A graph of minimal distances between bent functions

A graph of minimal distances between bent functions is introduced as an undirected graph $(V, E)$, where $V$ is the set of all bent functions in $2k$ variables and $(f, g) \in E$ if the Hamming distance between $f$ and $g$ is equal to $2^k$ (it is the minimal possible distance between two bent functions). It is shown that its subgraph induced by all functions affine equivalent to the Maiorana—McFarland bent functions is connected.