Hey guys it is Casey back here again with yet another post where today I am in math's looking at the question of when is a network transferable. A network in this sense for those of you who do not know is a series of nodes that are connected by branching paths to form a network of nodes.
What is a transferable network?
A transferable network is a network where you can draw a single line across the network while going over each part only once. This is a very simple concept to grasp but it also raises the question of how do you determine if a network is transferable or not?.
A way of determining if a network is transferable or not is by the amount of paths that are connected to each node. You simply need to see if the network has 2 odd nodes or not. what an odd node is sums up to a node that has an odd number of paths connected to it. If the network has more than 2 of these kind of nodes then it is considered not a transferable network. An example of this is the Konigsberg bridge problem.

The Konigsberg bridge problem is a rather famous one in the world of networks and is an example of a non transferable network. A man by the name of Leonhard Euler who is a famous Swiss mathematician, physicist, astronomer, geographer, logician and engineer who had said that it is impossible to make a journey across all 7 of these bridges while crossing each one only once. This is a true statement and Euler made a rule to tell if a network is transferable or not. That rule was if the network had 2 and only 2 odd nodes or no odd nodes at all then it is transferable. If you look at the bridges and count up the nodes then you can see that they are all odd and none are even meaning that this network is not transferable.
There are a couple of things you should keep in mind when determining if a network is transferable or not aside from the rule that Euler had stated. There are three rules that should be easy to remember with the hard part being remembering them.
The network is transferable when
1.If all nodes are even then you can start and finish anywhere on the network
2.Are two nodes odd. You can only start and finish on these parts
3.If there are more than two odd nodes then the network is non transferable
Another thing you can use to help you with this is called the order of the nodes which is very simple to make and put into effect. Basically all you need to do is take note of which node is which in alphabetical sequence so you would have something like A1,B3,C4 etc.
If you find more than 2 odd numbers in that order then your network is non transferable as stated by the third rule. These rules should be easy to remember if network of nodes is transferable or not.
Anyway I hope you guys all enjoyed and I will see you all in the next post bye bye.
Square: This can be described as a shape with multiple sides of equal length whose angles are all 90 degrees. If you were to draw a diagonal line from one corner to the opposite then you will see that all diagonals are equal as well as the lengths and angles.
Rectangle: This is very similar to a square but with one key difference, not all the lengths are equal. two of the sides are one length while the other two are either larger or smaller. All of the angles are still 90 degrees each. The diagonals are also equal for this shape as is the case with most quadrilaterals.
Parallelogram: This is a shape with 2 pairs of parallel lines whose angles are not right angles. There is also no line of symmetry like with most shapes on a parallelogram.


