Centrality measures describe structural properties of nodes (and edges) in a network. Betweenness centrality (Freeman 1977) is one of them, characterizing on how many shortest paths a node is. So far, network analysis concentrates on structural, i.e., topological properties of networks, and on static formulations of centrality. Although travel networks can be studied this way, they deviate from other networks in two significant ways: their embeddedness in geographic space is relevant, and their dynamic properties can not be neglected. For example, a physical urban street network constrains travel behavior in a way that people seek to satisfy their demands from physically near, not topologically near resources. Also, a physical street can have significant temporal constraints, such as night time closures, dynamic lane allocation, or current traffic volume, besides of slow rates of change in the network itself. This means, it is not appropriate to compare traffic flow on street networks with traditional betweenness centrality.
Traffic flow is the process of physical agents moving along an urban travel network. These agents are autonomous, purposeful, flexible, and volatile. They establish a social network: agents near to each other can communicate and interact (other social ties, like kinship or friendship, are not considered here). Since the agents are mobile this social network is highly dynamic. Also agents are volatile. They enter traffic at any time, and leave as soon as they have reached their destination. The places where they emerge or disappear are distributed over space and time, but not in a random manner. Additionally, agents in urban traffic are purposeful. They have individual travel, sensing and communication capabilities, maybe even preferences, and a specific travel demand (to reach a destination by a specified time or specified costs). Especially, during travel they can interact with their fellow agents, be it by coordination (communication) or collaboration (transport), and they can sense and act in their physical environment, and thus, change their travel plans at any time to satisfy their travel demand. This means travel plans—if not the underlying travel demand itself—can be dynamic. This social network of agents in traffic can also be characterized by centrality measures; however, these measures are attributes of the agents, not of the nodes of the physical travel network, and they are constantly changing—hence, infeasible to track in a central database.
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