Fig. 2

Geometrical versus topological approaches for urban street networks: a four-step visual construction of their respective abstract networks. Each construction is performed on the notional sample exhibited in Fig. 1. The left four-step sequence (g₁)–(g₄) and its right counterpart (t₁)–(t₄) sketch for this sample the geometrical and topological abstract network constructions, respectively. At Step 1, street-segments and roads are identified: the street-segments are labelled with indexed s and coloured in distinct pallid colours; the roads are labelled with indexed r and coloured in distinct vivid colours. Meanwhile, the junctions and the impasses are coloured in grey and labelled with indexed j and i, respectively. In Subfigure g₂, the extended junctions j_∗ and i_∗ and the street-segments s_∗ spontaneously become nodes and edges, respectively. In Subfigure t₂, each road r_∗ is reduced to a node and each road-node pair {r_∗,r_⋆} is linked whenever r_∗ and r_⋆ share at least a common junction. At Step 3, the raw material is being dissolved to highlight the emerging abstract networks. Finally, at Step 4, the resulting abstract networks are rearranged to stress their relevant traits: the size of each node is proportional to its valence; the impasses i_∗ are neglected because they are rather free-ends than nodes; the road-node r_h was flipped to avoid a confusing edge crossing; and so forth