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When considering disintegration of spatial networks, the topological relationships between nodes and their geographical positions are taken into account. In the case of regional attacks, the targeted nodes are determined based on the size of the region and the geographical relationships between nodes. In this paper, a new metric is proposed on top of region centrality (RC) to describe the importance of nodes within local regions in spatial networks. We define the weighted sum of the number of connections between nodes within a local region and the number of connections between nodes within the local region and nodes outside the local region as local connectivity. This metric integrates topological information with geographical information. From a mathematical perspective, RC is a special case of local connectivity. In addition, we propose a hybrid spatial network disintegration strategy based on two metrics, namely local connectivity and RC. From experimental results, our strategy outperforms traditional approaches and demonstrates a stronger ability to completely disintegrate the network. [ABSTRACT FROM AUTHOR]

Network disintegration is a fundamental issue in the field of complex networks, with its core in identifying critical nodes or sets and removing them to weaken network functionality. The research on this problem has significant strategic value and has increasingly attracted attention, including in controlling the spread of diseases and dismantling terrorist organizations. In this paper, we focus on the problem of network disintegration with discrete entity resources from the attack view, that is, optimizing resource allocation to maximize the effect of network disintegration. Specifically, we model the network disintegration problem with limited entity resources as a nonlinear optimization problem and prove its NP-hardness. Then, we design a method based on deep reinforcement learning (DRL), Net-Cracker, which transforms the two-stage entity resource and network node selection task into a single-stage object selection problem. Extensive experiments demonstrate that compared with the benchmark algorithm, Net-Cracker can improve the solution quality by about 8∼62%, while enabling a 30-to-160-fold speed up. Net-Cracker also exhibits strong generalization ability and can find better results in a near real-time manner even when the network scale is much larger than that in training data. [ABSTRACT FROM AUTHOR]

Identifying critical nodes or sets in large-scale networks is a fundamental scientific problem and one of the key research directions in the fields of data mining and network science when implementing network attacks, defense, repair and control. Traditional methods usually begin from the centrality, node location or the impact on the largest connected component after node destruction, mainly based on the network structure. However, these algorithms do not consider network state changes. We applied a model that combines a random connectivity matrix and minimal low-dimensional structures to represent network connectivity. By using mean field theory and information entropy to calculate node activity, we calculated the overlap between the random parts and fixed low-dimensional parts to quantify the influence of node impact on network state changes and ranked them by importance. We applied this algorithm and the proposed importance algorithm to the overall analysis and stratified analysis of the C. elegans neural network. We observed a change in the critical entropy of the network state and by utilizing the proposed method we can calculate the nodes that indirectly affect muscle cells through neural layers. [ABSTRACT FROM AUTHOR]

Network disintegration is a fundamental issue in the field of complex networks, with its core in identifying critical nodes or sets and removing them to weaken network functionality. The research on this problem has significant strategic value and has increasingly attracted attention, including in controlling the spread of diseases and dismantling terrorist organizations. In this paper, we focus on the problem of network disintegration with discrete entity resources from the attack view, that is, optimizing resource allocation to maximize the effect of network disintegration. Specifically, we model the network disintegration problem with limited entity resources as a nonlinear optimization problem and prove its NP-hardness. Then, we design a method based on deep reinforcement learning (DRL), Net-Cracker, which transforms the two-stage entity resource and network node selection task into a single-stage object selection problem. Extensive experiments demonstrate that compared with the benchmark algorithm, Net-Cracker can improve the solution quality by about 8∼62%, while enabling a 30-to-160-fold speed up. Net-Cracker also exhibits strong generalization ability and can find better results in a near real-time manner even when the network scale is much larger than that in training data.

While link redundancy has long been acknowledged as a critical factor in network robustness, current approaches frequently neglect the inherent heterogeneity of structure, thereby falling short of optimal network disintegration. This study introduces the novel Neighborhood Dissimilarity Community Heterogeneity (NDCH) framework, which systematically investigates redundancy elimination from a new perspective of neighborhood dissimilarity, while concurrently integrating structural heterogeneity derived from community structure. Extensive experiments on both synthetic and diverse real-world networks reveal that strategies developed under NDCH framework markedly outperform existing state-of-the-art methods in network disintegration, with performance improvements reaching up to 60.151% and 31.000% for Schneider R and the critical removal fraction f c , respectively. Notably, additional analysis consistently indicates low correlations (Kendall's Tau < 0.6) and distinct value distributions between NDCH-based strategies and the state-of-the-art approaches. In summary, the novel framework underscores the significance of both redundancy and structural heterogeneity when devising network disintegration strategies, offering a substantial leap forward in enhancing network robustness against malicious attacks and various disruptions, especially in infrastructure networks. [ABSTRACT FROM AUTHOR]

Modern war is highly dependent on intelligent, unmanned combat systems. Since many intelligent, unmanned combat systems have network attributes, it is meaningful to research combat systems from the perspective of complex network. Heterogeneous network provides a suitable model to describe real combat network. Previous studies of combat network only concentrate on homogeneous networks. However, on the real battlefield, military networks are composed of a large number of heterogeneous nodes and edges with different functions. In the paper, a superior, intelligent, heterogeneous combat network disintegration strategy (HDGED) are obtained by DQN, which embeds heterogeneous networks into a low-dimensional representation vector as input, rather than ignore the differences of the nodes and their connections. A method of heterogeneous graph embedding is first introduced, which adopts type encoding and aggregation. Besides, a normalized combat capability index was designed, which could assess the performance of the dynamic heterogeneous combat networks. On this basis, HDGED was experimented on networks with uneven node combat capabilities and the results show that HDGED has improved disintegration effectiveness for heterogeneous networks of different sizes compared with traditional methods. Our work provides a new approach to realize the disintegration of heterogeneous combat networks by deep reinforcement learning, which is of great significance for optimizing the command operation process, and deserves further study.

The problem of network disintegration, such as interrupting rumor spreading networks and dismantling terrorist networks, involves evaluating changes in network performance. However, traditional metrics primarily focus on the topological structure and often neglect the crucial spatial attributes of nodes and edges, thereby failing to capture the spatial functional losses. Here we first introduce the concept of spatial coverage to evaluate the spatial network performance, which is defined as the convex hull area of the largest connected component. Then a greedy algorithm is proposed to maximize the reduction of the convex hull area through strategic node removals. Extensive experiments verified that the spatial coverage metric can effectively quantify changes in the performance of spatial networks, and the proposed algorithm can maximize the reduction of the convex hull area of the largest connected component compared to genetic algorithm and centrality strategies. Specifically, our algorithm reduces the convex hull area by up to 30% compared to the best-performing strategy. These results indicate that the critical nodes influencing network performance are a combination of numerous peripheral spatial leaf nodes and a few central spatial core nodes. This study substantially enhances our understanding of spatial network robustness and provides a novel perspective for network optimization. [ABSTRACT FROM AUTHOR]

The problem of network disintegration, such as suppression of an epidemic spread and destabilization of terrorist networks, possesses extensive applications and has lately been the focus of growing interest. Many real-world complex systems are represented by spatial networks in which nodes and edges are spatially embedded. However, existing disintegration approaches for spatial network disintegration focus on singular aspects such as geospatial information or network topography, with insufficient modeling granularity. In this paper, we propose an effective and computationally efficient virtual node model that essentially integrates the geospatial information and topology of the network by modeling edges as virtual nodes with weights. Moreover, we employ Kernel Density Estimation, a well-known non-parametric technique for estimating the underlying probability density function of samples, to fit all nodes, comprising both network and virtual nodes, to identify the critical region of the spatial network, which is also the circular geographic region where disintegration occurs. Extensive numerical experiments on synthetic and real-world networks demonstrate that our method outperforms existing methods in terms of both effectiveness and efficiency, which provides a fresh perspective for modeling spatial networks. • Introduces a virtual node model integrating geospatial data and topology in spatial network disintegration. • Employs Kernel Density Estimation for identifying critical regions in spatial networks. • Demonstrates superior effectiveness and efficiency over existing methods in real-world applications. • Proposes adaptive method linking disintegration circle radius with method parameters. • Provides new insights for spatial network modeling. [ABSTRACT FROM AUTHOR]

Relationships between terrorists are amorphous, invisible, distributed, and dispersed. The information on these networks is often incomplete and even erroneous. The key to disrupting the terrorists' network is to find the critical nodes whose removal will lead to network collapse, and however, most of the previous studies are based directly on the observed networks while neglecting an important fact that the observed networks may be incomplete. In this paper, we address the terrorist network disintegration problem based on link prediction. An effective method is proposed to find the critical nodes by the assistance of a link prediction algorithm. We make a case study of September 11th hijackers to illustrate our method. Five different disintegration strategies are applied to validate our method. The result shows that, with no more than 40% magnitude of missing information, by using the link prediction method to recover partial missing relationships information, our method can improve the network disintegration performance remarkably. Besides, we find that when the size of missing information is not too much, our method even outperforms than the results based on complete information. We refer to this phenomenon as the “comic effect” of link prediction, which means that the original network has been reshaped through the addition of some links by link prediction. As a result, the reshaped network is like an exaggerated but characteristic comic of the original one, where the important parts are emphasized.

Recently, research in the field of network disintegration, which includes controlling the spread of disease and collapsing terrorist organizations, has found broad applications and attracted increased attention. In this paper, we focus on the network disintegration with heterogeneous cost, in which there may be unequal disintegration costs associated with deleting different nodes. First, we present a cost model for a disintegration strategy with both cost-sensitive and cost-constraint parameters in complex networks. Then, we propose an optimization model for the disintegration strategy with heterogeneous cost and introduce the genetic algorithm to identify the optimal disintegration strategy. Extensive experiments in synthetic and real-world networks suggest that the heterogeneity of the disintegration cost and the tightness of the cost constraint significantly affect the optimal disintegration strategy. We demonstrate that, in contrast to the classical hub node strategy, low-cost nodes play a key role in the optimal disintegration strategies if the cost constraint is tight and the disintegration cost is strongly heterogeneous. [ABSTRACT FROM AUTHOR]

From social networks to complex infrastructures, many systems could be described by multiplex networks formed by a set of nodes connected via more than one type of links. Network disintegration, which is the problem of identifying a set of nodes or edges whose removal would maximize the network collapse, is significant for dismantling harmful networks. In this article, we consider the optimal disintegration strategy problem in multiplex networks and extend the attack mode to the layer node-based attack. An optimization model is proposed to search the optimal strategy of a multiplex network under layer node-based attack with fix attack length. Two types of strategies based on the information of multiplex nodes and layer nodes, respectively, are also given for comparison. Through experiments in both model networks and real networks, we found that the approximate optimal strategies could be identified by solving the model. The properties of the optimal strategies are also summarized. [ABSTRACT FROM AUTHOR]

Network disintegration has been an important research hotspot in complex networks for a long time. From the perspective of node attack, researchers have devoted to this field and carried out numerous works. In contrast, the research on edge attack strategy is insufficient. This paper comprehensively evaluates the disintegration effect of each structural similarity index when they are applied to the weighted-edge attacks model. Experimental results show that the edge attack strategy based on a single similarity index will appear limited stability and adaptability. Thus, motivated by obtaining a stable disintegration effect, this paper designs an edge attack strategy based on the ordered weighted averaging (OWA) operator. Through final experimental results, we found that the edge attack strategy proposed in this paper not only achieves a more stable disintegration effect on eight real-world networks, but also significantly improves the disintegration effect when applied on a single network in comparison with the original similarity index.

Critical nodes identification in complex networks is significance for studying the survivability and robustness of networks. The previous studies on structural hole theory uncovered that structural holes are gaps between a group of indirectly connected nodes and intermediaries that fill the holes and serve as brokers for information exchange. In this paper, we leverage the property of structural hole to design a heuristic algorithm based on local information of the network topology to identify node importance in undirected and unweighted network, whose adjacency matrix is symmetric. In the algorithm, a node with a larger degree and greater number of structural holes associated with it, achieves a higher importance ranking. Six real networks are used as test data. The experimental results show that the proposed method not only has low computational complexity, but also outperforms degree centrality, k-shell method, mapping entropy centrality, the collective influence algorithm, DDN algorithm that based on node degree and their neighbors, and random ranking method in identifying node importance for network connectivity in complex networks.

From social networks to complex infrastructures, many systems could be described by multiplex networks formed by a set of nodes connected via more than one type of links. Network disintegration, which is the problem of identifying a set of nodes or edges whose removal would maximize the network collapse, is significant for dismantling harmful networks. In this article, we consider the optimal disintegration strategy problem in multiplex networks and extend the attack mode to the layer node-based attack. An optimization model is proposed to search the optimal strategy of a multiplex network under layer node-based attack with fix attack length. Two types of strategies based on the information of multiplex nodes and layer nodes, respectively, are also given for comparison. Through experiments in both model networks and real networks, we found that the approximate optimal strategies could be identified by solving the model. The properties of the optimal strategies are also summarized.

The problem of network disintegration has broad applications and recently has received growing attention, such as network confrontation and disintegration of harmful networks. This paper presents an optimized attack strategy model for complex networks and introduces the tabu search into the network disintegration problem to identify the optimal attack strategy, which is a heuristic optimization algorithm and rarely applied to the study of network robustness. The efficiency of the proposed solution was verified by comparing it with other attack strategies used in various model networks and real-world network. Numerical experiments suggest that our solution can improve the effect of network disintegration and that the “best” choice for node failure attacks can be identified through global searches. Our understanding of the optimal attack strategy may also shed light on a new property of the nodes within network disintegration and deserves additional study. [ABSTRACT FROM AUTHOR]

Network disintegration or strengthening is a significant problem, which is widely used in infrastructure construction, social networks, infectious disease prevention and so on. But most studies assume that the cost of attacking anyone node is equal. In this paper, we investigate the robustness of complex networks under a more realistic assumption that costs are functions of degrees of nodes. A multi-objective, elitism-based, evolutionary algorithm (MOEEA) is proposed for the network disintegration problem with heterogeneous costs. By defining a new unit cost influence measure of the target attack node and combining with an elitism strategy, some combination nodes' information can be retained. Through an ingenious update mechanism, this information is passed on to the next generation to guide the population to move to more promising regions, which can improve the rate of convergence of the proposed algorithm. A series of experiments have been carried out on four benchmark networks and some model networks, the results show that our method performs better than five other state-of-the-art attack strategies. MOEEA can usually find min-cost network disintegration solutions. Simultaneously, through testing different cost functions, we find that the stronger the cost heterogeneity, the better performance of our algorithm. • A multi-objective disintegration algorithm considering actual cost factor is proposed. • By combining cost and node importance, a new unit cost importance measure is defined. • The combination information of nodes is added by ingenious elitism and update strategy. • Our algorithm performs better than five other state-of-the-art disintegration methods. [ABSTRACT FROM AUTHOR]

Network disintegration has been an important research hotspot in complex networks for a long time. From the perspective of node attack, researchers have devoted to this field and carried out numerous works. In contrast, the research on edge attack strategy is insufficient. This paper comprehensively evaluates the disintegration effect of each structural similarity index when they are applied to the weighted-edge attacks model. Experimental results show that the edge attack strategy based on a single similarity index will appear limited stability and adaptability. Thus, motivated by obtaining a stable disintegration effect, this paper designs an edge attack strategy based on the ordered weighted averaging (OWA) operator. Through final experimental results, we found that the edge attack strategy proposed in this paper not only achieves a more stable disintegration effect on eight real-world networks, but also significantly improves the disintegration effect when applied on a single network in comparison with the original similarity index. [ABSTRACT FROM AUTHOR]

Critical nodes identification in complex networks is significance for studying the survivability and robustness of networks. The previous studies on structural hole theory uncovered that structural holes are gaps between a group of indirectly connected nodes and intermediaries that fill the holes and serve as brokers for information exchange. In this paper, we leverage the property of structural hole to design a heuristic algorithm based on local information of the network topology to identify node importance in undirected and unweighted network, whose adjacency matrix is symmetric. In the algorithm, a node with a larger degree and greater number of structural holes associated with it, achieves a higher importance ranking. Six real networks are used as test data. The experimental results show that the proposed method not only has low computational complexity, but also outperforms degree centrality, k-shell method, mapping entropy centrality, the collective influence algorithm, DDN algorithm that based on node degree and their neighbors, and random ranking method in identifying node importance for network connectivity in complex networks. [ABSTRACT FROM AUTHOR]

• A new heuristic probabilistic algorithm is proposed for network disintegration. • A novel centrality measure, namely importance measure(IM), is defined and used. • The effect of node combinations is evaluated. • Simulations show that our proposed approach is more effective than other three methods. Many real-world applications can be modelled as complex networks, and such networks include the Internet, epidemic disease networks, transport networks, power grids, protein-folding structures and others. Network integrity and robustness are important to ensure that crucial networks are protected and undesired harmful networks can be dismantled. Network structure and integrity can be controlled by a set of key nodes, and to find the optimal combination of nodes in a network to ensure network structure and integrity can be an NP-complete problem. Despite extensive studies, existing methods have many limitations and there are still many unresolved problems. This paper presents a probabilistic approach based on neighborhood information and node importance, namely, neighborhood information-based probabilistic algorithm (NIPA). We also define a new centrality-based importance measure (IM), which combines the contribution ratios of the neighbor nodes of each target node and two-hop node information. Our proposed NIPA has been tested for different network benchmarks and compared with three other methods: optimal attack strategy (OAS), high betweenness first (HBF) and high degree first (HDF). Experiments suggest that the proposed NIPA is most effective among all four methods. In general, NIPA can identify the most crucial node combination with higher effectiveness, and the set of optimal key nodes found by our proposed NIPA is much smaller than that by heuristic centrality prediction. In addition, many previously neglected weakly connected nodes are identified, which become a crucial part of the newly identified optimal nodes. Thus, revised strategies for protection are recommended to ensure the safeguard of network integrity. Further key issues and future research topics are also discussed. [ABSTRACT FROM AUTHOR]