Calculate local clustering coefficient of a vertex

I found an example showing how to calculate LCC by hand (see image).

How can I replicate these steps in R? Focus is on finding the "Actual number of links among Neighbors" (middle step)

I would preferably have to calculate it by hand

*Does the igraph package provide this number?

Example adjacency matrix:

matrix(data = c(0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0), ncol = 4)

All of this can be done in igraph. It is nice that you gave an example, but since the graph is fully connected, all vertices have LCC=1. I decided to use a somewhat more complicated graph. I will go through the "by hand" part in detail for vertex 1.

Sample graph

library(igraph)

set.seed(1234)
g = erdos.renyi.game(5, 0.7)
LO = matrix(c(0,2,1,1,1,0,0,-1,1,0), nrow=5, ncol=2)
plot(g, layout=LO)

To start with, yes, igraph has a built-in function transitivity for LCC. For my sample graph, you can get this with

transitivity(g, type="localundirected")
[1] 0.6666667 0.0000000 0.3333333 0.3333333 0.6666667

But the main part of your question is the hand computation. The only things that you need from the graph are the first two steps - the Degree Centrality and the Actual Links Among Neighbors.

Degree Centrality is given by the degree function

degree(g)
[1] 3 2 3 3 3
degree(g, 1)        ## Vertex 1 only
[1] 3

As you suggested in your question, the only challenging part is the Actual Links Among Neighbors. You can get this by taking the subgraph induced by the neighbors of a point and then checking the number of edges. So for vertex 1 we get

ecount(induced_subgraph(g, neighbors(g, 1)))
[1] 2

Here is the full computation for vertex 1

(DC   = degree(g, 1))
[1] 3
>(ALAN = ecount(induced_subgraph(g, neighbors(g, 1))))
[1] 2
(MaxPoss = DC*(DC-1)/2)
[1] 3
(LCC = ALAN/MaxPoss)
[1] 0.6666667

which agrees with transitivity given above.