Entropy and order in urban street networks

Abstract

Many complex networks erase parts of their geometry as they develop, so that their evolution is difficult to quantify and trace. Here we introduce entropy measures for quantifying the complexity of street orientations and length variations within planar networks and apply them to the street networks of 41 British cities, whose geometric evolution over centuries can be explored. The results show that the street networks of the old central parts of the cities have lower orientation/length entropies - the streets are more tightly ordered and form denser networks - than the outer and more recent parts. Entropy and street length increase, because of spreading, with distance from the network centre. Tracing the 400-year evolution of one network indicates growth through densification (streets are added within the existing network) and expansion (streets are added at the margin of the network) and a gradual increase in entropy over time.

Edge anisotropy and the geometric perspective on flow networks

“…[22][23][24] Beyond the latter concepts, the present work has introduced a new measure for quantifying the anisotropy of edges adjacent to a given vertex in a spatial network. The proposed approach can be generally applied to characterizing the spatial structure of networks in a variety of fields.…”

“…While this replacement still suffers from the same conceptual problems as the corresponding vertex characteristics when considering the mean local properties, a corresponding modification of the global anisotropy concept relieves the previous problem of too small sample sizes (arising especially in the case of sparse networks). In case of the Shannon entropy, a corresponding measure (referred to as trend entropy [22][23][24] ) has been recently used for the analysis of street network patterns.…”

Matrix pixel and Kernel density analysis from the topographic maps

“…In addition human road networks present the progress of civilization and a degree of self-organized structures that respond to changes in internal and external pressure by gradual geometric changes. The other important view is the changes of building structures and their properties in the city (Gudmundsson & Mohajeri, 2013). The urban road network and building density have been displayed as the city growth through different methods of assessment.…”

Planarity as a driver of Spatial Network structure

“…The chief aim being to investigate the extent to which constraining connectivity in a manner related to node proximity influences system organisation. Application domains for these techniques include city science (Cardillo et al, 2006;Xie and Levinson, 2007;Jiang, 2007;Barthélemy and Flammini, 2008;Masucci et al, 2009;Chan et al, 2011;Courtat et al, 2011;Strano et al, 2012;Levinson, 2012;Rui et al, 2013;Gudmundsson and Mohajeri, 2013), electronic circuits (i Cancho et al, 2001;Bassett et al, 2010;Miralles et al, 2010;Tan et al, 2014), wireless networks (Huson and Sen, 1995;Lotker and Peleg, 2010), leaf venation (Corson, 2010;Katifori et al, 2010), navigability (Kleinberg, 2000;Lee and Holme, 2012;Huang et al, 2014) and transportation (Gastner and Newman, 2006;Louf et al, 2013).…”