How can i plot an undirected connected graph in R?

I want to plot graph (which is an undirected connected graph) like the uploaded picture.

I want to use the adjacency matrix in order to plot it.

So my question is how can I plot a graph from its adjacency matrix.

Ideally I want the plot to look like the attached picture.

I tried the igraph package in R :

data <- matrix(c(0,1,0,0,1,
                 1,0,1,0,0,
                 0,1,0,1,0,
                 0,0,1,0,1,
                 1,0,0,1,0),nrow=5,ncol = 5)
colnames(data) = rownames(data) = LETTERS[1:5]
data

network <- graph_from_adjacency_matrix(data)


plot(network)

But it creates a cycle.

Any help ?

You need only the upper (or lower) triangle of the matrix to be 1, but 0 elsewhere. Make sure you also set mode = "upper"

library(igraph)

data <- matrix(0, 5, 5, dimnames = list(LETTERS[1:5], LETTERS[1:5]))
data[upper.tri(data)] <- 1

data
#>   A B C D E
#> A 0 1 1 1 1
#> B 0 0 1 1 1
#> C 0 0 0 1 1
#> D 0 0 0 0 1
#> E 0 0 0 0 0

network <- graph_from_adjacency_matrix(data, mode = 'upper')

plot(network)

Or, if you want a much more customized appearance (I think your sketch has a nicer aesthetic than the default igraph plot), use ggraph:

library(ggraph)

ggraph(network) +
  geom_edge_link(aes(label = paste0('a', 1:10)), angle_calc = 'along',
                 vjust = -0.5, label_colour = 'red') +
  geom_node_circle(aes(r = 0.1), fill = "#dbdccf") +
  geom_node_text(aes(label = name), color = 'blue4', fontface = 2,
                 size = 8) +
  coord_equal() +
  theme_graph() +
  theme(plot.background = element_rect(color = NA, fill = "#f5f6e9"),
        panel.grid.major.y = element_line(size = 0.5, color = 'gray90'),
        panel.grid.minor.y = element_line(size = 0.5, color = 'gray90'))