Transportation Geography and Network Science/What can Transportation Geography and Network Science teach each other?
In considering the relationship between transport geography and network science, the two fields must first be clearly defined and delineated. Following Rodrigue, et. al., "Transport geography is a subdiscipline of geography concerned about movements of freight, people and information. It seeks to link spatial constraints and attributes with the origin, the destination, the extent, the nature and the purpose of movements." Three central concepts related to this definition are nodes (locations that are linked, including access (origin), transshipment, and destination points), networks (the spatial structure and organization of infrastructures that enable and characterize movements), and demand (an interaction that gives rise to flows and corresponding transportation modes on networks). Transportation is itself a complex subject, incorporating dimensions of history, economics, sociology, politics, and environmental studies, and geographical concepts of importance include location (a spatial place somehow associated with movement), complementarity (a relationship between locations that gives rise to a demand for movement in order to create equilibrium), and scale (which relates the network of movements created to a physical geography and thereby to transportation modes). In order to distill the complex contributions of varied fields to transport geography, Rodrigue, et. al., specifically identify that "the role of transport geography is to understand the spatial relations that are produced by transport systems." In this respect, transport geography sits at the intersection of the study of transport systems (with an emphasis on nodes, networks, and demand) and of geography (which is concerned with spatial relations and specifically the three concepts above). For the purpose of this paper, transport geography will be considered to concern, for any given purpose, the translation of geographical realities into simplified network models, and the assessment of the appropriateness of those models with respect to geographical reality.
Network science is the study of networks, which Newman defines as "[collections] of points joined together in pairs by lines," later adding that "a network is a simplified representation that reduces a system to an abstract structure capturing only the basics of connection patterns and little else... thus a general yet powerful means of representing patterns of connections or interactions between parts of a system." For the purpose of this paper, network science will be considered to include both the knowledge common to all networks across disciplines (bearing with it the mathematical legacy of graph theory) as well as the practice and understanding specific methods that are used when considering, e.g., transportation networks in particular insofar as the network is just that – a simplified and abstracted model.
The two fields, by this definition, meet at the point where transport geography has framed a reality in the language of networks, and where network science has come with an arsenal of methods and experience in handling such abstracted problems. The term "transportation network," while commonly broader than here defined, will be restricted in this paper to mean such a network at the intersection of these fields. Transport geography has formulated many network problems and forced network science to expand its vocabulary to handle this subset of network problems. The reverse remains to happen in the future, as network science gains cohesion and sophistication as a discipline and begins to exert a shaping force upon transport geography. Transport geography will always contribute its valuable role of validation, but can perhaps learn from network science in how it poses its problems and how it draws similarities between transportation networks and other types of networks.
Past relationships 
What Transport Geography has taught Network Science 
Given these definitions, one will readily contend that transport geography's contributions to network science have been, essentially, to craft the entire arm of the science responsible for handling problems based on transportation networks. Aside from some pedantic examples, the arm of network science that engages transport geography has grown because transport geography has given network science problems for research and development of its science, and real data to validate its representation of real networks. Particularly, transport geography brought to the table a class of problems with dynamic networks and link weights, often further complicated by the requirement that these networks interact with human decisions and behavior. In seeking to translate these complex realities into language familiar to network science, transport geography has, in turn, required the network scientist to devise new means and methods of meaningfully approaching these complexities. Taking the case of accessibility, concepts from transportation science were sometimes translated into mathematical, network-friendly expressions as a means of aiding communication between the disciplines.
As it has expanded network science's views, transport geography has also restricted aspects of network science that can be used to address its problems. Spatial realities "[have] important effects on [transport networks'] topological properties and consequently on the processes which take place on them," and networks that are spatially constrained "display very distinctive features which call for new models." For instance, road networks – and most planar transportation networks – have peaked degree distributions and limited feasible link lengths. Such common characteristics can be productive to the extent that they are exploited by network scientists addressing transportation networks in particular, and such limitations also usefully eliminate a subset of network science (which may be useful for analyzing, e.g., social or biological networks) from use in analysis of transportation networks.
What Network Science has taught Transport Geography 
In return, network science has given transportation geography a set of mathematical foundations and formulations with which to address its problems. Network science's strong relationship with graph theory has allowed for concepts such as the minimum spanning tree and other mathematically optimal networks to be used in crafting measures of cost and efficiency of actual networks. Optimization of problems of traffic on networks and network structure "have a long tradition in mathematics and physics," and there is extensive literature handling such idealized networks. The concept of reductionism that network science engenders has been important for the growth of the relationship of the two fields, as well as for network science's ability to draw upon advances in fields other than transportation for applications to transport networks.
Network science's specific contributions to the study of transportation networks includes measures, such as the handful of useful indices used in quantifying and classifying networks, which help identify characteristics and relate networks to one another where similarities and outliers may have previously not been obvious. Both analytical and empirical results of handling such systems allow researchers to draw useful conclusions from features such as network link weights, identifying and predicting possible network features and behaviors. The recent availability of massive data sets, as well as the ability to process them brought about by the advent of computing, have made the systematic methods of network science critical in handling the sorts of problems that transport geography grapples with. The wealth of algorithms, often developed in other branches of network science or in graph theory, that are used on transportation networks take advantage of the strengths lent by generalization and some degree of homogeneity: Jiang showed remarkable quantitative similarities in the road networks of very different cities. While it may be said that transport geography helped shape parts of network science, it did so with good reason, and the relationship has been a fruitful one.
Future directions 
What Transport Geography can teach Network Science 
Transport geography will continue to contribute its complex problems, such as empirical observations of (yet poorly-explained) heterogeneities in optimal networks, and the definition it lends to the abstract network science. For example, while community detection methods remain varied and inconclusive for network science as a whole (see ), given the context of transportation networks, the types of detection methods eligible for use can be trimmed to exclude those known not to work on transportation networks. Barthélemy suggests that such community detection may prove useful "in geography and in the determination of new administrative boundaries.". In instances where network science fails to draw expected conclusions, such as von Ferber, et. al.'s finding that the number of stations in a city's public transportation network is independent of population, transport geography may be able to enrich its network models by incorporating aspects such as historical or socio-economic indicators.
While transport geography stands to further contribute important attributes of nodes and links to flesh out network science's reductionist and topological models, it can also learn from network science in how it poses its problems, thereby helping network science to take advantage of advances in other branches of the science. Barthélemy identifies areas of growth for spatial network science as "connection with socio-economic indicators," "evolution of transportation (and spatial) networks" and "urban studies," which clearly require major contributions from transport geography for their advancement. With respect to the first, he goes on to highlight "recent studies which tried to relate topological structures of networks to socio-economical indicators," such as that of Backstrom, Sun, and Marlow. The implication herein is that network science is already capable of handling problems that incorporate these factors, and just needs transport geographers to pose them in a fitting manner. By striving to cast problems in a more common language (as opposed to integrating complexities in such a way as to reduce the generality of a given transportation network), transport geography can help both to enrich network science in general, as well as the ties transportation networks share with other networks of interest.
Finally, transport geography will continue to fulfill its valuable role of validation of transport network models. For instance, in recent studies of optimal networks which incorporate high loop densities, the existence of fluctuations on the network is shown to be important for the peculiar network structure. By studying the fluctuations on transportation networks with an eye toward the hypotheses in network science, transport geography could contribute data to back up models that are applicable beyond just transportation networks (in this case, biological networks are of particular interest), aiding in the synthesis of overarching topics within network science. In sum, transport geography will continue to explore the correlations between space, topology and traffic, posing problems and offering validation for solutions, meanwhile maturing in the ways in which it relates to network science as network science matures and transport geographers become more familiar with the field.
What Network Science can teach Transport Geography 
Network science, on the other hand, will continue to contribute results of its reductionist means. For instance, important effects of coupled networks, such as the coupling of space and road structure networks, is beginning to be understood as readily related by betweenness centrality. Strano, et. al., also demonstrate a clear correlation between betweenness centrality and commercial activities on a transportation network. The hub location problem posed by O'Kelly has been refined and reworked recently, and preliminary work has been done on this topic (see ), but much work remains to be done, and Barthélemy suggests that "statistical physics could bring interesting insights on these problems usually tackled by mathematicians and engineers expert in optimization." As transport geographers make the problem statement more complex, e.g., by adding transfer delays, network scientists will have to continue developing models that incorporate increasing layers of complexity. Indeed, as transportation infrastructure continues to evolve with response to emerging modern topics such as self-guided vehicles and terrorist threats, questions that have been relatively peripheral to transport geography, such as system robustness to targeted attacks or propagating failures, will be readily handled by network science, which has already tackled such problems in different contexts. Such problems are indeed the bread and butter of network science, since the weak points of infrastructure networks are those with large betweenness centrality, meaning that a global network perspective is required to understand the importance of individual nodes. As network science gains cohesion and sophistication broadly, and as means are devised to address problems posed in fields even distantly related to transport geography, network science will more ably contribute to specific problems concerning transportation networks.
In studies of behavior on networks, its use of agent-based models and relevant simplifying assumptions may allow network scientists to get a handle on dynamic networks which respond to interactions from individual, independent agents. Such problems are subsets of a growing field in network science studying interdependence of coupled networks. For transport geography, work with agent-based models stands to help outline a range of assumptions that can be made (and those that cannot) for the use of such models in relation to reality – this outline, in turn, represents a set of criteria which network scientists must meet or address in their models in order to keep their elegant but abstract models grounded in some reality and practical utility. Barthélemy posits that "in parallel to empirical studies, we also need to develop theoretical ideas and models in order to describe the evolution of spatial networks." For example, a simplified model of network growth can demonstrate that relatively few assumptions are needed for self-organized, hierarchical structures to arise as the system converges to a user equilibrium. As such a model is fleshed out and becomes more realistic, the relationship of a network formed by progressive growth of the user equilibrium to that which is system optimal at any given time-point can be illustrated and more completely understood. Such a study in network science would then prove useful to those transport geographers engaged in directing and advising policy pertaining to network construction. Elegant models of transportation networks, accounting for the complex user relationships that contribute to traffic structure and devised in network science, will help to modify optimization procedures used by transport geographers for tackling real problems.
Transport geography has formulated many network problems and forced network science to expand its vocabulary to handle this subset of network problems. The reverse remains to happen in the future, as network science gains cohesion and sophistication as a discipline and begins to exert a shaping force upon transport geography. Transport geography will always contribute its valuable role of validation, but can perhaps learn from network science in how it poses its problems and how it draws similarities between transportation networks and other types of networks.
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