Fig. 1

Notional urban street network meant to pattern throughout this paper a real-world urban street network. The planar graph representation (\({{\bf g}}\)) emphasizes a literal geometric interpretation where junctions \(j_{*}\) (and impasses \(i_{*}\)) are nodes and street-segments \({\bar{s}}_{*}\) are edges. The street maps (\({{\bf m}}\)) and (\({{\bf m}}^{\prime }\)) show two of the possible configurations of streets associable to graph (\({{\bf g}}\)). The information networks (\({{\bf t}}\)) and (\({{\bf t}}^{\prime }\)) emphasize the topological information contained in street maps (\({{\bf m}}\)) and (\({{\bf m}}^{\prime }\)), respectively: they associate streets \(r_{*}\) to nodes and they link streets sharing common junctions \(j_{*}\). Information networks of self-organized or unplanned urban street networks exhibit in general a scale-free valence distribution, namely, they are scale-free networks. This observational fact has led us to a fluctuating model for which configurations of streets are fluctuating as part of a social process. So, along this paper, a street map such as (\({{\bf m}}\)) or (\({{\bf m}}^{\prime }\)) is abstracted as a state (see Footnote 1) of a fluctuating system