Entropy Measures of Street-Network Dispersion: Analysis of Coastal Cities in Brazil and Britain

Abstract

Geographical location and landforms of various types have strong effects on the developments of many cities and associated street networks. This study presents new results of landform effects, in particular the geometry of shorelines, on the grid street networks (a total of 10,442 streets) of three Brazilian coastal cities. The results are compared with the street networks of three coastal cities in Britain (a total of 22,002 streets) that have evolved through a more natural "bottom-up" process. Gibbs/Shannon entropy (a measure of dispersion) generally has a positive linear correlation with length ranges and the average lengths of the street, and for the power-law tails in particular. The geometry of the adjacent shorelines has great effect on the spatial orientation of streets in the Brazilian cities but less so for the networks of the British cities. More specifically, the more curved the shoreline, the greater is the dispersion in the street orientation and the greater the associated entropy. The results also show that the length-entropies of the outer parts of the Brazilian cities are generally lower than those of the inner parts, whereas the entropies of outer parts of the British cities are higher than those of the inner parts, indicating dispersion during streetnetwork growth in the British cities.

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.…”

“…In the field of road network analysis, a conceptually related approach, the orientation or trend entropy, has been proposed recently, which also characterizes the heterogeneity of road orientations in physical space. [22][23][24] Here, we take a more formal approach by describing the anisotropy of edges at both, vertex level and global network scale.…”

Edge directionality properties in complex spherical networks

“…The concept of edge anisotropy [17] as a local (pernode) and global characteristic of spatially embedded networks has extended previous studies on node-based distributions of edge directions [27][28][29][30]. In [17], the authors describe the direction of an edge by the ddimensional unit vector e mn , centered at the position of a node m and pointing towards that of another node n. Assigning each connection of a single node m a corresponding unit vector enables us to define the local anisotropy of the edges adjacent to m [17],…”

Urban Spatial Order: Street Network Orientation, Configuration, and Entropy

“…The former measures street curvature and how this relates to other urban patterns and processes (Boeing, 2019;Giacomin & Levinson, 2015;Levinson & El-Geneidy, 2009). The latter quantifies and visualizes the entropy of street orientations to assess how ordered they are (Courtat, Gloaguen, & Douady, 2011;Mohajeri, French, & Gudmundsson, 2013;Mohajeri, French, & Batty, 2013;Mohajeri & Gudmundsson, 2012: entropy measures the fundamentally related concepts of disorder, uncertainty, and dispersion. However, less is known about cross-sectional trends in the spatial ordering of street networks worldwide.…”