities
(A) An unstructured network where anyone can in principle connect with anyone else, subject to limitations deriving from cost of movement. Such a network is characterized by increasing connectivity with city population size, with mean degree k(N) = k0 Nδ, δ ∼ 1/6. (B) A structured socioeconomic network. In this case, interactions between individuals are regulated by social groups and institutions (black squares) and may be damped by a factor s<1, for each level of institutions involved. If the parameter s<1, the net effect of institutions is to weaken social possibilities and thus reduce agglomeration effects, taking the exponent of the scaling of area with population for settlements closer to unity.