信息流介数分布熵测度的C4ISR网络抗毁性

doi:10.19665/j.issn1001-2400.2022.02.014

Abstract

Abstract:

Currently,many researches on invulnerability focus on statistical analysis of the network structure which is not suitable for the C4ISR network with specific functions.In view of this problem,this paper proposes “information flow intermediate number centrality distribution entropy” to measure the invulnerability of the C4ISR network.It goes from the perspective of the function of information flow and uses the theory of “intermediate number centrality of complex networks” and “information entropy”.The shortest information path from reconnaissance node to attack node is regarded as an operational information chain,and the “information flow intermediate number centrality ” is proposed to measure the number of operational information chains passing through a node in the C4ISR network.The uniformity of information flow intermediate number centrality is measured by “information flow intermediate number centrality distribution entropy”,and the effectiveness of this index is analyzed which can reflect the invulnerability of the C4ISR network function.Based on a representative C4ISR network structure,the invulnerability of the network after random attack,degree attack,intermediate number centrality attack and information flow attack is simulated,with the application of information flow intermediate number centrality distribution entropy in improving the invulnerability of C4ISR network functions also analyzed.Simulation results show that this indicator is more sensitive and accurate than structural invulnerability indicators such as average network efficiency of complex networks,natural connectivity,degree distribution entropy,intermediate number centrality distribution entropy,and so on and that it can find the critical point of C4ISR network function failure,and can provide guidance for improving the functional invulnerability of the C4ISR network.

Key words: information flow, betweenness centrality, entropy, complex networks, C4ISR, invulnerability

CLC Number:

E917

YU Changren,JIA Lianxing,ZHANG Bin. Invulnerability measurement for the C4ISR network based on information flow betweenness centrality distribution entropy[J].Journal of Xidian University, 2022, 49(2): 116-124.

Figures/Tables 12

抗毁性指标	计算公式	符号说明
复杂网络平均网络效率	E= $2 N (N - 1) ∑ j = i + 1 N ∑ i = 1 N 1 d i j$	N为节点数,d_ij为节点i、j间考虑权重的最短距离
自然连通度	$λ ¯$ =ln $1 N ∑ i = 1 N e λ i$	λ_i为网络邻接矩阵的特征根
复杂网络介数分布熵	E_B=- $S B (v i) ∑ i = 1 N$ lb $S B (v i)$	B(v_i)为节点v_i的介数, $S B (v i)$ =B(v_i) $/ ∑ i = 1 N B (v i)$
度分布熵	E_D=- $S D (v i) ∑ i = 1 N$ lb $S D (v i)$	D(v_i)为节点v_i的度, $S D (v i)$ =D(v_i) $/ ∑ i = 1 N D (v i)$
信息流介数分布熵	E_BI=- $S B I (v k) ∑ k = 1 N$ lb $S B I (v k)$	见式(4)

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Invulnerability measurement for the C4ISR network based on information flow betweenness centrality distribution entropy

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Figures/Tables 12

References 25

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实验步数	0	1	2	3	4	5	6	7	8	9	10	11	12
攻击步数	1	2	3	4	5	6	7	8	9	10	11	12	13
信息流介数分布熵	3.170	3.176	3.183	3.189	3.210	3.231	3.250	3.271	3.290	3.309	3.328	3.346	3.364
实验步数	13	14	15	16	17	18	19	20	21	22	23	24
攻击步数	13	13	13	13	13	13	13	13	13	13	13	13
信息流介数分布熵	3.366	3.368	3.370	3.382	3.394	3.405	3.417	3.428	3.439	3.450	3.461	3.470

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