Calculating Adjacency Matrix

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I'm having trouble understanding the concept, I know it is pretty simple but could someone help me out.

Assume that I have the following:

$V = \begin{bmatrix} 0&0&1 \\ 0&0&1 \\ 1&0&0 \end{bmatrix}$

This is an undirected graph, now I want to find the Adjacency matrix, which, is all the elements that are in the set.

So I will have

$V \in V = \left\{\begin{matrix}(v1, v1), (v1, v2), (v1, v3), (v2, v2), (v2, v1) ...... \end{matrix}\right.$

I don't understand this however, in the formula, it says to put a "1" it's in the subset.. However, do I put a 1 if it's in the subset WHERE the value is "1" in the matrix $V$ or is "1" put where only the subset can exist.. I.e. $(v1, v1)$ would therefore have "0"?

Thanks

EDIT:

In this example, the following is given:

G = [0, 0, 1; 0, 0, 1; 1, 1, 0]; xy = [1 1; 0 0 ; 2 0];

Therefore, what does xy represent in this example, if G is the adjacency matrix? I'm guessing that it represents the edges, but, I don't know how to calculate these for a given matrix.

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1 Answer

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If $V$ is the adjacency matrix, then the graph has verices $\mathcal V=\{v_1,v_2,v_3\}$ and edges $\mathcal E = \{(v_1,v_3), (v_2,v_3), (v_3,v_1)\}$

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