When is a network traversable

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. If there are no odd nodes or if there are two odd nodes, that means that the network it traversable.

Networks with only two odd nodes are in a traversable path and networks with no odd nodes are in a traversable circuit. If not, the pen must start or finish at the node. As you can start and finish at only twonodes start at one, finish at the other any network with more than 2 odd nodes is not traversable.

For a network to be traversable, it must be fully connected. A connected network is traversable if:. If a network has more than two vertices of odd degree, it is not traversable. If we go back to our previous Traversable Network examples, we can see that they are all Connected Networks. We can also manually trace over these Networks by hand, and see that they are indeed Traversable. For each Network we can find a route which passes along all of the Edge paths, without repeating any of the paths.

Hint: When manually tracing over a traversable network by hand, which has odd degree vertices, always start at one of the odd vertices. Traversable Network Questions. Answers to Traversable Network Questions.

They are both definitely not Traversable. The Blue Network is not Traversable because it has more than two vertices of odd degree. There are four vertices with Degree equal to the odd number 3, and we are only allowed to have a mximum of two odd numbered Vertices.

We can fully Traverse the Red Network with no repeats if we start at the end of the loop, go around the loop, and then up and around the square following its trianges. We can manually traverse the Pink Network, but finding the exact route which is Traversable is fairly challenging.

Networks and Six Degrees of Separation. The Mathematics of Networks involves a wide variety of everyday situations from social interactions to biochemistry. The following video covers the idea of hubs in Networks making any member of the network separated from another member by a maximum of six connections.

Additional Information. Introduction to Network Mathematics. PayPal does accept Credit Cards, but you will have to supply an email address and password so that PayPal can create a PayPal account for you to process the transaction through. 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? What about traversable networks where you started and finished in different places?

What do you notice about the number of times you visited each vertex point? For the networks which are not transversable, what is the smallest number of edges that you need to add or remove so that the resulting network is traversable? Can you find a condition that guarantees a network is not traversable? Can you explain why?