hash map / collection choice

Hello,

I need help to create a data structure. I have got a class

class myEdge {
    private int m_edgeid = 0;
???.

       @Override
    public int compareTo(myEdgep_edgelink) {
        if (m_edgeid > p_edgelink.m_edgeid)
            return 1;
        if (m_edgeid < p_edgelink.m_edgeid)
            return -1;

        return 0;
    }

    @Override
    public boolean equals(Object p_object) {
        if ( (p_object == null) || (!(p_object instanceof myEdge)) )
            return false;

        return this.m_edgeid == ((myEdge)p_object).m_edgeid;
    }

    @Override
    public int hashCode() {
        return m_edgeid;
    }
}

The edge ID is always unique. So I would like to create a collection in
which I can do something like

myEdge x = edgecollection.get( searching edge id )

So the collection stores the edge objects and I can get an object with
the internal id. The collection
should use the the edgeid value to identify the object.

A set should be the correct structure, but I can not get the object
itself of the map without iteration over all
items. A HashMap needs a key, value pair, so I need also a key class
which stores the edge id (redundant data).

I'm a little bit uncertain, which collection is the correct choice.

Thanks a lot

Phil