Dimension of Geographical Networks

Suggested by: Franz-Benjamin Mocnik

Keywords: spatial networks, dimension, street network, OpenStreetMap

Objective: Developing and implementing algorithms for detecting subnetworks the local network dimension of which is homogeneous.

Short description:

Networks occur virtually everywhere. The World-Wide Web, metabolic networks, and communciation networks are typical examples.  Also in Geography, such networks occur.  Mocnik (2018a) has examined the degree of influence space has on such networks.  He showed, for instance, that transport and road networks, as well as social networks to a lesser degree, are influenced by space.  Further more, the dimension of the space has a strong impact on the topological structure of such a network, which is why a dimension can be assigned to a network.  Besides exposing very similar qualities, street networks in cities are very similar with respect to their dimensionality (Mocnik 2018b).  In order to model such networks, Mocnik (2015a, 2015b) has proposed a spatial network model.

This thesis aims to develop strategies in order to identify subnetworks that expose a similar dimension in every neighbourhood.  That is, a network that is homogeneous and is thus similar to the spatial network model proposed.  Such networks naturally arise as has been discussed at the example of street networks in cities (Mocnik 2018b), and at the example of road networks as multi-layered networks (Mocnik 2018a).  The thesis will pay particular attention to the example of street networks, which can be extracted from the OpenStreetMap dataset, an open and freely available dataset.  As a result of this thesis, it will be tested whether such homogeneous subnetworks have a geographical relevance and can/should be considered to be geographical entities?  Would such an algorithm, for instance, be able to identify cities by their network dimension?

Literature references: 

• FB Mocnik (2018a): The Polynomial Volume Law of Complex Networks in the Context of Local and Global Optimization. Scientific Reports 8(11274), 2018
• FB Mocnik (2018b): Dimension as an Invariant of Street Networks. Proceedings of the 7th International Conference on Complex Networks and Their Applications, 2018, 455–457
• FB Mocnik (2015a): A Scale-Invariant Spatial Graph Model. PhD Thesis. Vienna University of Technology, 2015
• FB Mocnik, AU Frank (2015b): Modelling Spatial Structures. Proceedings of the 12th Conference on Spatial Information Theory (COSIT), 2015, 44–64
  

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Prerequisites / qualifications: This topic requires some previous knowledge in network science and a good understanding of algorithms.