Intersection of random spanning trees in complex networks

Applied Network Science

Table 1 Network statistics and random spanning tree intersection values of some real-world network. Data sources: Mark Newman’s network data, Network Repository, Kunegis (2013), Stanford Large Network Dataset Collection

network	n	m	ρ	cc	\({\overline{\ell }}\)	Min. exp.	Obs. mean	RTI
Florentine	15	20	0.190	0.191	2.486	9.8	10.5 (0.888)	0.166
Zachary	34	78	0.140	0.256	2.408	13.961	15.00 (2.291)	0.052
Dolphins	62	159	0.084	0.309	3.357	23.40	28.34 (2.19)	0.131
Iceland	75	114	0.041	0.157	3.200	48.035	57.21 (2.08)	0.353
Adjnoun	112	425	0.068	0.157	2.535	29.00	38.8 (4.3)	0.120
Jazz	198	2742	0.141	0.520	2.235	14.15	23.51 (3.66)	0.051
C-elegans	297	2148	0.049	0.180	2.455	40.79	57.8 (5.5)	0.067
NetSci	379	914	0.013	0.431	6.042	156.328	182.12 (7.98)	0.116
Wiki-Vote	889	2914	0.007	0.127	4.096	270.61	430.47 (9.66)	0.259
EuroRoad	1039	1305	0.002	0.035	18.395	825.63	853.5 (7.07)	0.131
Polblogs	1222	16717	0.022	0.226	2.737	89.18	300 (10.55)	0.186
Arxiv GR-QC	4158	13428	0.002	0.629	6.053	1287	2102 (21.65)	0.284
Erdős	4491	7428	0.0006	0.042	5.51	3352	4160 (17.45)	0.493
Power grid	4941	6594	0.0005	0.103	18.99	3700.87	3921 (16.71)	0.178
Email-Enron	33696	180811	0.0003	0.085	4.025	6279.225	16602 (64.73)	0.376