If you study graphs in which edges can link more than two nodes, you're more properly called a hyperedgelord.
This is the third comic on How to annoy people. Here Cueball annoys White Hat, a graph theory Ph.D., by calling him an edgelord.
The exact same setting, with different text, was later used in 2744: Fanservice, and 2654: Chemtrails also used the same setting except it is Ponytail that gets annoyed.
"Edgelord" is modern slang describing a brash, pretentious provocateur on social media, often provoking in a satirical way that if taken literally would be found disturbing or insensitive. The term derives from the word "edgy", which is used to describe things which are designed to be provocative. "Edgy" and "edgelord" are quite derogatory, carrying further implications of being style over substance, or having appeal only with rambunctious teenagers.
In mathematics, graph theory is the study of graphs, mathematical structures made up of nodes (points) which are connected by edges (or lines). This comic plays on the fact that graphs have edges. Calling someone with a graph theory Ph.D. an 'edgelord' (a master of edges) is somewhat analogous to calling an engineering student a 'forcelord', an astronomy Ph.D. a 'starlord', or a pharmacologist a 'druglord'.
In reply to being called an edgelord by Cueball, White Hat shouts "No" and clenches his fists in anger - which is ironic, as he seems to be on edge. Because "edgelord" is perceived as an insult by socially aware adults, Cueball is actually provoking White Hat, making Cueball an edgelord in this interaction. Similar situational humor is also found in 2008: Irony Definition.
The title text makes the same joke, except that the title would be hyperedgelord instead of edgelord. A hypergraph is a generalization of a graph in which each edge may have more than two endpoints. The term "hyper edge" could easily be considered stereotypically "edgy."