14.11 Higher-Order Neighbors

If we wish to create an object showing to neighbours, where $i$ is a neighbour of $j$, and $j$ in turn is a neighbour of $k$, so taking two steps on the neighbour graph, we can use nblag (automatically removes $i$ to $i$ self-neighbours)

nb_q |> nblag(2) -> nb_q2

Returning to the graph representation of the same neighbour object, we can ask how many steps might be needed to traverse the graph?

igraph::diameter(g1) #where g1 is a graph object

## [1] 52

We step out from each observation across the graph to establish the number of steps needed to reach each other observation by the shortest path (creating an $n \times n$ matrix sps), once again finding the same maximum count.

g1 |> shortest.paths() -> sps

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

sps |> apply(2, max) -> spmax

spmax |> max()

## [1] 52

The municipality with the maximum count is called Lutowiska, close to the Ukrainian border in the far south east of the country.

mr <- which.max(spmax)
pol_pres15$name0[mr]

## [1] "Lutowiska"

pol_pres15$sps1 <- sps[,mr]
tm_shape(pol_pres15) +
          tm_fill("sps1", title = "Shortest path\ncount")