You can do something similar. Take a look at the following function:
diagramsJHA[branch_Integer,level_Integer,opts:OptionsPattern[]]:=
KaryTree[Sum[branch^k,{k,0,level}],branch,
FilterRules[{opts}, Options[KaryTree]],
GraphLayout->"RadialEmbedding",
PlotTheme->"LargeGraph"
]
To understand how it works look up in docs every single function from this definition starting with KaryTree. Example with different branches and levels:
Grid[Table[diagramsJHA[b, l], {b, 2, 5}, {l, 4}]]
Example of a large diagram:
diagramsJHA[5, 5, ImageSize -> 1000]
