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math.CO2023
Modularity and Graph Expansion
Baptiste Louf, Colin McDiarmid, Fiona Skerman
We relate two important notions in graph theory: expanders which are highly connected graphs, and modularity a parameter of a graph that is primarily used in community detection. M…
math.CO2023
On graphs with modularity zero or near-zero
Colin McDiarmid, Fiona Skerman
It is known that complete graphs and complete multipartite graphs have modularity zero. We show that the least number of edges we may delete from the complete graph to obtain…