Machine Learning/Kaggle Social Network Contest/Network Description

Here we can put the descriptive statistics of the network:

• Number of fully sampled nodes: 37,689
  • ie the unique "outnodes" in the edge list
• Total number of nodes: 1,133,547
• number of edges: 7,237,983

Conectivity

"A digraph is strongly connected if every vertex is reachable from every other following the directions of the arcs. On the contrary, a digraph is weakly connected if its underlying undirected graph is connected. A weakly connected graph can be thought of as a digraph in which every vertex is "reachable" from every other but not necessarily following the directions of the arcs. A strong orientation is an orientation that produces a strongly connected digraph." wikipedia

• The Graph is not weakly connected
• It contains 27 subgraphs This means that it can be broken down into at least two discrete subgraphs.
  • c.f. igraph clustering
  • There is one very large cluster containing all but 154 verticies, then 4 with size 10 - 37, 8 sized 3 - 7, 13 size 2 and one lonely dude.

• I also grabbed the number of strongly connected subgraphs

Cluster Size	1	2	3	4	5	9	10	32464
freq	1100647	162	18	5	4	1	1	1

• Diameter of the directed graph
  • This is the longest of the shortest directed paths between two nodes
  • R igraph
    • diameter (dg, directed = TRUE, unconnected = TRUE)
    • Was taking forever so I aborted (after 34 minutes...)
• Total number of direct neighbours out: 7 275 672, in: 508 688, all: 7 473 273
  • For each of our 38k I calculated the number of outbound neighbours and summed it
  • R igraph:
    • sum(neighborhood.size(dg, 1, nodes=myGuys, mode="out"))
    • mode = "in", "out" or "all"