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Engrima18/cayley-graphs-384-to-447

Cayley Graphs — orders 384–447 This dataset contains Cayley graphs of finite groups: one row per group, covering groups whose order is between 384 and 447. Each graph is the Cayley graph built from the group's minimal generating set (see Provenance below). Rows (groups): 21,814 Group orders covered: 384–447 (64 distinct orders) Task: binary graph classification (default label: IsMonolithic). About the CayleyNet collection This dataset is part of a census of 131… See the full description on the dataset page: https://huggingface.co/datasets/Engrima18/cayley-graphs-384-to-447.

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Cayley Graphs — orders 384–447

This dataset contains Cayley graphs of finite groups: one row per group, covering groups whose order is between 384 and 447. Each graph is the Cayley graph built from the group's minimal generating set (see Provenance below).

—Rows (groups): 21,814
—Group orders covered: 384–447 (64 distinct orders)
—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`	139	0.64%
`IsNilpotent`	2,589	11.87%
`IsSimple`	10	0.05%
`IsPerfect`	0	0.00%
`IsSolvable`	21,813	100.00%
`IsMonolithic`	157	0.72%
`IsCyclic`	64	0.29%

Numeric column statistics

Column	Min	Mean	Max
`GroupOrder`	384	386.8	447
`GroupIndex`	1	9,341	20,169
`MinNumOfGens`	1	3.636	7
`NumEdges`	389	3,032	3,072

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