How to find multiplicity on a graph?

It is very easy to check whether or not a graph is connected or not. If there’s a path between any two nodes, the graph is connected. If not, the graph is disconnected. But what if you want to find out if your graph has more than one connected component? In other words, how do you find the number of connected components of a graph? There are many ways to do this, but one of the most intuitive and easy ways I’ve found so far

How to find multiplicity on a tree?

A tree is a graph in which every vertex has only one parent. To find the multiplicity on a tree is a little easier. If there are exactly two children for every parent, then it is a binary tree. If there is more than one child per parent, you have a multi-ary tree. The most common way to represent a tree is a parent-child relationship.

How to find multiplicity on a path graph?

One of the easiest ways to spot indirect connections is by finding high-multiplicity paths. If there are many nodes on a path, then it’s likely they are connected to each other. The simplest way to find these high-multiplicity paths is with a breadth-first search. You can find more about the BFS algorithm here.

How to find multiplicity on a trivalent tree?

A tree graph is a connected graph where each node has at most three edges. To check whether a tree is simple or not, we use the following procedure: We start with checking whether the graph contains cycles. If it doesn’t, then the graph is a tree. If the graph does contain cycles, then the graph is a multi-tree.

How to find multiplicity on a tree with cut vertices?

To find the multiplicity of a tree with cut vertices, one must find the number of connected components of the graph after removing the cut vertices. If the number of connected components is greater than 1, the tree has a multiple root. If the number of connected components is 1, the tree has no multiple roots.