Table 4.

The spectral radius Λ₁ and its bounds B₁, B₂ and B₃ based on the sum of all walks of length one, two and three respectively. Bounds b₁ and b₂ obtained from local walks from the core, or from the local connectivity of the core nodes. The entries $r_c^{\left(1\right)}$ and $r_c^{\left(2\right)}$ are the number of nodes that constitute the core obtained from b₁ and b₂. The entry N is the total number of nodes in the network.

Network	B1	B2	B3	BM	b1	b2	Λ1	${\mathit{r}}_{\mathit{c}}^{\mathbf{(}\mathbf{1}\mathbf{)}}$	${\mathit{r}}_{\mathit{c}}^{\mathbf{(}\mathbf{2}\mathbf{)}}$	N
Nouns	7.58	10.22	10.94	12.66	9.30	11.34	13.15	49	66	112
Airports	11.92	25.32	30.49	44.77	38.02	42.70	48.07	71	71	500
C. elegans	16.40	20.62	21.82	24.58	17.99	21.22	25.94	172	197	279
Dolphins	5.12	5.90	6.17	6.75	6.04	6.46	7.19	41	39	62
Football	10.66	10.69	10.71	10.74	10.66	10.69	10.78	115	115	115
Hep-Th	4.13	5.99	7.25	11.00	9.82	15.05	23.00	70	70	7610
Karate	4.50	5.97	5.98	6.50	5.00	5.98	6.72	22	33	34
Les Miss	6.59	8.91	9.59	11.20	10.00	10.97	12.00	28	24	77
Net Sci	4.82	6.21	6.64	7.62	5.69	7.19	10.37	192	4	379
Political blog	27.31	47.11	53.21	69.08	54.45	63.16	74.08	323	321	1224
Political book	8.40	10.01	10.46	11.48	8.85	10.33	11.93	68	68	105
Power	2.66	3.21	3.42	3.87	2.88	4.44	7.48	3715	32	4941
Protein	6.30	12.34	13.54	17.38	12.86	16.79	21.16	733	1	4713
AS-Internet	4.18	33.35	28.51	41.81	20.20	48.97	60.32	77	2	11174