Halide perovskite materials are intensively studied with respect to their optoelectronic properties, in the quest for novel stable and reliable solar cell materials. Computational methods complement experimental data adequately but the associated computational costs and the extremely large number of potential materials, call for shortcuts that can narrow down our search, in the form of trustable structure-property correlations. Here, we employ graph theory to extract quantitative descriptors of the crystal structure, and correlate them with physical properties. In particular, we use atom-atom proximity to define adjacency relations and to map the structure of selected halide perovskite compounds to graphs preserving their topology. These graphs are processed according to the concept of equitable partition or, alternatively, on the basis of chemical composition, to derive the corresponding quotient graphs. We calculate the spectra of all these graphs and compute an appropriately defined compression ratio that compares the original graph with its equitable partition and quantifies the symmetry and regularity of the former. Important spectral information as the Perron-Frobenius and Fiedler eigenvalues, as well as the compression ratio, are compared with measured physical properties and interesting correlations come to the fore. These observations may pave the way to novel structure-property relation schemes allowing the prediction of properties and, ideally, identify the best materials for optoelectronic devices.

1.
A. M.
Glazer
,
Acta Cryst.
B28
,
3384
3392
(
1972
).
2.
J. Y.
Kim
,
J.-W.
Lee
,
H. S.
Jung
,
H.
Shin
, and
N.-G.
Park
,
Chem. Rev.
120
,
7867
7968
(
2020
).
3.
X.
Li
,
J. M.
Hoffman
, and
M. G.
Kanatzidis
,
Chem. Rev.
121
,
2230
2291
(
2021
).
4.
P.
Roy
,
N. K.
Sinha
,
S.
Tiwari
, and
A.
Khare
,
Solar Energy
198
,
665
688
(
2020
).
5.
A.
Kaltzoglou
,
M.
Antoniadou
,
A. G.
Kontos
,
C. C.
Stoumpos
,
D.
Perganti
,
E.
Siranidi
,
V.
Raptis
,
K.
Trohidou
,
V.
Psycharis
,
M. G.
Kanatzidis
, and
P.
Falaras
,
J. Phys. Chem. C
120
,
11777
11785
(
2016
).
6.
N.
Trinajstić
,
Chemical Graph Theory
(
CRC Press
,
Boca Raton, Ann Arbor, London, Tokyo
,
1992
).
7.
S.
Wagner
and
H.
Wang
,
Introduction to Chemical Graph Theory
(
CRC Press, Taylor & Francis Group
,
Boca Raton, Florida, U.S.A
.,
2019
).
8.
M. A.
Spackman
and
D.
Jayatilaka
,
CrystEngComm
11
,
19
32
(
2009
).
9.
F. R. K.
Chung
,
Spectral Graph Theory
(
American Mathematical Society
,
Fresno, California, U.S.A
.,
1994
).
10.
M.
Fiedler
,
Czechoslov. Math. J.
23
,
298
305
(
1973
).
11.
D.
Cardoso
,
C.
Delorme
, and
P.
Rama
,
Eur. J. Comb.
28
,
665
673
(
2007
).
12.
D. M.
Cvetković
,
M.
Doob
, and
H.
Sachs
,
Spectra of Graphs
(
Academic Publisher
,
1980
).
13.
D. M.
Cvetković
,
P.
Rowlinson
, and
S.
Simić
,
An Introduction to the Theory of Graph Spectra
(
Cambridge University Press
,
Cambrdige, U.K
.,
2010
).
14.
D.
Krob
,
J.
Mairesse
, and
I.
Michos
,
Discrete Math.
273
,
131
162
(
2003
).
15.
N.
O’Clery
,
Y.
Yuan
,
G.-B.
Stan
, and
M.
Barahona
,
Phys. Rev. E 88
, p.
042805
(
2013
).
16.
A.
Bondi
,
J. Phys. Chem.
68
,
441
451
(
1964
).
17.
M.
Mantina
,
A. C.
Chamberlin
,
R.
Valero
,
C. J.
Cramer
, and
D. G.
Truhlar
,
J. Phys. Chem. A
113
,
5806
5812
(
2009
).
18.
S. S.
Batsanov
,
Inorg. Mater.
37
,
1031
1046
(
2001
).
19.
S.
Alvarez
,
Dalton Trans.
42
,
8617
8635
(
2013
).
20.
T.
Hahn
(ed.),
International Tables of Crystallography. Brief Teaching Edition of Vol. A: Space Group Symmetry
(
John Wiley & Sons
,
Chichester, U.K
.,
2014
).
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