  Spatial road networks have been widely employed to model the structure and
connectivity of cities. In such representation, the question of spatial scale
of the entities in the network, i.e. what its nodes and edges actually embody
in reality, is of particular importance so that redundant information can be
identified and eliminated to provide an improved understanding of city
structure. To address this, we investigate in this work the relationship
between the spatial scale of the modelled network entities against the amount
of useful information contained within it. We employ an entropy measure from
complexity science and information theory to quantify the amount of information
residing in each presentation of the network subject to the spatial scale and
show that it peaks at some intermediate scale. The resulting network
presentation would allow us to have direct intuition over the hierarchical
structure of the urban organisation, which is otherwise not immediately
available from the traditional simple road network presentation. We demonstrate
our methodology on the Singapore road network and find the critical spatial
scale to be 85 m, at which the network obtained corresponds very well to the
planning boundaries used by the local urban planners, revealing the essential
urban connectivity structure of the city. Furthermore, the complexity measure
is also capable of informing the secondary transitions that correspond well to
higher-level hierarchical structures associated with larger-scale urban
planning boundaries in Singapore.
