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In graph A, there are 5 links [(1,2), (2,1), (2,3), (4,3), (4,4)] and 3 connections [(1-2), (2-3), (3-4)]. On graph B, there is a path between 1 and 3, but on graph C there is no path between 1 and 3.

Simple graphs have their nodes connected by only one link type, such as road or rail links. A multigraph can contain more than one link type between the same two nodes. In the above example, the multigraph is a combination of the two simple graphs.

Graph A is planar since no link overlaps with another. Graph B is non-planar since many links are overlapping. Also, the links of graph B cannot be reconfigured in a manner that would make it planar.

This simple graph has the following definition: G = (v,e)v = (1,2,3,4,5)e = (1,2), (1,3), (2,2), (2,5), (4,2), (4,3), (4,5)

The goal of a graph is to represent the structure, not the appearance of a network. The conversion of a real network into a planar graph is a straightforward process that follows some basic rules: The outcome of this abstraction, as portrayed in the above figure, is the actual structure

Authors: Dr. Cesar Ducruet and Dr. Jean-Paul Rodrigue Graph theory relies on several measures and indices that assess the efficiency of transportation networks. 1. Measures at the Network Level Transportation networks are composed of many nodes and links, and as they rise in complexity, their comparison becomes challenging. For instance,

Authors: Dr. Jean-Paul Rodrigue and Dr. Cesar Ducruet Graph theory is a branch of mathematics concerned about how networks can be encoded, and their properties measured. 1. Basic Graph Definition A graph is a symbolic representation of a network and its connectivity. It implies an abstraction of reality so that

Source: adapted from J. Rubin and B. Tal (2008) “Will Soaring Transport Costs Reverse Globalization?”, CIBC World Markets Inc., StrategEcon, May 27. The usage of China as a privileged location in the global manufacturing system has been linked with low input costs (mainly labor) as well as lower long distance

Source: adapted from Notteboom, T. and P. Carriou (2009) “Fuel surcharge practices of container shipping lines: Is it about cost recovery or revenue making?”. Proceedings of the 2009 International Association of Maritime Economists (IAME) Conference, June, Copenhagen, Denmark. Fuel consumption by a containership is mostly a function of ship size

Transportation relies on the use of energy. As most transportation modes rely on the usage of petroleum, a rise in oil prices can impact several dimensions of the transport system. Six interdependent types of impacts can be expected: Usage level. Users of a specific transportation mode generally respond to higher