how to work out traversable networks

who was leonhard euler  

eonhard Euler  15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory

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The Königsberg bridge problem was an old puzzle concerning the possibility of finding a path over every one of seven bridges that span a forked river flowing past an island—but without crossing any bridge twice. Euler argued that no such path exists.

you could only solve the problem there and 2 or no odd nodes witch there are not 

if it was an even number of bridges it could be solved but with 7 bridges you would have to go past the same point more than once to solve the problem 

Why is Konigsberg bridge problem Impossible?

Thus, each such landmass must serve as an endpoint of a number of bridges equaling twice the number of times it is encountered during the walk. ... However, for the landmasses of Königsberg, A is an endpoint of five bridges, and B, C, and D are endpoints of three bridges. The walk is therefore impossible.

A “Traversable Network” is one where we can find a route through the network, along the edges, that uses all of the edges only once. A network is said to be traversable when it is possible to start at a Node and trace out the whole network without having to retrace over any of the connector “Edges”

if there are more the 2 odd nodes the network is not transferable

 

could you solve it without taking your pen off the page or going over the same point twice