Understanding distance in a family tree

distance one Mathematicians, computer scientists, genealogists, and many others use trees to organize data, and distance is one measurement within a tree. In a family tree, we say that the distance between two people is the shortest "distance" between them by traversing the tree. To understand this, consider yourself as the "center" or focal point. (No, you are not the center of the universe, but thinking like this for the moment helps you to understand the concepts here.)

Consider those who are closest to you in your family. Your list may include your parents, your spouse(s), and your children. You may also include your siblings or an aunt or uncle. For purposes of a family tree, those whose distance from you is 1 includes those in the first list: your parents, your spouse(s), and your children. See diagram on the left that illustrates this.

Note that even though one may be emotionally close to a sibling, by this method of measuring distance, one first goes up to a parent and then down to a sibling. Thus, a sibling has distance 2 from a person. Note also that grandparents are distance 1 from either of your parents, so they are a distance 2 from you. Similarly, your grandchildren are also a distance 2 from you. Likewise, so are your spouse's parents, your father-in-law and mother-in-law. Finally, your son-in-laws and daughter-in-laws are also given a distance of 2 since they are your children's spouses. Note that to find those at distance 2, we simply take all those at distance 1 and ask who their parents, children and spouse are. So, below is a summary of relations of distances discussed so far:

  1. father, mother, spouse, child
  2. grandparents, grandchildren, siblings, mother-in-law, father-in-law, children's spouses

Now continuing, who are those at distance 3? Take all those at distance 2 and ask who are their parents, children, and spouses (and not including those that have already been counted). The parents of your grandparents are your great-grandparents, the children of your grandparents are your aunts and uncles, and their spouses are already counted. For your grandchildren, there are your great-grandchildren, your grandchildren's spouses, and their parents have already been counted. Considering your siblings, the new ones to include are their spouses and their children. Considering your spouse's parents, you will need to add their parents and their children (more brother and sister-in-laws). Now considering your children's spouses, the parents of your spouses need to be added. Unless I missed someone, I think that this is it. Here is the new list.

  1. father, mother, spouse, child
  2. grandparents, grandchildren, siblings, mother-in-law, father-in-law, children's spouses
  3. great-grandparents, aunts, uncles, great-grandchildren, grandchildren's spouses, sibling's spouses (brother and sister in-laws), sibling's children (nieces and nephews), spouse's grandparents, spouse's siblings, children's spouse's parents.

Can you now extend this? How far are your cousins? What about your great uncle? What about your spouse's cousins or his/her aunts? See if you can do these. Below, we include distance 4 folks.

  1. father, mother, spouse, child
  2. grandparents, grandchildren, siblings, mother-in-law, father-in-law, children's spouses
  3. great-grandparents, aunts, uncles, great-grandchildren, grandchildren's spouses, sibling's spouses (brother and sister in-laws), sibling's children (nieces and nephews), spouse's grandparents, spouse's siblings, children's spouse's parents.
  4. great-great-grandparents, great-aunts, great-uncles, aunt's parents (those married in), uncle's parents (those married in), cousins, spouse's of great-grandchildren, great-great-grandchildren, grandchildren's spouse's parents, sibling's spouse's parents, spouses to nieces and nephews, children of nieces and nephews, spouses great-grandparents, spouse's aunts and uncles, spouse's sibling's spouses, spouse's nieces and nephews, children's spouse's grandparents, children's spouse's siblings

For a really nice calculator for relations, go to http://stevemorse.org/relation/calculator.html. While it doesn't calculate distances, it does give the name of a relationship. For example, what is the name of the relation of your cousin's (your father's sister's child) child to you? Go to this site, click on father, then sister, then daughter, then child. This shows that this is first cousin, once-removed.