[1][2] It can be constructed by joining 2 copies of the cycle graph C3 with a common vertex and is therefore isomorphic to the friendship graph F2.

The butterfly graph has diameter 2 and girth 3, radius 1, chromatic number 3, chromatic index 4 and is both Eulerian and a penny graph (this implies that it is unit distance and planar).

[3] A graph is bowtie-free if it has no butterfly as an induced subgraph.

Ando, Kaneko, Kawarabayashi and Yoshimoto proved that every k-vertex-connected bowtie-free graph has a k-contractible edge.

The characteristic polynomial of the butterfly graph is