Recent decades have brought growing interest in the study of a
structure of surgery graphs of low-dimensional objects. After giving a
brief introduction to the theory of Dehn surgery we present a recently
discovered geometric pattern in the Big Dehn Surgery Graph, following
the ideas of Hirasawa and Uchida. The argument combines classic
Kirby calculus tricks with Johannes’ result on the Casson–Walker–
Lescop invariant.