Above, concept of dual-extended graph. Bottom, current existing operations that transform a graph into its dual pseudograph or dual graph. As we can see, the dual-extended graph combines simultaneously the graph and its dual-pseudo graph, including connections between their edges, which extends the notion of neighbourhood, providing a data structure that is able to capture all the aspects of spatial data.

Phenotypes of the possible configurations that can be created by using a proposed grammar that generates a dual-extended graph. The examples are generated by using closeness as a method to choose the new cell to divide.

Possible configurations generated by the use of sub-topologies

Generated network. In the figure we can observe the initial road network, its graph and line graph, the analysis of metric and angular betweenness and the KDE analysis extracted from them, plus the final generated network.

Example of a generated network showing all the scales that can be generated.

Different metric analysis comparing generated networks with real systems.

Different structural analysis comparing generated networks with real systems.

These images show the approach for generative urban and regional networks using the concept of dual-extended graphs and a combination of centrality mesures and KDE (Kernel-density estimator) to characterize the land uses.