Q:

Get node descendants in a tree graph

I have a directed graph (grafopri1fase1) the graph has no loops and it has a tree structure (not binary tree).
I have an array of nodes (meterdiretti) that i have extracted from the graph (grafopri1fase1) matching a condition.
I would like to know starting from each node of Meterdiretti how many nodes are under each node of Meterdiretti.
The result I would like to have is a Matrix with the following format 
first column------------     second column       
meterdiretti[1] -------- total amount of nodes reachable starting from meterdiretti[1] 

meterdiretti[2] -------- total amount of nodes reachable starting from meterdiretti[2] 

.... 

meterdiretti[n]  ----------total amount of nodes reachable starting from meterdiretti[n]

A:

Take a punt at what you want - it would be good if you could add a reproducible example to your question.
I think what you want is to count the descendents of a node. You can do this with neighborhood.size and mode="out" argument.
library(igraph)

# create a random graph
g <- graph.tree(17, children = 2)
plot(g, layout=layout.reingold.tilford)

# test on a single node    
neighborhood.size( g, vcount(g),  "1", "out") - 1
# [1] 16

# apply over a few nodes
neighborhood.size( g, vcount(g),  c(1,4,7), "out") - 1
[1] 16  4  2

