Mathematically we can describe a marriage by a graph. People are vertices and two spouses are connected by an edge.
Mathematical models tend to oversimplify life, so let us assume that a person can only be one of two genders. Therefore, the vertices of a graph are colored in two colors: pink and blue. In this article I explore the graph theory of different types of marriages.
A monogamous couple is represented as a complete K2 graph: two vertices connected by an edge. The graph is bipartite, no matter how you color it. But actually our vertices are already colored from the start. If we are considering traditional marriage, one vertex is pink and the other is blue.
Historically, the second most common type of marriage is polygyny, in which one man has several wives. Less common in history, but a mathematically equivalent type, is polyandry, in which one woman has several husbands. Both these types of marriages emphasize inequality, as husbands and wives have completely different sets of rights.
From a mathematical point of view, polygyny and polyandry are described by star graphs. Star graphs are bipartite graphs and the natural coloring is the one that proves bipartiteness.
The final type of marriage is polygynandry, which refers to a group marriage, where more than one man and more than one woman create a family. Everyone can have sex with everyone else of the other gender. Mathematically this type of marriage corresponds to a complete bipartite graph Kn,m. Actually, in this case I can imagine that a particular pair of people of different genders wouldn’t like each other and might not consummate their marriage. So this graph is not necessarily complete.
How can same-sex marriages change the graph theory of marriages? As a graph, a monogamous same-sex marriage is the same bipartite K2 graph as a heterosexual marriage. It will just be less colorful, as both vertices will be of the same color.
But what happens if we add the same-sex idea to polygamous marriages?
Suppose a homosexual man wants to live with several spouses at the same time. What name can we give to a family unit of more than two homosexual men? Homopolygamy? Their marriage graph will be a star graph in which all the vertices are of the same color.
If a man can have several spouses, what about his spouses? Can they form multiple marriages too? If only one person is allowed to engage in several marriages, then we will see inequality within the same gender. If any spouse is allowed to form other marriages, then we will have a situation in which several men are all spouses to each other. So mathematically we will see complete graphs with more than two vertices to represent a marriage. If two people in a group do not like each other and do not want to be married, then the corresponding graph doesn’t need to be complete.
By symmetry we can describe a marriage of several women, and mathematically it will be similar to a marriage of several men.
Another interesting aspect is the idea of mixed types of marriages involved in polygamy. Suppose a husband has several wives. Some of them might get bored waiting for his attention, and start spending so much time with each other that they end up developing feelings for each other. Suppose two wives of the same man decide to marry each other. What name would we give to this type of marriage? I am afraid that we do not have enough words to cover all the potential situations.
Suppose we have a heterosexual married couple and the man decides to bring another woman into their house. Thus the transition from a traditional marriage to a polygyny is created. If they got along so well that the first wife decides to marry the second wife, this would require a transition to a new type of marriage. Oh, I see that my essay just went in another direction — how different types of marriages might evolve into each other. For now, I’ll leave this for future research.
Talking about different directions. I recently wrote a piece about condoms. Now I have a new generalization for the classic condom puzzle. Suppose we have a mixed-type marriage defined by a graph. Suppose tonight every couple of people corresponding to the edge of this graph wants to have sex with each other. What is the smallest number of condoms they can use? In my condom essay, I didn’t define the condom usage for the sex of two women. I will leave it to your imagination and definition.Share: