Before starting, make sure you have igraph installed and loaded.

#install.packages("igraph")
library(igraph)
## 
## Attaching package: 'igraph'
## 
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## 
## The following object is masked from 'package:base':
## 
##     union
from_nodes = c("Anna", "Bob", "Bob", "Charlie", "Charlie", "Denise", "Denise", "Fred")

to_nodes = c("Bob", "Charlie", "Denise", "Denise", "Fred", "Fred", "Evan", "Gina")
el_m = matrix(c(from_nodes, to_nodes), ncol = 2)
el_g = graph.edgelist(el_m, directed = FALSE)

This last line should give you the igraph object description:

el_g
## IGRAPH UN-- 7 8 -- 
## + attr: name (v/c)
## + edges (vertex names):
## [1] Anna   --Bob     Bob    --Charlie Bob    --Denise  Charlie--Denise 
## [5] Charlie--Fred    Denise --Fred    Denise --Evan    Fred   --Gina

The number of nodes (7) and edges (8) are displayed along with the UN for undirected named node network.

Finally, plot your graph (with a few plotting modifications added):

plot.igraph(el_g, vertex.size = 45, vertex.label.color = "red", vertex.color = "gray", edge.color = "black")

Learn more at:

?igraph.plotting