Degree of order n of a graph

I'd like to calculate the number of adjacent edges in an extra step of the degree() function. This would be a degree() of order 2, for example.

For example, the graph on the left illustrates the classic degree() function, but I'm looking for an additional level of degree() (graph on the right). The degree() of vertex "1" corresponds to 2 but the additional level is 5. Is there a way of calculating this degree of order n for each vertex?

Code:
g1 <- graph(edges=c(1,2,1,3,2,3,3,5,2,4,4,5,5,6,4,6,4,7,6,7),n=7,directed=F)
plot(g1)

I guess you can try ego

> ego(g1, 2)
[[1]]
+ 5/7 vertices, from 47df27b:
[1] 1 2 3 4 5

[[2]]
+ 7/7 vertices, from 47df27b:
[1] 2 1 3 4 5 6 7

[[3]]
+ 6/7 vertices, from 47df27b:
[1] 3 1 2 5 4 6

[[4]]
+ 7/7 vertices, from 47df27b:
[1] 4 2 5 6 7 1 3

[[5]]
+ 7/7 vertices, from 47df27b:
[1] 5 3 4 6 1 2 7

[[6]]
+ 6/7 vertices, from 47df27b:
[1] 6 4 5 7 2 3

[[7]]
+ 5/7 vertices, from 47df27b:
[1] 7 4 6 2 5

or ego_size

> ego_size(g1,2)
[1] 5 7 6 7 7 6 5