Is it necessary for vertex labels to be distinct within a graph?

I am currently developing a browser-based application that allows users to create graphs, manipulate them, and run algorithms on them. At the moment, each vertex is represented by a unique positive integer. However, I am considering implementing labeled vertices, where the label can be any string. This presents a dilemma as to whether duplicate labels should be allowed and how they should be stored. Several options are being considered:

  1. Maintain integer vertex ids and enforce unique labels. This may lead to confusion between labels and vertex ids, particularly with JavaScript automatically converting numbers to strings.
  2. Stick with integer vertex ids but permit duplicate labels. While this offers more flexibility, it could also result in user confusion.
  3. Do away with numeric vertex ids entirely and identify vertices solely by their unique labels. But elevating something that seems like a property to an identifier doesn't feel quite right.
  4. Explore alternative approaches?

After researching various graph libraries, I've noticed that each has its own method for dealing with this issue. I understand that there may not be a definitive answer to my question, so I welcome opinions and insights. Thank you in advance!

Answer №2

In order to maintain a graph with unique node values, we can implement an adjacent list where each node value is assigned a unique ID generated by the hash value of the previous node. Deleting a new node may incur some cost as it requires recalculating the hash.

For example:
Let count = 1
class HashValue
{
   getUniqueNodeGenerator();
}
---------------------------------------------------------------------------------------------------------------------------------------
Whenever a new node is created, the hash value is calculated from existing values to compute the new hash value.
UniqueID: Hash value calculated by (1 and String Name)
UniqueID: Hash value calculated by Hash Value Of Node 1 and New Node
UniqueID: Hash value calculated by Hash Value Of Node 2 and New Node
UniqueID: Hash value calculated by Hash Value Of Node 3 and New Node
UniqueID: Hash value calculated by Hash Value Of Node 4 and New Node
UniqueID: Hash value calculated by Hash Value Of Node 5 and New Node    
------------------------------------------------------------------------------
Label Here 
string getUniqueNode()
{
    calculate unique node
}
struct user
{
   string name;
   string UniqueID;
}
class graph
{
    int numvertices;
    list<user> *adjLists;
    bool *visited ;
public:
    graph(int V);
    void addEdge(int src,int dest);
    void DFS(int vertex);
};

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