Module 3 | Network Analysis

The topic of Module III: Network Analysis has a special meaning to me. I have worked and teach a bit on networks and accessibility. In my case, on ground transportation networks and spatial distribution of assets in the urban environment. These networks are usually planar, and links are constrained by the spatial location of the nodes and by the costs of constructing (and maintaining) the transportation infrastructure. Other physical networks (aerial, maritime, logistical) are less constrained by the physical determinants of the connections (see Rodrigue, 2020):

No doubt, the topologies of social networks can get much more complex! Apart from that, I would say that the vast majority of metrics about the geometry and structure of a network (and the process of solving an optimization problem in a network environment) are pretty similar in transportation and social networks. For example, there are technical equivalences in solving least-cost paths, Hamiltonian paths, and service areas (I recommend de Smith et al, 2018, Ch. 7 for an updated overview of these techniques for spatial planning applications). In social networks, for example, least-cost paths, Hamiltonian problems, and “topological” service areas could be used to optimize transmission of information between target nodes. They could also be used to detect regions in the social network that remain beyond the limits of a "social" catchment area (e.g. beyond the reach of a marketing campaign launched on social media).

The basic idea in both network models is to use a “graph”, which is a mathematical way to represent systems as a collection of points (a.k.a. nodes, vertices) and lines (a.k.a. edges, vertices, arcs) that connect such points. Vertices in transportation networks can also be directed (different directions along the road may involve different travel costs) or undirected (travel costs are irrespective of direction). Typically, links in transportation networks are weighted based on distance or a combination of costs (time, fuel, maintenance, personnel…). Clearly, single-mode and two-mode networks are typical in transportation systems too. In the transportation case, however, adjacency matrices have become the standard for the tabular representation and analysis of the network.

 

I also see some equivalent uses of network metrics in social and transportation network modeling. To give a few examples (apologies for the quality of the next images):

Another interesting development has been that of Spatial Syntax for urban design, where the primal syntax problem (= to regard streets as nodes connected by junctions) is transformed to the dual syntax problem (= to relate street junctions through streets). In the next image, we go from the physical planar network (a) to the primal syntax representation (b) to the dual syntax representation (c) (Batty, 2004):

References

• J.P. Rodrigue (2020). The Geography of Transport Systems. [URL]

• M.J. de Smith, M.F. Goodchild, P.A. Longley (2018). Geospatial Analysis, 6^th edition. Drumlin Security Ltd. [URL]

• M. Batty (2004). A new theory of space syntax. CASA Working Papers Series, 75. Casa, UCL, ISSN: 1467-1298 [URL]