What makes a network traversable

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Enjoy, Passy. You must be logged in to post a comment. Passy's World of Mathematics. Skip to content. In the remainder of this lesson we will be looking at the Mathematics of Traversable Networks. A connected network is traversable if: all vertices are of even degree; or exactly two vertices are of odd degree and the rest are of even degree. This is shown in the following diagram. Networks and Six Degrees of Separation The Mathematics of Networks involves a wide variety of everyday situations from social interactions to biochemistry.

Help us to maintain this free service and keep it growing. Eva from Benenden School and Georgina both worked out that the traversable diagrams are: 1, 2, 3, 7, 8, 9, An anonymous contributor explained that: "The rule to find whether a network is traversable or not is by looking at points called nodes.

Nodes are places where two or more lines meet. On these networks, the nodes are clearly shown by the black points in the diagrams. Now you are probably wondering what this has to do with the network being traversable or not.

The node either would have an odd or even number of lines connected to it. Do not count the nodes with an even number of lines connected to it. Count the number of nodes with an odd number of lines connected to it. You may find it useful to download a printable copy of the networks What do you notice about traversable networks where you started and finished in the same place? To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

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