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Engrima18/cayley-graphs-256

Cayley Graphs — order 256 This dataset contains Cayley graphs of finite groups: one row per group, covering groups of order 256. Each graph is the Cayley graph built from the group's minimal generating set (see Provenance below). Rows (groups): 56,092 Group orders covered: 256–256 (1 distinct order) Task: binary graph classification (default label: IsMonolithic). About the CayleyNet collection This dataset is part of a census of 131,406 Cayley graphs covering… See the full description on the dataset page: https://huggingface.co/datasets/Engrima18/cayley-graphs-256.

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Cayley Graphs — order 256

This dataset contains Cayley graphs of finite groups: one row per group, covering groups of order 256. Each graph is the Cayley graph built from the group's minimal generating set (see Provenance below).

—Rows (groups): 56,092
—Group orders covered: 256–256 (1 distinct order)
—Task: binary graph classification (default label: IsMonolithic).

About the CayleyNet collection

This dataset is part of a census of 131,406 Cayley graphs covering every finite group of order at most 767 (except order 512), built to study how finite-group structure is reflected in the network geometry of Cayley graphs. Each group is recorded with exact algebraic property labels alongside a broad collection of graph, cycle, distance, and spectral statistics. The census provides benchmarks for predicting group properties directly from graph data — comparing classical models, an MLP, and graph neural networks (GIN/GCN) — and contributes new OEIS sequences for monolithic groups and for groups generated by at most 3, 4, and 5 elements.

Code: https://github.com/Engrima18/CayleyNet

Columns

Column	Type	Description
`GroupOrder`	`int32`	Order of the finite group (first entry of the GAP SmallGroup id).
`GroupIndex`	`int32`	Index of the group among all groups of that order (second entry of the GAP SmallGroup id).
`AdjMatrixNonZerEnt`	`large_string`	Directed edge list of the Cayley graph as a JSON-style nested list `[[src, dst], ...]`; nodes are 0-indexed group elements.
`EdgeFeatures`	`large_string`	One-hot generator matrix of shape `[num_edges, num_generators]`; row `e` indicates which generator produced edge `e`.
`MinNumOfGens`	`int16`	Size of a minimal generating set of the group.
`IsAbelian`	`bool`	Whether the group is abelian.
`IsNilpotent`	`bool`	Whether the group is nilpotent.
`IsSimple`	`bool`	Whether the group is simple.
`IsPerfect`	`bool`	Whether the group is perfect (G = [G, G]).
`IsSolvable`	`bool`	Whether the group is solvable.
`IsMonolithic`	`bool`	Whether the group is monolithic, i.e. has a unique minimal normal subgroup. Primary classification label.
`IsCyclic`	`bool`	Whether the group is cyclic.

Group-property / label balance

Column	# True	% True
`IsAbelian`	22	0.04%
`IsNilpotent`	56,092	100.00%
`IsSimple`	0	0.00%
`IsPerfect`	0	0.00%
`IsSolvable`	56,092	100.00%
`IsMonolithic`	1,130	2.01%
`IsCyclic`	1	0.00%

Numeric column statistics

Column	Min	Mean	Max
`GroupOrder`	256	256	256
`GroupIndex`	1	2.805e+04	56,092
`MinNumOfGens`	1	4.398	8
`NumEdges`	2,048	2,048	2,048

Parsing the list-valued columns

AdjMatrixNonZerEnt and EdgeFeatures are stored as strings holding a JSON-style nested list. Decode them with:

python

import ast
edges = ast.literal_eval(row["AdjMatrixNonZerEnt"])   # [[src, dst], ...]
edge_feats = ast.literal_eval(row["EdgeFeatures"])    # one-hot [E, n_gens]

Provenance

—Generated with GAP / SageMath and NetworkX (scripts/generate_data.py).
—Distributed as typed Parquet: the source Id is split into GroupOrder and GroupIndex, and integer statistics are stored as nullable integers.

Usage