To Do

1. (DONE) Put -1 into database for BYUID if we create the record (marriage and person)
2. Finish abstract tonight, send out a copy tomorrow to Kathleen, Joseph, and Worthy
   • If no other comments, submit by Sunday.
3. Write scripts to suck BYU data into our database
4. Toolbag of interesting measures (see below)

Discussion

• We want to really look at these measures over evolutionary graphs
  • Get a large toolbag of interesting measures first, then worry about the efficiencies and computational complexity later.
  • In fact, we want to grab any interesting measures we can think of, which might be interesing to computer scientists and others, then pass our ideas by Kathleen and see what she think is interesting to her project.
• What do we mean by time interval, when looking at measures over time?
  • Absolute time interval OR number of changes the node/edge underwent?
  • Do we look at “one month” or “three changes” of an object
  • What does number of changes mean for a graph?
    • 3 changes
      • For one node, this might be a week of absolute time
      • For another, it might be a decade of absolute time
    • How do we deal with edges in this case, which might not overlap in the “number of changes,” but may actually have an overlap temporally?
  • For the rest of this note, interval may refer to either.

Toolbox of Evolutionary Measures

1. Degree (in/out) over an interval
   • Maximum degree for that time interval
   • Minimum degree for that time interval
   • Change in degree
     • Average degree over the interval
     • $\Delta degree$: Graph the function degree x time, then take the derivative.
     • Rate of change of the degree (or acceleration of degree)
       • Node X was growing the most (highest $\delta$out-degree – having the most children) during time interval Y.
       • Node X was marrying the most (highest $\delta$in-degree – most new incoming wives) during time interval Y.
     • Total increase (or decrease) in degree (think total elevation change in gps)
2. Connectivity
   • Explaining by example for now:
     • We have these two notions, Sankey diagrams of marriages (geneological flow), and collections of people in church organizations (annointed quorum). Both of which change over time.
     • Question: what is the driver? Does family structure drive church organization, or church organization drive family structure?
     • Take the subgraphs (lineage) for each person in a church organization (Ex: BY, JS, …), with their descendants
       • There will be some connectedness, likely in the individual descendant Sankey diagrams
     • “Join” all the subgraphs for that group.
       • Note: each subgraph is evolutionary, so it changes over time.
       • Basically connect back up the person links that exist between those subgraphs just considered.
     • Answer: How does the connectedness change over time in this new graph? Does the connectedness increase (positive derivative)? Does the connectedness (number of connections within the graph) remain the same? Does it increase and then decrease?
       
       • If church drives family, we would expect increasing connectedness. They are interconnecting based on hierarchy faster than normal.