fullerene_structures — Fullerene molecular structures (2017)

Description

Fifteen molecular graphs of fullerenes, closed-cage molecules made only of carbon atoms, with sizes from 60 atoms (C60, buckminsterfullerene) to 6000 atoms. Nodes are carbon atoms and undirected edges are the chemical bonds between them; as in every fullerene graph, each atom is bonded to exactly three others, and the bonds form 12 pentagonal and otherwise hexagonal rings. The graphs were assembled by S. Aref and M. C. Wilson from published three-dimensional atomic coordinates (the Yoshida fullerene library and a collection of icosahedral fullerenes), and published in a collection of networks used in their study of balance and frustration in signed networks (Aref and Wilson, 2019), where they were used to compute the bipartite edge frustration and other bipartivity measures, which have been proposed as indicators of the chemical stability of fullerenes. Each network is named after the molecular formula of the fullerene (e.g. C240). The other networks of the same collection are in the entries lazy_portfolios, cow_signed_relations, signed_biological and signed_social_relations; the atomic coordinates from which the graphs were built are also part of the collection but are not included.

The networks have the following properties:

(Node) label: the index of the atom in the source file.
(Edge) weight (edges): always 1.

Tags

Chemical Unweighted Spatial

Added

2020-08-11

Citation

S. Aref and M. C. Wilson, "Balance and frustration in signed networks." J. Complex Networks 7(2), 163–189 (2019) 10.1093/comnet/cny015 Sci-Hub

Upstream URL 403

https://doi.org/10.6084/m9.figshare.5700832

Upstream license

Creative Commons Attribution 4.0 International (CC BY 4.0), https://creativecommons.org/licenses/by/4.0/

Networks

Tip: click on a column header to sort the list, or hover over it for a description.

Column legend

$\left<k\right>$: Mean degree
$\sigma_k$: Standard deviation of the degrees
$\lambda_h$: Largest eigenvalue of the Hashimoto (non-backtracking) matrix
$\tau$: Random walk mixing time
$r$: Degree assortativity
$c$: Global clustering coefficient
$\oslash$: (Pseudo-) diameter
$S$: Relative size of the largest component
NPs: Node properties
EPs: Edge properties

Name	Nodes	Edges	$\left<k\right>$	$\lambda_h$	$\tau$	$r$	$\oslash$	$S$	Kind	Mode	NPs	EPs	gt	GraphML	GML	csv
C1500	1,500	2,250	3.00	2.00	310.00	nan	49	1.00	Undirected	Unipartite	label	weight	29 KiB	40 KiB	38 KiB	32 KiB
C180	180	270	3.00	2.00	36.74	nan	17	1.00	Undirected	Unipartite	label	weight	4 KiB	6 KiB	5 KiB	4 KiB
C2160	2,160	3,240	3.00	2.00	446.60	nan	59	1.00	Undirected	Unipartite	label	weight	40 KiB	55 KiB	53 KiB	47 KiB
C240	240	360	3.00	2.00	49.17	nan	19	1.00	Undirected	Unipartite	label	weight	5 KiB	7 KiB	7 KiB	6 KiB
C260	260	390	3.00	2.00	53.31	nan	19	1.00	Undirected	Unipartite	label	weight	6 KiB	7 KiB	7 KiB	6 KiB
C2940	2,940	4,410	3.00	2.00	608.03	nan	69	1.00	Undirected	Unipartite	label	weight	55 KiB	75 KiB	73 KiB	63 KiB
C320	320	480	3.00	2.00	65.74	nan	23	1.00	Undirected	Unipartite	label	weight	7 KiB	9 KiB	8 KiB	7 KiB
C3840	3,840	5,760	3.00	2.00	794.30	nan	79	1.00	Undirected	Unipartite	label	weight	72 KiB	97 KiB	96 KiB	82 KiB
C4860	4,860	7,290	3.00	2.00	1005.39	nan	89	1.00	Undirected	Unipartite	label	weight	90 KiB	124 KiB	123 KiB	107 KiB
C500	500	750	3.00	2.00	103.01	nan	29	1.00	Undirected	Unipartite	label	weight	10 KiB	13 KiB	13 KiB	11 KiB
C540	540	810	3.00	2.00	111.29	nan	29	1.00	Undirected	Unipartite	label	weight	11 KiB	15 KiB	14 KiB	12 KiB
C6000	6,000	9,000	3.00	2.00	1241.32	nan	99	1.00	Undirected	Unipartite	label	weight	111 KiB	156 KiB	154 KiB	130 KiB
C60	60	90	3.00	2.00	11.82	nan	9	1.00	Undirected	Unipartite	label	weight	2 KiB	3 KiB	2 KiB	2 KiB
C720	720	1,080	3.00	2.00	148.56	nan	35	1.00	Undirected	Unipartite	label	weight	14 KiB	18 KiB	18 KiB	16 KiB
C960	960	1,440	3.00	2.00	198.23	nan	39	1.00	Undirected	Unipartite	label	weight	19 KiB	26 KiB	25 KiB	21 KiB

Ridiculograms^*

^* These are automatically generated force-directed visualizations, and can be quite meaningless for networks both big and small. They should not be taken seriously as sources of scientific insight. See here for a discussion.