Complex systems and network science: a survey

doi:10.23919/JSEE.2023.000080

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (3): 543-573.doi: 10.23919/JSEE.2023.000080

• COMPLEX SYSTEMS THEORY AND PRACTICE •

Complex systems and network science: a survey

Kewei YANG(), Jichao LI(), Maidi LIU(), Tianyang LEI, Xueming XU(), Hongqian WU(), Jiaping CAO(), Gaoxin QI()

¹ College of Systems Engineering, National University of Defense Technology, Changsha 410073, China

Received:2022-11-23 Online:2023-06-15 Published:2023-06-30
Contact: Kewei YANG E-mail:kayyang27@nudt.edu.cn;ljcnudt@hotmail.com;lmdnudt@hotmail.com;xueming_x2m@163.com;wuhongqian19@nudt.edu.cn;jiapingcao@126.com;qi198@foxmail.com
About author:
YANG Kewei was born in 1977. He is a professor with National University of Defense Technology. He serves as the director of Systems Engineering Society of China, and the vice president of Systems Engineering and Management Society of Hunan Province. He has been the head of Technology Innovation Group of Hunan Province named Big Data and System of Systems Engineering since 2020. His research interests focus on system-of-systems engineering, complex systems theory and complex equipment test and evaluation. E-mail: kayyang27@nudt.edu.cn

LI Jichao was born in 1990. He received his B.E. degree in management science, M.E. and Ph.D. degrees in management science and engineering from National University of Defense Technology, Changsha, Hunan, China, in 2013, 2015, and 2019, respectively. He is currently an associate professor of management science and engineering at National University of Defense Techno-logy. In 2017−2019, he was a visiting predoctoral fellow at the Northwestern Institute on Complex Systems (NICO) and Kellogg School of Management at Northwestern University, USA. His research interests focus on studying complex systems with a combination of theoretical tool and data analysis, including mathematical modeling of heterogeneous information networks, applying network methodologies to analyze the development of complex system-of-systems, and data-driven studying of the collective behavior of humans. E-mail: ljcnudt@hotmail.com

LIU Maidi was born in 1995. He received his B.E. degree in management engineering from National University of Defense Technology, Changsha, Hunan, China, in 2017. He is currently a Ph.D. student in management science and engineering at the College of Systems Engineering, National University of Defense Technology. His research interests focus on complex systems, complex network, and data mining. E-mail: lmdnudt@hotmail.com

LEI Tianyang was born in 1994. He received his B.S. and M.S. degrees from Taiyuan University of Technology and University of Chinese Academy of Sciences in 2017 and 2020, respectively. He is currently a Ph.D. candidate at the College of Systems Engineering, National University of Defense Technology, Changsha, China. His research interests include Internet of Things, graph neural network, data mining, and complex networks. E-mail: leitianyang20@163.com

XU Xueming was born in 1998. She received her B.E. degree in management science and engineering from Hefei University of Technology, Hefei, Anhui, China, in 2020. She is a master’s student in management science and engineering from National University of Defense Technology. Her research interests include network disintegration and cascading effects. E-mail: xueming_x2m@163.com

WU Hongqian was born in 1997. She received her M.E. degree in marine science from National University of Defense Technology, Changsha, Hunan, China, in 2021. She is a Ph.D. student in management science and engineering from National University of Defense Technology. Her research interests include higher-order systems and networks. E-mail: wuhongqian19@nudt.edu.cn

CAO Jiaping was born in 1999. She received her B.E. degree in industrial engineering from Northeast Forestry University, Harbin, Heilongjiang, China, in 2021. She is an M.E. student in management science and engineering with National University of Defense Technology. Her research interests include complex system and complex network, and heterogeneous information network link prediction. E-mail: jiapingcao@126.com

QI Gaoxin was born in 1998. He received his B.S. degree in mathematics and applied mathematics from Harbin Institute of Technology, Harbin, Heilongjiang, China, in 2020. He is a postgraduate student at National University of Defense Technology. His research interest focuses on evolutionary game theory of complex networks. E-mail: qi198@foxmail.com
First author contact:
Co-first author
Supported by:
The work was supported by the State Key Program of National Natural Science Foundation of China (72231011), the National Natural Science Foundation of China (72071206; 72001209; 71971213), and the Science Foundation for Outstanding Youth Scholars of Hunan Province (2022JJ20047).

Abstract

Abstract:

Complex systems widely exist in nature and human society. There are complex interactions between system elements in a complex system, and systems show complex features at the macro level, such as emergence, self-organization, uncertainty, and dynamics. These complex features make it difficult to understand the internal operation mechanism of complex systems. Networked modeling of complex systems is a favorable means of understanding complex systems. It not only represents complex interactions but also reflects essential attributes of complex systems. This paper summarizes the research progress of complex systems modeling and analysis from the perspective of network science, including networked modeling, vital node analysis, network invulnerability analysis, network disintegration analysis, resilience analysis, complex network link prediction, and the attacker-defender game in complex networks. In addition, this paper presents some points of view on the trend and focus of future research on network analysis of complex systems.

Key words: complex system, complex network, invulnerability and resilience, network disintegration, link prediction, attacker-defender game theory

Kewei YANG, Jichao LI, Maidi LIU, Tianyang LEI, Xueming XU, Hongqian WU, Jiaping CAO, Gaoxin QI. Complex systems and network science: a survey[J]. Journal of Systems Engineering and Electronics, 2023, 34(3): 543-573.

Figures/Tables 8

Fig 1

Table 1

Table 2

Table 3

Typical research on three kinds of optimization methods"

Optimization method	Typical research
Constructing the optimal network by analytical method	Valente et al. [107] studied the optimal destructive network under random failure and intentional attack strategies. They analytically deduced the critical removal ratio and concluded that the optimal destructive network in the face of random failures or intentional attacks is a bimodal network with a fixed number of network edges (i.e., only two degrees for all nodes in the network).
	Paul et al. [108] also studied the robustness of networks with varying degrees of distribution. They analyzed and compared the critical removal ratios for scale-free, bi-power, and bimodal networks, and concluded that the best network with both random failures and intentional attack resistance is one with a bimodal distribution.
	Tanizawa et al. [109] studied the robustness of networks when random failures and deliberate attacks work together. They stated that a network attack is usually an “attack wave” composed of random failures and intentional attacks, and controlled the proportion of random failures to deliberate attacks by adjusting parameters.
Optimizing destruction by edge enhancement	Beygelzimer et al. [110] studied network invulnerability optimization results under different edge addition strategies. They found that moderate edge augmentation can effectively improve the vulnerability of scale-free networks to intentional attacks, especially when fewer nodes are attacked. When the number of attacked nodes is too large, the edge-increasing strategy has little impact on destructiveness.
	Zhao et al. [111] determined whether new edges are added between nodes with a high or low degree of traffic by adjusting the size of parameters and compared the results of the corresponding network invulnerability optimization. They found that adding a new edge at a small degree node can effectively improve the network’s ability to resist intentional attacks.
	Cao et al. [112] studied an edge-increasing strategy for network invulnerability optimization considering cascade failures. They found that both high-median and low-polarization edge-increasing strategies can effectively improve the network against cascade-invalid network attacks.
Optimizing destruction by edge reconnection	Non-guaranteed reconnection optimization	Liu et al. [113] studied the effect of network node degree value on network invulnerability in non-guaranteed reconnection optimization.
		Netotea et al. [114] used a genetic algorithm to optimize the robustness and efficiency of the network for heavy reconnection.
		Priester et al. [115] studied the trade-off optimization of network resilience against random failures and intentional attacks without guaranteed reconnection optimization.
	Guaranteed reconnection optimization	Peixoto et al. [116] optimized the seepage properties of a classical network based on a block model and found that the “core-periphery” structure of the network helps to improve the network’s ability to resist random failures.
	Guaranteed reconnection optimization	Herrmann et al. [117] studied the topological structure of the optimal destructive network obtained by optimizing the measure with preserved reconnection.

Table 3

Table 4

Fig 2

Table 5

Fig 3

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Category	Indicator	Review
Graph theory	Connectivity Toughness Integrity Tenacity Scattering number Coefficient of expansion Algebraic connectivity	Graph theory-based network invulnerability usually has high computational complexity. It is unrealistic and unscientific to measure the invulnerability of complex networks with huge scales and uncertain connection relationships.
Statistical physics	Network invulnerability of different attack strategies Seepage problems in generalized stochastic networks Network invulnerability with the repair mechanism Network invulnerability considering degree correlation condition Network invulnerability of the local world evolution model	While adapting to the current situation of the huge scale of network complexity, it also greatly expands the vision of the research on the resistance of complex networks, and relevant achievements are concentrated in the research fields of network learning, network propagation, network synchronization, etc.
Characteristic spectrum	Natural connectivity Helmholtz free energy of network Physical implications of natural connectivity	It contains a lot of network topology information. Derivation and analysis of the network characteristic spectrum are helpful to deepen our understanding of some properties and behaviors of the network.

Cascading failure model	Brief introduction
Load capacity model	When encountering some accidental failure or intentional damage, a node in the network will exceed the limit capacity and cause failure, which will then lead to the overload increase of other nodes or connections and cause failure until the entire network is restabilized [99].
Sandpile model	Assume that for sand in the sand pile, the sand surface gradually becomes steeper with the gradual increase of sand and the probability of a large area collapse of the sand pile increases [100].
OPA model	This model is based on the power grid with increasing energy demand. It can summarize the dynamic evolution process of the power grid, the engineering response process of system failures, and the continuous updating process of generation capacity. At the same time, it defines two types of cascading failure types, each with different dynamic characteristics [101].
CASCADE model	The model has two assumptions: for the nodes, the initial load is given randomly, and each node fails according to random probability; when the load of a node exceeds the limit capacity, it causes the node to redistribute its load so that other nodes in the network can obtain an equal amount of load [102].

Perspective	Type	Related work
Target object of disintegration	Node-based	[130-134]
Target object of disintegration	Edge-based	[135-138]
Type of disintegration network	For homogeneous networks	[132-139]
	For heterogeneous networks	[130, 140]
	For multilayer networks	[134, 141, 142]
Constraints of disintegration	Under the homogeneous cost constraint	[130, 132, 135, 140]
Constraints of disintegration	Under the heterogeneous cost constraint	[133, 134, 140]

Classification	Typical method	Advantages and disadvantages
Methods based on mathematical programming	Branch and bound method Mixed iterative rounding method Univariate decomposition Dynamic programming $ \vdots $	The optimal network disintegration scheme can be obtained. It has high requirements for the objective function and constraint conditions and is not applicable to large-scale networks.
Methods based on the centrality index	Degree centrality k-core centrality Intermediate centrality Proximity centrality $ \vdots $	Simple and easy to implement, but the important node set under a single index is not necessarily the optimal node removal set.
Methods based on heuristic algorithms	Tabu search algorithm Genetic algorithm Simulated annealing algorithm Random greedy adaptive search algorithm $ \vdots $	A good network disintegration scheme can be obtained that has high robustness and wide applicability. The time complexity is high.
Methods based on reinforcement learning	Q-learning Deep Q-network (DQN) $ \vdots $	It has nothing to do with specific knowledge and rules and is applicable to all kinds of problems; it is not interpretable.

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Complex systems and network science: a survey

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