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Encyclopedia > Transportation network (graph theory)

A transportation network is a type of directed, weighted graph or network. One major problem that has plagued graph theory since its inception is the consistent lack of consistency in terminology. ... A wide variety of systems of interconnected components are called networks. ...

Transportation networks are used to model the flow of commodity, information, or traffic (see transport network). The word commodity is a term with distinct meanings in business and in Marxist political economy. ... Information is a term with many meanings depending on context, but is as a rule closely related to such concepts as meaning, knowledge, instruction, communication, representation, and mental stimulus. ... In many parts of the world traffic is generally organized, flowing in lanes of travel for a particular direction, with interchanges, traffic signals, or signage at intersectons to facilitate the orderly and timely flow of traffic. ... A transport network is typically a network of roads or streets permitting vehicular movement, or rail or underground, or a combination of the two (multi-modal journeys). ...

A transportation network G is a graph with

• Exactly one vertex of in-degree 0 (no incoming edges or arcs), called the source;
• Exactly one vertex of out-degree 0 (no outgoing arcs), called the sink;
• Non-negative weight, called capacity assigned to each arc.

Flows represent commodity flowing along arcs from the source to the sink. The amount of flow along each arc may not exceed the arc's capacity, and none of the commodity may be 'lost' along the way (that is, the total flow out of the source must equal the total flow into the sink). In geometry, a vertex (Latin: whirl, whirlpool; plural vertices) is a corner of a polygon (where two sides meet) or of a polyhedron (where three or more faces and an equal number of edges meet). ... Edge may have one of the following special meanings, in addition to its dictionary definition: wiktionary:edge. ...

A cut in a network is a partition of its vertices into two sets, S and T, such that the source is in S and the sink is in T. In general, a partition is a splitting into parts. ...

The cut set is the set of all arcs that connect some vertex in S with some vertex in T. In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ...

Results from FactBites:

 Graph theory - Wikipedia, the free encyclopedia (1214 words) Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs) which can be directed (assigned a direction). Graphs are represented graphically by drawing a dot for every vertex, and drawing an arc between two vertices if they are connected by an edge. Firstly, analysis to determine structural properties of a network, such as whether or not it is a scale-free network, or a small-world network.
 Category:Graph theory - Wikipedia, the free encyclopedia (147 words) Graph theory is the branch of mathematics that examines the properties of graphs. Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs), which can also have associated directions. Typically, a graph is depicted as a set of dots (i.e., vertices) connected by lines (i.e., edges), with an arrowhead on a line representing a directed arc.
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