XIE Hanchen; WU Minggong; WEN Xiangxi; ZHANG Mingyu

doi:10.7498/aps.74.20250338

Abstract

In the face of the surge of air transport demand and the increasing risk of flight conflicts, it is very important to effectively manage flight conflicts and accurately identify key conflict aircraft. This paper presents a novel method for identifying critical nodes in flight conflict networks by integrating complex network theory with a weighted cycle ratio (WCR). By modeling aircraft as nodes and conflict relationships as edges, we construct a flight conflict network where the urgency of conflicts is reflected in edge weights. We extend the traditional cycle ratio (CR) concept to propose the WCR, which accounts for both the topological structure of the network and the urgency of conflicts. Furthermore, we combine the WCR with node strength (NS) to form an adjustable mixed indicator (MI) that adaptively balances the importance of nodes based on their involvement in cyclic conflict structure and their individual conflict strength. Through extensive simulations, including node deletion experiments and network robustness analyses, we demonstrate that our method can precisely pinpoint critical nodes in flight conflict networks. The results indicate that regulating these critical nodes can significantly reduce network complexity and conflict risks. Importantly, the effectiveness of our method increases with the complexity of the flight conflict network, making it particularly suitable for scenarios with high aircraft density and complex conflict patterns. Overall, this study not only deepens the theoretical understanding of complex aviation network analysis but also provides a practical tool for improving air traffic control efficiency and safety, thereby contributing to achieving more environmentally friendly and sustainable air transportation.

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Corresponding author: WEN Xiangxi, wxxajy@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No.71801221).

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Cited By

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节点	基本圈	WCR	WCR¹	CR	NS	BC	CC	EC
1	{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 5}	2.72	3.76	3.92	1.93	5	0.101	0.158
2	{2, 3, 1}, {2, 4, 1}, {2, 5, 1}, {2, 4, 3}	2.98	3.80	3.92	1.47	25.75	0.117	0.099
3	{3, 1, 4}, {3, 2, 4}, {3, 2, 1}, {3, 10, 11, 9}	3.63	4.78	5.67	2.60	22	0.109	0.170
4	{4, 1, 2}, {4, 1, 3}, {4, 2, 3}	1.90	2.33	2.50	1.47	2.25	0.100	0.080
5	{5, 1, 2}	1.32	1.57	1.50	2.13	21	0.105	0.143
6		0	0	0	0.60	0	0.051	0.031
7		0	0	0	2.07	17	0.070	0.092
8		0	0	0	0.53	0	0.053	0.027
9	{9, 11, 10, 3}	2.156	2.38	3.25	0.60	8	0.099	0.027
10	{9, 11, 10, 3}	1.90	2.38	3.25	1.73	0	0.058	0.117
11	{9, 11, 10, 3}	2.47	3	3.25	1.20	0	0.074	0.055

DownLoad: CSV

	节点	连边	平均度	同配性	平均聚类系数
Usa	332	2.1k	12	–0.20788	0.625
Dolphin	291	3.2k	21	0.177476	0.68233
Email	906	12.1k	26	–0.0878	0.6139
Rw496	496	2k	7	0.045056	0.395
Road	1.2k	1.4k	2	0.126684	0.0167
Advogato	5.2k	47.3k	18	–0.0834	0.2868

DownLoad: CSV

排名	指标
排名	CR	WCR	NS	BC	CC	EC
1	1874	1874	1874	1669	599	1874
2	1258	1258	1258	1874	1669	1258
3	453	999	999	599	1731	999
4	999	453	1586	453	1874	1963
5	1669	1963	1963	713	1854	1586
6	1586	1669	1576	1952	272	1576
7	1963	1586	1987	702	339	1987
8	203	1159	1120	1258	344	1792
9	1987	1768	1792	511	1453	1120
10	1159	203	1669	1159	1782	465
11	511	1377	419	272	74	1323
12	1768	1440	1440	585	92	419
13	412	511	1323	1563	108	1669
14	1440	1987	465	1987	136	1440
···	···	···	···	···	···	···
n	2029	2029	2028	2029	2028	984

DownLoad: CSV

排名	指标
排名	CR	WCR	NS	BC	CC	EC
1	202	202	43	89	118	43
2	32	118	118	79	202	118
3	118	32	32	32	129	232
4	185	185	173	271	173	243
5	173	173	202	202	174	49
6	4	43	232	133	4	185
7	271	4	107	174	32	107
8	222	232	243	4	35	202
9	174	107	185	222	42	173
10	43	174	49	35	133	32
11	201	222	20	47	135	164
12	232	271	164	118	218	20
13	86	201	4	291	222	266
14	47	243	86	201	243	225
···	···	···	···	···	···	···
n	156	156	156	285	156	274

DownLoad: CSV

Networks	CR	WCR	NS	BC	CC	EC
USAair	0.0740	0.0738	0.1047	0.0817	0.2520	0.1147
Dolphin	0.3801	0.3713	0.4293	0.3577	0.3793	0.3889
Email	0.0173	0.0141	0.0205	0.0146	0.0287	0.1003
Rw496	0.2177	0.1548	0.200	0.1919	0.2508	0.2150
Road	0.1341	0.1031	0.1221	0.0979	0.1838	0.3152
Advogato	0.2746	0.2575	0.2800	0.2632	0.706	0.3006

DownLoad: CSV

	CR	WCR	NS	BC	CC	EC
平均排名	3.67	1.5	4.167	1.67	4.67	5.3
R平均值	0.1830	0.1626	0.1928	0.1678	0.2275	0.2391

DownLoad: CSV

	t =1	t = 2	t = 4	t = 6	t = 8	t = 10	平均排名
CR	2.67	2. 83	2.83	2.67	2.67	2.67	2.72
WCR	1.67	1. 50	1.33	1.33	1.33	1.33	1.42
NS	3.50	4.00	4.50	4.50	4.50	4.50	4.25
BC	3.33	2.83	2.50	2.50	2.50	2.50	2.69
CC	4.67	4.67	4.67	4.83	4.83	4.83	4.75
EC	5.17	5.17	5.17	5.17	5.17	5.17	5.17

DownLoad: CSV

排名	Email		Advogato
排名	CR WCR		CR WCR
1	1874	1874	157	157
2	1258	1258	46	46
3	453	999	597	597
4	999	453	30	30
5	1669	1963	232	126
6	1586	1669	328	328
7	1963	1586	126	232
8	203	1159	438	438
9	1987	1768	286	286
10	1159	203	1223	610
11	511	1377	610	1223
12	1768	1440	429	62
13	412	511	9	1378
14	1440	1987	736	429
15	1792	412	62	736
16	1377	457	22	22
17	457	1792	1378	780
18	1706	1576	780	9
19	585	1587	19	604
20	1751	585	326	326
21	1587	852	604	19
22	1952	1144	194	175
23	1144	1833	329	739
24	852	1751	214	329
25	1278	1323	739	214
26	713	1278	1775	1992
27	1277	1277	1992	172
28	1576	1510	801	45
29	155	155	172	719
30	1287	1952	175	1775
31	350	329	45	801
32	1998	419	399	194
33	1833	1287	719	584
34	1550	1894	584	764
···	···	···	···	···
n	2029	2029	6550	6550

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