An approach for determining and measuring network hierarchy applied to comparing the phosphorylome and the regulome

Table 1 Hierarchical scores of eight directed networks

Network	Nodes (n)	Edges (n)	Levels (n)	1-DR	KHS	GRC	HS	CHS	PHS	Significance ^a	Reference
Worm neural	297	2,359	L = 4	0.184	0.186	0.133	2.805	2.364	2.707	1.60 (30.72)	Watts et al. [45]
Political blogs	1,224	19,087	L = 3	0.487	0.514	0.130	3.044	3.177	2.972	2.23 (251.38)	Adamic et al. [3]
Yeast TF	149	580	L = 4	0.559	0.611	0.381	4.675	3.869	4.330	1.97 (22.32)	Harbison et al. [10]
Human TF	112	513	L = 4	0.631	0.718	0.336	7.087	5.608	5.848	3.15 (53.30)	Gerstein et al. [23]
P2P file sharing	6,301	20,777	L = 4	0.486	0.772	0.628	4.348	5.878	2.401	1.71 (74.06)	Ripeanu et al. [58]
Foodweb	63	612	L = 3	0.259	0.261	0.582	5.788	6.407	5.788	4.26 (190.38)	Ulanowicz et al. [46]
Human kinase	373	2,171	L = 4	0.492	0.798	0.020	14.087	13.396	12.874	7.16 (275.89)	Newman et al. [38]
Yeast kinase	94	200	L = 4	0.645	0.775	0.447	17.455	13.982	11.777	4.81 (41.73)	Ptacek et al. [11]

^aSignificance is calculated by comparing a network with 1,000 Erdos-Renyi random networks. The first number is the ratio of its HS to the average HS of the random networks. The second number in the parenthesis is the t-statistics of the HS. All networks listed in the table are significant (P <2e-16).
1-DR: 1-dyadic reciprocity; CHS: corrected hierarchy score; GRC: global reaching centrality; HS: hierarchy score; KHS: Krackhardt hierarchy score; PHS: probabilistic hierarchy score.

ISSN: 1474-760X