Characterizing structure of cross-disciplinary impact of global disciplines: A perspective of the Hierarchy of Science

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Descriptive statistics of the bibliometric features of the 19 0-level disciplines_

Category	Variable	Mean	Std	Min	Max
Hardness	Number of authors	6.566	10.756	1	97
	Number of references	78.101	79.820	1	8,724
	Number of cited disciplines	5.216	2.059	1	19
	Citation distribution	1.980	0.329	0	2.964
	Price index	0.022	0.023	0	1
Citation dynamic	First citation year	1.339	1.509	0	5
	First citation count	4.990	29.901	1	7,848
	First peak year	2.132	2.068	0	5
	First peak Citation count	10.001	33.349	1	7,848

Regression results for the structure of cross-disciplinary impact, as well as the balance and disparity of cross-disciplinary impact_

Variable	Model 1 - variety		Model 2 - balance		Model 3 - disparity
	B	Sig.	B	Sig.	B	Sig.	VIF
Number of authors	-0.006	0.745	0.016	0.411	0.026	0.411	1.935
Number of references	1.700	0.000***	1.170	0.001***	-1.113	0.001***	5.672
Number of cited disciplines	2.405	0.000***	1.992	0.000***	-1.005	0.000***	4.315
Citation distribution	12.722	0.001***	7.770	0.000***	-2.160	0.000***	4.778
Price index	23.584	0.001***	1.013	0.900	7..713	0.900	3.954
First citation year	1.909	0.371	-0.482	0.577	0.244	0.577	2.047
First citation count	-0.016	0.769	0.049	0.368	-0.460	0.368	3.126
First peak year	-0.353	0.214	-0.066	0.774	-0.095	0.774	2.372
First peak citation count	-0.004	0.912	-0.069	0.026	0.610	0.026	3.579
Observations	291		291		291
Intercept	29.3		12.4		-3.93
R2	0.784		0.509		0.473

Result of robust check for the structure of cross-disciplinary impact_

Variable	Model 4 - variety		Model 5 - balance		Model 6 - disparity
	B	Sig.	B	Sig.	B	Sig.
Number of authors	-0.011	0.708	0.015	0.392	0.027	0.337
Number of references	1.577	0.000***	1.453	0.000***	-1.08	0.000***
Number of cited disciplines	2.418	0.000***	1.987	0.000***	-0.912	0.000***
Citation distribution	12.174	0.000***	7.81	0.001***	-2.35	0.000***
Price index	24.548	0.001***	1.128	0.889	8.727	0.814
First citation year	1.416	0.483	-0.467	0.571	0.361	0.557
First citation count	-0.065	0.796	0.047	0.366	-0.024	0.459
First peak year	-0.347	0.236	-0.061	0.768	-0.084	0.762
First peak citation count	-0.017	0.816	-0.0703	0.025	0.563	0.121
Observations	291		291		291
Intercept	27.625		10.975		-3.615
R2	0.786		0.522		0.470

The selected bibliometric indicators of publications_

Aspect	Variable	Definition	Key refs.
Hardness	Number of authors xauthor	The number of authors who wrote the publication.	(Zuckerman & Merton, 1973)
	Number of references xreference	The number of references listed in the publication.	(Skilton, 2006)
	Number of cited disciplines xdiscipline	The number of disciplines corresponding to the references in the publication.	(Leydesdorff & Probst, 2010)
	Citation distribution xdistribution	The Shannon entropy of disciplines corresponding to the references in the publication.	(Leydesdorff & Probst, 2010)
	Price index xprice	The ratio of citation counts of papers published for no more than five years to total citation counts.	(Price, 1970)
		Price= citationn<5 citationn≥0${\rm{Price}} = {{{\rm{citatio}}{{\rm{n}}_{n 5}}} \over {{\rm{citatio}}{{\rm{n}}_{n \ge 0}}}}$
Citation dynamic	First citation year xfirst_year	The year between the publication of the paper and its first citation.	(Min et al., 2018)
	First citation count xfirst_count	Citation counts in the year of its first citation.	(Min et al., 2018)
	First peak year xpeak_year	The year between the publication of the paper and the first citation peak.	(Min et al., 2021)
	First peak citation count xpeak_count	Citation counts in the first citation peak.	(Min et al., 2021)