Graphs: Nodes & Edges - Part I and II Kyle Hicks/Anthony Smith

Wednesday June 2, 2010 - Kyle Hicks began his presentation in the BiRG Lab by distilling the term “Dyad – two nodes and an edge”. It’s refreshing how Kyle boils the topic down to easy-to remember terms.  He next introduced us to the pioneers of graph & network theory, Jacob Moreno (1937).  Next Kyle hit us with homophily and contagion; “…love of the same…” and “…yours spreads to theirs…” Kyle described  Barack Obama’s  presidential campaign as effectively developing a contagion of popularity and  inferred that Barack was successful at claiming himself to be the ‘every man’ hence, “homophily will kick in to create networks between the “infected”, and was able to, “spread his awareness and popularity via social networks”.

Kyle continued with “forced-based algorithms (fba)”. One of the most popular; Fructerman-Reingold   layout is determined by the forces pulling nodes together and pushing them apart with each iteration of the applied algorithm, the forces are measured and the nodes settle into place. Another Kamada-Kawai, - relates the graph layout to a spring system the strength of a spring between two nodes is inversely proportional to the square of the shortest between those two nodes the stronger springs are translated as nodes connected by shorter edges. Kyle visually demonstrated the fba’s with a column of text data on the left and a “sociogram type diagram” a hexagon with a tail, representing ten of the column lines of text data which pictured the relationships vividly; people (node) relationship (edge).

Kyle concluded by stating an earlier thought about transitivity (the dyad adding another node and producing a trans - configuration around the double bonds), contagion, and homophily, “…work with each other to form and strengthen social networks”.  He added, “Visualization through network graphs allows informaticians to bring meaning out of the data.”

Part II of this discourse was offered by Anthony Smith beginning with James Joseph Sylvester in 1878 first using the term “graph - an abstract representation of a set of objects where some pairs of the objects are connected by links.” Anthony described three types of graphs, “ Simple  Graphs - at most one edge may connect any two vertices (nodes), and Multigraph - multiple edges, and Pseudograph - self-connected vertices and multiple edges.

Anthony presented further insights of an expanding network of dyads by using the term

Military Squad – A tightly interconnected group, the periphery being less and the center being more “embedded.”

Being a coordinated effort between Kyle and Anthony some of the same material was presented in both presentations, but both had uniqueness. One example was Anthony’s treatment of “Hubs - a number of nodes that are more connected than the others; they have far more lines connecting them with other nodes than the average node.”