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Ne=N2+1Here Ne=no. of leaf nodesN2= no. of nodes of degree 2
"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."
The Network Backbone
To determine the number of pairs for 6 nodes using a formula, you can use combination formula. In this case, the formula would be nC2, where n represents the number of nodes. Substituting n=6, the formula becomes 6C2, which is equal to 15. Therefore, there would be 15 pairs of nodes for 6 total nodes.
Graph theory - a mathematical circuit requires a)transportation between nodes (points) b) w/o returning to the original node via a line segment already used. The most simplistic circuit in math would be three nodes (a triangle, containg six unique pathways). One line seg (2 nodes) has 2 pathways but both violate b) QED