Matriarchy

Definition: A matriarchy is a social system organized around the principle of mother-rule in which mothers, or females, are at the top of the power structure. There is no solid evidence that a matriarchal society has ever existed. Even in societies with matrilineal descent, the power structure is either egalitarian or dominated formally by the father or some other male figure. In order for a social system to be considered a matriarchy, it would need the support of a culture that defined women’s dominance as desirable and legitimate.

So, even though women are the authority figures in single-parent families, they are not considered matriarchies.