Network

A network is a connected set of lines representing some geographic phenomenon, typically to do with transportation. The “goods” transported can be almost anything: people, cars and other vehicles along a road network, commercial goods along a logistic network, phone calls along a telephone network, or water pollution along a stream/river network.

Direct vs. Non-directed Networks

A fundamental characteristic of any network is whether the network lines are considered to be directed or not. Directed networks associate with each line a direction of transportation; undirected networks do not. In the latter, the “goods” can be transported along a line in both directions. We discuss here vector network analysis, and assume that the network is a set of connected line features that intersect only at the lines’ nodes, not at internal vertices. (But we do mention under- and overpasses.)

Planar vs. Non-Planar Networks

For many applications of network analysis, a planar network, i.e. one that can be embedded in a two-dimensional plane, will do the job. Many networks are naturally planar, such as stream/river networks. A large-scale traffic network, on the other hand, is not planar: motorways have multi-level crossings and are constructed with underpasses and overpasses. Planar networks are easier to deal with computationally, as they have simpler topological rules. Not all GISs accommodate non-planar networks, or they can only do so using “tricks”. These tricks may involve the splitting of overpassing lines at the intersection vertex and the creation of four lines from the two original lines. Without further attention, the network will then allow one to make a turn onto another line at this new intersection node, which in reality would be impossible. In some GISs we can allocate a cost for turning at a node—see our discussion on turning costs below—and that cost, in the case of the overpass trick, can be made infinite to ensure it is prohibited. But, as mentioned, this is a work around to fit a non-planar situation into a data layer that presumes planarity. The above is a good illustration of geometry not fully determining the network’s behaviour. Additional application-specific rules are usually required to define what can and cannot happen in the network. Most GISs provide rule-based tools that allow the definition of these extra application rules.