By Definition Alpha Male comes up like this:

1)The dominant male animal in a particular group.
2)A man tending to assume a dominant or domineering role in social or professional situations

By This definition although we apply it, we represent much more then just this definition. Alpha by definition is Dominance.

We Represent Confidence.

We laugh when tested, We control the frame. We are not threatened. We are established. We get respect from other women and men, When we talk they listen. We are Domineering. But we are granted this, We don't intend to take this, We are this. Formed and refined over time and experience. Given to us by our social environment. What we represent is what the people see and react accordingly.

The Definition of Sovereignty is as follows:

Sovereignty is understood in jurisprudence as the full right and power of a governing body to govern itself without any interference from outside sources or bodies. In political theory, sovereignty is a substantive term designating supreme authority over some polity.

So although being Alpha is apart of being sovereign. Its only part of it. I am a Sovereign Man.