def METHOD_NAME(self, v):
    """
    add vertex v into the Graph as a new component
    """
    for c in self.components:
        if v in c.verticesPoset:
            return c.verticesPoset.get(v)
    g = self.component_class(directed = self.directed)
    v = g.add_single_vertex(v)
    self.components.append(g)
    print("add vertex v into the Graph as a new component")
    return v