Talk:Signed graph

This article could really use some illustrations

I'm trying to follow the text as closely as possible, but I find it hard to bring any understanding to the material without some illustrations. Is this article unusual, or is this problem common? I would think someone who could provide the text would also be able to provide some illustrations, if only of their own understanding. Kinda puzzling. --TheLastWordSword (talk) 16:55, 27 December 2010 (UTC)

It makes sense to ask for illustrations, but someone who knows how to write WP text may not know how to prepare WP illustrations. Such as me. Will someone help? Zaslav (talk) 09:47, 20 January 2011 (UTC)

The "Examples" section is not comprehensible

The terms loop, negative loop, and half-edge must be defined. A well-labeled illustration, as Zaslav suggests above, could help.

Arthur.Goldberg (talk) 20:21, 2 April 2020 (UTC)

Orientation

Sections called Adjacency matrix, Orientation, Incidence matrix and Switching were deleted as impertinent to this article. No references were given and wikilinks were unhelpful. This is a large deletion and invites comment. Rgdboer (talk) 03:53, 26 March 2022 (UTC) The sections claim to relate to Lie algebra classification C_n:

The sections are highly pertinent. I do not understand your objection. I will restore the sections if you do not explain. Zaslav (talk) 20:59, 12 January 2023 (UTC)

Examples

• The complete signed graph on n vertices with loops, denoted by ±K_n^o, has every possible positive and negative edge including negative loops, but no positive loops. Its edges correspond to the roots of the root system C_n; the column of an edge in the incidence matrix (see below) is the vector representing the root.
• The complete signed graph with half-edges, ±K_n', is ±K_n with a half-edge at every vertex. Its edges correspond to the roots of the root system B_n, half-edges corresponding to the unit basis vectors.
• The complete signed link graph, ±K_n, is the same but without loops. Its edges correspond to the roots of the root system D_n.
• An all-positive signed graph has only positive edges. If the underlying graph is G, the all-positive signing is written +G.
• An all-negative signed graph has only negative edges. It is balanced if and only if it is bipartite because a circle is positive if and only if it has even length. An all-negative graph with underlying graph G is written −G.
• A signed complete graph has as underlying graph G the ordinary complete graph K_n. It may have any signs. Signed complete graphs are equivalent to two-graphs, which are of value in finite group theory. A two-graph can be defined as the class of vertex sets of negative triangles (having an odd number of negative edges) in a signed complete graph.

These "examples" do not illustrate the article. Rgdboer (talk) 04:05, 26 March 2022 (UTC)

They are examples of signed graphs. I do not understand your objection. Zaslav (talk) 20:57, 12 January 2023 (UTC)

The tables at root system do not represent graphs as they are not endorelations. The signed graph structure is a definite system, not just a table with +1 and −1 entries. It is suggested that you try to fit a link to this article into that one if you think it fits. But still, no references have been provided! Rgdboer (talk) 04:35, 13 January 2023 (UTC)

Is your objection the lack of references? I can provide a reference for all these. As for tables at root system, I'm not sure what you mean; there is no reference to any tables at root system. Maybe you mean there is some confusion about how the incidence matrix connects to the root system. This can be omitted. Zaslav (talk) 07:37, 2 March 2023 (UTC)

By the way, a graph is not an "endorelation". There are several reasons, e.g., lack of direction, multiple edges, self-loops. But this is a side issue. Zaslav (talk) 07:41, 2 March 2023 (UTC)

See Root systems#Explicit construction of the irreducible root systems for tables containing 0s, 1s, and −1s. They are tables but not signed graphs. There does not appear to be a connection between Lie algebra root systems and signed graphs. — Rgdboer (talk) 01:16, 3 March 2023 (UTC)