Centers are edges

Centers are not nodes, in fact junctions are not nodes. In graphs (representation of transportation networks for modeling and analysis), nodes are aspatial representations of the intersection of links, which themselves are aspatial representations of the structure of network. However real nodes, i.e. centers and junctions, take space. As such they provide a spatial separation between areas that adjoin them. They serve as edges to adjoining areas (e.g. neighborhoods).
As Alfred Korzybski once said, “the map is not the territory”. Similarly, the graph is not the place. Network elements separate as they connect.