How Do I Generate the Graphs?

The graphs are just a way to visualize genetic distance. The idea behind genetic distance is that mutations are fairly uncommon, and when they do occur, one of the markers will change by one, either up or down. The number of mutations (and, therefore, some idea of the relationship closeness) is approximated by the genetic distance, which is mathematically the sum of the absolute values of the differences in corresponding markers. In simpler terms, subtract numbers for the same markers in two different people, treat the results as positive numbers, and add them.

I use a program to generate the graphs, but here's a description of how you could do it manually.

Step 1: Gather Your Data

For this example, here is the data being used. A smaller number of markers makes the example easier to work with. This is fictional data with an unrealistically small number of markers. Perhaps we're doing DNA tests on cockroaches, or only looking at a subset of the markers.

Name	Markers
	111	222	333	444	555	666
Andy	11	12	13	27	15	12
Bob	11	12	13	26	15
Charles	11	12	13	27	15	13
David	11	12	13	26	16	12
Frank	11	12	13	26
George	11	12	13	27
Harry	12	12	11	25	15

Step 2: Decide How Many Markers and Distance for the Graph

You can make a graph for any set of markers and distances 1 (don't create any intermediate nodes at all), 2, or 3. But you have to decide now. For this simplified example, I'll be using 5 markers and distance 1. The more markers you use, the more detail you get but you also lose people who didn't get the tests for those markers. The obvious values to use for Family Tree DNA tests are 12, 25, 37, and 67. You probably want to use all 4 values if all 4 types of tests are in the data.

Step 3: Throw Out Incomplete Data

Eliminate any people who don't have data for all the markers required. For this example, goodbye Frank and George. They would show up on a 3-marker graph.

Step 4: Group Identical Results

Find all of the people with identical markers, subject to the number of markers being used, and form groups of them. For our example, Andy and Charles have identical markers (marker 666 doesn't count, since we are only using 5 markers). So, our groups are (Andy and Charles), (Bob), and (David) and (Harry).

Step 5: Generate Intermediate Nodes

Intermediate nodes are created to force a connection between nodes that are "close enough to be interesting", but not of distance 1. (This is especially true of 37 and 67 marker FTDNA tests).

For a graph of distance 1, you don't create any intermediate nodes. For a graph of distance 2, you create intermediate nodes between each pair of original nodes that are distance 2. For a graph of distance 3, you create intermediate nodes between each pair of original nodes that are distance 2 or 3. Ignore nodes that duplicate the DNA of nodes you've already got.

If you're reading this for the first time, and don't need all the gory details, you might want to skip the rest of this section.

Normally, for two nodes of distance N, there are N*N-2 intermediate nodes to create. (2 nodes for distance 2 (looks like a square), 6 nodes for distance 3 (looks like a cube), and 14 nodes for distance 4 (resembles a 4-dimensional "cube", whatever that looks like). An exception to this happens when the difference involves a step of more than 1 in any single marker. Some of the intermediate nodes end up having the same DNA, so there are fewer of them when duplicates are removed.

You create intermediate nodes between pairs of nodes by noting which markers differ between the two. For example, the (Andy, Charles) node and the (David) node are distance 2 apart, and differ in markers 444 and 555. Now take the markers from the (Andy, Charles) node, change one of the markers one step towards the (David) node. Repeat for each of the other markers that are different. Now you've got nodes for 11:12:13:26:15 and 11:12:13:27:16. Compare these to existing nodes. 11:12:13:26:15 duplicates the node for Bob, so you don't need to create a new one. 11:12:13:27:16 is new, so give it a temporary name (e.g. t1) and add it to the list.

Step 6: Link Groups With Distance 1

Group (Andy and Charles) is distance 1 from group (Bob), so link these two (marker 444 is different). Group (Bob) is distance 1 from group (David), so link these two (marker 555 is different). If we're using the intermediate node t1, it's distance 1 from (Andy and Charles) and distance 1 from (David), so link these.

Step 7: Draw the Graph

Draw ovals for each group, label the group, and draw lines between each pair of linked groups. Label each line with the name of the marker that's different between the two. I use some free graph visualization software to come up with reasonable placement of the groups, but doing it by hand with a small number of groups is fairly simple. It's also not that hard to do for a graph with many small clusters of interconnected groups, and many isolated (entirely unconnected) groups.

Here's what the graph looks like for distance 1 (no intermediate nodes added):

And here's what the graph looks like for distance 2 (an intermediate node was added):

Interpreting the Graphs

People listed in the same node have the same DNA (for the given number of markers), as in Andy and Charles. People listed in connected nodes have a genetic distance of 1 (for the given number of markers), as in Andy and Bob. In the above graph, Andy and Charles are distance 2 from David, and are connected through Bob. This probably means that Andy and David are more distantly related than Andy and Bob or Bob and David, and that Andy and David's relationship is probably through Bob's ancestors. Harry's node is not connected, so it's distant from the others.