Quiz 2 - Algo’s in Networks

• Which two nodes in the network above have the greatest potential for brokerage?

  const <- constraint(g)
  invConstraint <- 1.125 - const  # (Inverse constraint = brokerage potential)
  
  round(invConstraint, 3)

  ## [1] 0.590 0.667 0.625 0.657 0.657 0.290 0.748 0.344

Nodes 2, 7 have the highest brokerage potential in Burts constraint

• How did you find them?

• Of the two, which do you think should be considered as having the greatest potential for brokerage? Why?

par(mar=rep(0,4))

E(g)$width <- edge_betweenness(g)


plot.igraph(g,
            edge.width = igraph::edge.betweenness(g)+1,              # The "+1" was added to make edgewidths non-zero.
            edge.color = heat.colors(igraph::edge.betweenness(g)+1), # The "+1" was added to make edgewidths non-zero.
            vertex.shape="sphere",  # Here, we are using sphere because it looks cool.
     
            vertex.size=20,
            vertex.label.font=2,    # Here, we are using bold font.
            vertex.color="lightgreen")

## Warning: `edge.betweenness()` was deprecated in igraph 2.0.0.
## ℹ Please use `edge_betweenness()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

There are no cutpoints in this small network

ap <- articulation_points(g)
cp <- as.list(ap)
Cut.Points <- names(cp)
cuts <- as.data.frame(Cut.Points)

cuts

Brokerage in Statnet

net <- asNetwork(g)

brokerage(net, cl=get.vertex.attribute(net, "party"))$raw.nli

##   w_I w_O b_IO b_OI b_O  t
## 1   4   0    0    0   0  4
## 2   4   0    0    0   0  4
## 3   2   0    0    0   0  2
## 4   8   0    0    0   0  8
## 5   8   0    0    0   0  8
## 6   0   0    0    0   0  0
## 7  10   0    0    0   0 10
## 8   0   0    0    0   0  0

    w_I is a coordinator role (A -> A -> A)
    w_O is an “itinerant broker” (or a Consultant) (A -> B -> A)
    b_{IO} is a representative (A -> B -> B)
    b_{OI} is a gatekeeper (A -> A -> B)
    b_O is a liaison (A -> B -> C)
    t is simply the total number of times a node fills any of the above roles.