Friday, August 2, 2013

Bipartite Networks: Application in Transit Networks

A bipartite network is a kind of network in which the nodes are grouped into two independent classes of U and V and every link connects a node in U to a node in V.

A transit network can be viewed as a bipartite network such that group U consists of different geographical locations in the city (origins and destinations) and V consists of different transit lines or routes. A node in U (e.g. an origin) can only connect to another node in U (e.g. a destination) if and only if a transit line/route exists that connects them. Therefore, an origin will be connected to a destination (both nodes in U group) via a transit line/route (a node in V group). Such network representation illustrates a transit network with no transfer on-route. Note that transfers are possible in this representation but only through reaching an intermediate destination in U.


The bipartite network can be modified to represent transit networks with one or more transfers. The modified bipartite network includes two independent groups of nodes (U and V) in which every link connects a node in U to a node in V. Also, there are links that connects nodes in V, representing transfers between different transit routes/lines. Thus, an origin in U can also be connected to a destination, also in U, via two or more transit lines/routes.

The discussed application of bipartite networks in transit networks and the proposed modification to illustrate transit networks with transfers is an ongoing work and not yet published. No reproduction is allowed without written permission.


Following is an example of the bipartite and modified partite of Chicago transit network.

 


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