These simple matrilateral and patrilateral relationships can be diagrammed as follows:
Ego's cross cousins (in yellow) are distinguished from his parallel cousins (in green) as the children of opposite and same sexed siblings, respectively. Patrilateral cousins are related to Ego on his father's side of the family. Matrilateral cousins are related to ego on his mother's side of the family.
The same relationships would of course obtain for a female ego. However, cross cousin marriage rules per se are specified from a male perspective. Thus for matrilateral cross cousin marriage, a man marries his mother's brother's daughter, although his wife is marrying patrilaterally, i.e., to her father's sister's son. In the patrilateral case, a man marries his father's sister's daughter and a woman, her mother's brother's son.
Male and Female Perspectives
While not necessarily recognized as such, matrilateral and patrilateral cross cousins are present in every kinship network, bilateral cross cousins occur only in special marriage situations, where two men marry each other's sisters.
In the above diagram, two men (1 and 3) marry each other's sisters (2 and 4), a practice referred to as direct exchange marriage. (Note that marriages are indicated by lines joining partners from below rather than by equal signs.) Couple 2 and 3 beget Ego. Couple 1 and 4 have two children, 5 and 6, who assume a compound relationship to Ego. In one direction they are his father's sister's children; in another, they are his mother's brother's children. (Each pathway is indicated in the diagram in yellow.) As such they are related to ego both patrilaterally and matrilaterally and are therefore termed his bilateral cross cousins.
The widespread presence of cross cousin marriage in its varous forms has been of special importance to the structuralist anthropologist, Claude Levi-Strauss, and to his formulation of alliance theory (Levi-Strauss 1969). He views marriage as a form of exchange that simultaneously expresses differences between groups and unites them into coherent social systems. His observations focus on the significance of the three alternative marriage rules for the emergence of different social dynamics.