Is make_line_graph() in rigraph the same as in Mathematica, or as defined in the C-library?

Usage
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1

Note that,

library(igraph)
g   <- graph(~ A--B)
gll <-make_line_graph(make_line_graph(g))

gives an empty graph. where I would expect g.

See also:
(1) https://igraph.org/c/pdf/latest/igraph-docs.pdf, page 651.
(2) igraph R manual pages

2

The result makes sense to me:

  • g has a single edge
  • Therefore L(g) has a single vertex, and no edges
  • Since L(g) has no edges, L(L(g)) cannot have any vertices

Why do you think L(L(g)) should be the same as g?

3

However, some things in how line graphs are computed seem inconsistent to me. I just opened this issue: Should loop edges be considered self-adjacenct for the purpose of line-graph computation? · Issue #2524 · igraph/igraph · GitHub

4

I was thinking as follows:

Let g <- graph(~ a--b, simplify=FALSE).
I expected L(g) to be a single vertex with two loops for each distinct endpoint in g an edge, like:
Lg <- graph(~ ab--ab, ab--ab, simplify=FALSE). Strictly speaking, this is not a simple graph but a pseudograph.
By applying L(Lg), I expected to retrieve g.

At a later point I learned that loops in simple undirected graphs are not part of the standard definition of line graphs.
See:
(1) line_graph — NetworkX 3.2.1 documentation.
(2) Spectra of Graphs, p.18.