# Connectivity Of Graphs

1. Aug 26, 2004

### samirg

Hi Guys
I need some help on graph connectivity problem.
Given a graph is connected with probability p, what is the probablity that its subgraph is also connected?
In other words, we have to find the probablity that a subgraph of a connected graph is connected?

I hope i have made my question clear. Any help in this matter is really appreciated.

Thanks

Samir

2. Aug 27, 2004

### matt grime

It is impossible to answer the question without you saying more about the original graph. Given a "star graph" ie one central node and all vertices rays from it, then any subgraph must be connected, given another graph this will almost certainly fail to be true.

3. Aug 27, 2004

### samirg

connectivity of graph(problem redefinition)

Hi matt

The problem can be stated as
Given a random graph G(n,p) where n is number of nodes in the graph and p is the probability that an edge exits between two nodes, (when p=0 graph does not have any edges and when p = 1 graph is fully connected.) then if i take a subgraph of this random graph based on criteria that all the nodes of this subgraph are at a particular distance from one fixed node, then what is the probability that this subgraph is connected? I want to know whether this probability will be less than p, and if yes how much less?

I hope this makes question a bit clearer.

Thanks again

Samir

4. Aug 29, 2004

### matt grime

Double and triple posting is generally frowned upon.

Now you've introduced the word distance. the usual distance on graph is the length of the shortest path between nodes, which when defined explicitly tells you the subgraph you've picked must be connected (assuming the fixed node is in the subgraph).