A graph consists of vertices and edges. So at the top level the XML description should look like this
<graph>
<vertices>...</vertices>
<edges>...</edges>
</graph>
The <vertices>
container will have <vertex>
elements to carry the information for each vertex. In particular, you will need a unique identifier by which edges can refer to a vertex. So, something like this
<vertices>
<vertex id="A">other information, if needed</vertex>
<vertex id="B">...</vertex>
...
</vertices>
Each <edge>
inside the <edges>
container will need at least three pieces of information: the vertices connected, and the weight on the edge. Thus, for example
<edges>
<edge ends="A B">7</edge>
<edge ends="B C">8</edge>
...
</edges>
You can put all this into a schema where, for example, you can enforce a requirement that the 'ends' attribute carries references to ids of vertices that do exist in the graph (viz., look up xs:ID and xs:IDREF in the XML Schema documentation).