Effect of degree correlation on edge controllability of real networks

doi:10.1088/1674-1056/ab99ab

摘要/Abstract

Abstract:

We use the controllability limit theory to study impact of correlation between in- and out-degrees (degree correlation) on edge controllability of real networks. Simulation results and analytic calculations show that the degree correlation plays an important role in the edge controllability of real networks, especially dense real networks. The upper and lower controllability limits hold for all kinds of real networks. Any edge controllability in between the limits is achievable by properly adjusting the degree correlation. In addition, we find that the edge dynamics in some real networks with positive degree correlation may be difficult to control, and explain the rationality of this anomaly based on the controllability limit theory.

Key words: complex network, edge controllability, degree correlation, controllability limit

中图分类号: (Control theory)

02.30.Yy

89.75.Fb (Structures and organization in complex systems)

Shu-Lin Liu(刘树林), Shao-Peng Pang(庞少鹏). [J]. 中国物理B, 2020, 29(10): 100202-.

Shu-Lin Liu(刘树林) and Shao-Peng Pang(庞少鹏)†. Effect of degree correlation on edge controllability of real networks[J]. Chin. Phys. B, 2020, 29(10): 100202-.

图/表 6

Type	No.	Name	N	M	P	$ {n}_{{\rm{D}}}^{{\rm{real}}} $	$ {m}_{{\rm{D}}}^{{\rm{real}}} $	$ {n}_{{\rm{D}}}^{{\rm{rand}}} $	$ {m}_{{\rm{D}}}^{{\rm{rand}}} $	$ {n}_{{\rm{D}}}^{{\rm{U}}} $	$ {n}_{{\rm{D}}}^{{\rm{L}}} $	$ {m}_{{\rm{D}}}^{{\rm{U}}} $	$ {m}_{{\rm{D}}}^{{\rm{L}}} $
Regulatory	1	Ownership-USCorp^[28]	8497	6726	−0.031	0.136	0.924	0.086	0.848	0.159	0.028	1.000	0.738
	2	TRN-EC-2^[29]	423	578	−0.082	0.220	0.829	0.166	0.762	0.274	0.071	0.879	0.545
	3	TRN-Yeast-1^[30]	4684	15451	0.044	0.052	0.947	0.049	0.947	0.064	0.025	0.984	0.803
	4	TRN-Yeast-2^[29]	688	1079	–0.236	0.177	0.952	0.138	0.841	0.190	0.063	0.968	0.610
Trust	5	Prison inmate^[31]	67	182	0.201	0.403	0.319	0.450	0.359	0.761	0.179	0.511	0.110
	6	Wiki Vote^[32]	7115	103689	0.318	0.281	0.653	0.279	0.834	0.335	0.066	0.987	0.192
Food web	7	St.Marks^[33]	45	224	−0.292	0.533	0.563	0.479	0.483	0.711	0.156	0.701	0.143
	8	Seagrass^[34]	49	226	−0.192	0.449	0.518	0.441	0.46	0.714	0.102	0.655	0.097
	9	Grassland^[35]	88	137	−0.179	0.318	0.606	0.302	0.559	0.341	0.148	0.620	0.314
	10	Ythan^[35]	135	601	0.168	0.304	0.597	0.333	0.637	0.474	0.052	0.844	0.195
	11	Silwood^[36]	154	370	0.014	0.188	0.797	0.174	0.806	0.214	0.084	0.897	0.508
	12	Little Rock^[37]	183	2494	−0.138	0.639	0.603	0.654	0.601	0.831	0.497	0.818	0.299
Electronic	13	S208a^[29]	122	189	−0.177	0.451	0.344	0.430	0.326	0.549	0.311	0.413	0.201
circuits	14	s420a^[29]	252	399	−0.154	0.456	0.348	0.439	0.327	0.560	0.325	0.416	0.206
	15	s838a^[29]	512	819	−0.146	0.459	0.350	0.441	0.327	0.564	0.332	0.418	0.208
Neuronal	16	C. elegans^[38]	297	2359	0.291	0.549	0.374	0.494	0.477	0.923	0.081	0.639	0.069
Citation	17	Small World^[39]	233	1988	−0.094	0.210	0.729	0.206	0.735	0.309	0.047	0.869	0.469
	18	SciMet^[39]	2729	10416	0.068	0.360	0.623	0.352	0.638	0.613	0.037	0.830	0.153
	19	Kohonen^[40]	3772	12731	0.044	0.230	0.715	0.215	0.724	0.381	0.029	0.876	0.436
Internet	20	Political blogs^[41]	1224	19090	0.379	0.619	0.525	0.553	0.710	0.870	0.165	0.908	0.162
	21	p2p-1^[42]	10876	39994	0.145	0.334	0.591	0.344	0.647	0.381	0.255	0.870	0.325
	22	p2p-2^[42]	8846	31839	0.101	0.344	0.628	0.344	0.659	0.387	0.265	0.878	0.352
	23	p2p-3^[42]	8717	31525	0.107	0.343	0.625	0.344	0.658	0.383	0.264	0.878	0.347
Organizational	24	Freeman-1^[43]	34	695	0.642	0.353	0.111	0.454	0.199	0.735	0.118	0.285	0.047
	25	Consulting^[44]	46	879	0.482	0.522	0.150	0.497	0.266	0.848	0.109	0.369	0.078
Language	26	English words^[31]	7381	46281	0.857	0.158	0.210	0.326	0.755	0.479	0.003	0.862	0.087
	27	French words^[31]	8325	24295	0.905	0.157	0.216	0.254	0.676	0.333	0.009	0.736	0.092
Transportation	28	USair97^[45]	332	2126	0.608	0.437	0.400	0.440	0.689	0.762	0.030	0.861	0.045

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