Dismantling Of Networks Research Articles

ABCDE: Approximating Betweenness-Centrality ranking with progressive-DropEdge.

Betweenness-centrality is a popular measure in network analysis that aims to describe the importance of nodes in a graph. It accounts for the fraction of shortest paths passing through that node and is a key measure in many applications including community detection and network dismantling. The computation of betweenness-centrality for each node in a graph requires an excessive amount of computing power, especially for large graphs. On the other hand, in many applications, the main interest lies in finding the top-k most important nodes in the graph. Therefore, several approximation algorithms were proposed to solve the problem faster. Some recent approaches propose to use shallow graph convolutional networks to approximate the top-k nodes with the highest betweenness-centrality scores. This work presents a deep graph convolutional neural network that outputs a rank score for each node in a given graph. With careful optimization and regularization tricks, including an extended version of DropEdge which is named Progressive-DropEdge, the system achieves better results than the current approaches. Experiments on both real-world and synthetic datasets show that the presented algorithm is an order of magnitude faster in inference and requires several times fewer resources and time to train.

Machine learning dismantling and early-warning signals of disintegration in complex systems

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features – e.g., heterogeneous connectivity, mesoscale organization, hierarchy – affect their robustness to external perturbations, such as targeted attacks to their units. Identifying the minimal set of units to attack to disintegrate a complex network, i.e. network dismantling, is a computationally challenging (NP-hard) problem which is usually attacked with heuristics. Here, we show that a machine trained to dismantle relatively small systems is able to identify higher-order topological patterns, allowing to disintegrate large-scale social, infrastructural and technological networks more efficiently than human-based heuristics. Remarkably, the machine assesses the probability that next attacks will disintegrate the system, providing a quantitative method to quantify systemic risk and detect early-warning signals of system’s collapse. This demonstrates that machine-assisted analysis can be effectively used for policy and decision-making to better quantify the fragility of complex systems and their response to shocks.

Long-loop feedback vertex set and dismantling on bipartite factor graphs.

Network dismantling aims at breaking a network into disconnected components and attacking vertices that intersect with many loops has proven to be a most efficient strategy. Yet existing loop-focusing methods do not distinguish the short loops within densely connected local clusters (e.g., cliques) from the long loops connecting different clusters, leading to lowered performance of these algorithms. Here we propose a new solution framework for network dismantling based on a two-scale bipartite factor-graph representation, in which long loops are maintained while local dense clusters are simplistically represented as individual factor nodes. A mean-field spin-glass theory is developed for the corresponding long-loop feedback vertex set problem. The framework allows for the advancement of various existing dismantling algorithms; we developed the new version of two benchmark algorithms BPD (which uses the message-passing equations of the spin-glass theory as the solver) and CoreHD (which is fastest among well-performing algorithms). New solvers outperform current state-of-the-art algorithms by a considerable margin on networks of various sorts. Further improvement in dismantling performance is achievable by opting flexibly the choice of local clusters.

Fate of articulation points and bredges in percolation.

We investigate the statistics of articulation points and bredges (bridge edges) in complex networks in which bonds are randomly removed in a percolation process. Because of the heterogeneous structure of a complex network, the probability of a node to be an articulation point or the probability of an edge to be a bredge will not be homogeneous across the network. We therefore analyze full distributions of articulation point probabilities as well as bredge probabilities, using a message-passing or cavity approach to the problem. Our methods allow us to obtain these distributions both for large single instances of networks and for ensembles of networks in the configuration model class in the thermodynamic limit, through a single unified approach. We also evaluate deconvolutions of these distributions according to degrees of the node or the degrees of both adjacent nodes in the case of bredges. We obtain closed form expressions for the large mean degree limit of Erdős-Rényi networks. Moreover, we reveal and are able to rationalize a significant amount of structure in the evolution of articulation point and bredge probabilities in response to random bond removal. We find that full distributions of articulation point and bredge probabilities in real networks and in their randomized counterparts may exhibit significant differences even where average articulation point and bredge probabilities do not. We argue that our results could be exploited in a variety of applications, including approaches to network dismantling or to vaccination and islanding strategies to prevent the spread of epidemics or of blackouts in process networks.

Dismantling Networks by Skeleton Extraction and Greedy Tree Breaking

Network dismantling is one of the important NP-hard problems in the field of social network analysis. It aims to break down networks into many small components of limited size by only removing a small group of nodes. One feasible way is to decycle (eliminating all the cycles) the network first and then break the acyclic graph. However, existing decycling-based algorithms mainly concentrate on the decycling step, ignoring the importance of the tree breaking process. Besides, none of the algorithms try to pre-process the network, which may bring improvement in both effectiveness and efficiency. In this paper, we fill these two gaps by proposing a novel network dismantling algorithm that combines skeleton extraction and greedy tree breaking (SEGTB). Network skeleton supports the whole network structure, whose removal would leave a much looser structure and serves as an effective pre-processing for the dismantling problem. The presented tree breaking method is provided with theoretical proofs on its lower bound. Experiments on ten real-world datasets show that our proposed SEGTB algorithm is both effective and efficient, outperforming the state-of-the-art.

Brazilian Border Closures in Pandemic Times: A Comparative Approach to Four Regions

This paper discusses the context and the effects of border closures related to the COVID-19 pandemic in four border regions between Brazil and its neighbors, namely Venezuela, Colombia, Paraguay, and Argentina, from March to July 2020. The study highlights the low level of coordination among countries, bilateral or regional, in the course of the sanitary emergency. It also analyses the local impacts of the restrictive measures, especially on the twin cities due to their high level of interdependence, in which the inhabitants suffered from the dismantling of supply networks, the precarity of health services, and the economic downturn related to border closures.

Effectiveness of dismantling strategies on moderated vs. unmoderated online social platforms

Online social networks are the perfect test bed to better understand large-scale human behavior in interacting contexts. Although they are broadly used and studied, little is known about how their terms of service and posting rules affect the way users interact and information spreads. Acknowledging the relation between network connectivity and functionality, we compare the robustness of two different online social platforms, Twitter and Gab, with respect to banning, or dismantling, strategies based on the recursive censor of users characterized by social prominence (degree) or intensity of inflammatory content (sentiment). We find that the moderated (Twitter) vs. unmoderated (Gab) character of the network is not a discriminating factor for intervention effectiveness. We find, however, that more complex strategies based upon the combination of topological and content features may be effective for network dismantling. Our results provide useful indications to design better strategies for countervailing the production and dissemination of anti-social content in online social platforms.

Revisiting the power of reinsertion for optimal targets of network attack

Understanding and improving the robustness of networks has significant applications in various areas, such as bioinformatics, transportation, critical infrastructures, and social networks. Recently, there has been a large amount of work on network dismantling, which focuses on removing an optimal set of nodes to break the network into small components with sub-extensive sizes. However, in our experiments, we found these state-of-the-art methods, although seemingly different, utilize the same refinement technique, namely reinsertion, to improve the performance. Despite being mentioned with understatement, the technique essentially plays the key role in the final performance. Without reinsertion, the current best method would deteriorate worse than the simplest heuristic ones; while with reinsertion, even the random removal strategy achieves on par with the best results. As a consequence, we, for the first time, systematically revisit the power of reinsertion in network dismantling problems. We re-implemented and compared 10 heuristic and approximate competing methods on both synthetic networks generated by four classical network models, and 18 real-world networks which cover seven different domains with varying scales. The comprehensive ablation results show that: i) HBA (High Betweenness Adaption, no reinsertion) is the most effective network dismantling strategy, however, it can only be applicable in small scale networks; ii) HDA (High Degree Adaption, with reinsertion) achieves the best balance between effectiveness and efficiency; iii) The reinsertion techniques help improve the performance for most current methods; iv) The one, which adds back the node based on that it joins the clusters minimizing the multiply of both numbers and sizes, is the most effective reinsertion strategy for most methods. Our results can be a survey reference to help further understand the current methods and thereafter design the better ones.

A novel learning-based approach for efficient dismantling of networks

Dismantling of complex networks is a problem to find a minimal set of nodes in which the removal leaves the network broken into connected components of sub-extensive size. It has a wide spectrum of important applications, including network immunization and network destruction. Due to its NP-hard computational complexity, this problem cannot be solved exactly with polynomial time. Traditional solutions, including manually-designed and considerably sub-optimal heuristic algorithms, and accurate message-passing ones, all suffer from low efficiency in large-scale problems. In this paper, we introduce a simple learning-based approach, CoreGQN, which seeks to train an agent that is able to smartly choose nodes that would accumulate the maximum rewards. CoreGQN is trained by hundreds of thousands self-plays on small synthetic graphs, and can then be able to generalize well on real-world networks across different types with different scales. Extensive experiments demonstrate that CoreGQN performs on par with the state-of-art algorithms at greatly reduced computational costs, suggesting that CoreGQN should be the better choice for practical network dismantling purposes.

Scaling of percolation transitions on Erdös-Rényi networks under centrality-based attacks.

The study of network robustness focuses on the way the overall functionality of a network is affected as some of its constituent parts fail. Failures can occur at random or be part of an intentional attack and, in general, networks behave differently against different removal strategies. Although much effort has been put on this topic, there is no unified framework to study the problem. While random failures have been mostly studied under percolation theory, targeted attacks have been recently restated in terms of network dismantling. In this work, we link these two approaches by performing a finite-size scaling analysis to four dismantling strategies over Erdös-Rényi networks: initial and recalculated high degree removal and initial and recalculated high betweenness removal. We find that the critical exponents associated with the initial attacks are consistent with the ones corresponding to random percolation. For recalculated high degree, the exponents seem to deviate from mean field, but the evidence is not conclusive. Finally, recalculated betweenness produces a very abrupt transition with a hump in the cluster size distribution near the critical point, resembling some explosive percolation processes.

Community Detection Boosts Network Dismantling on Real-World Networks

Network dismantling techniques have gained increasing interest during the last years caused by the need for protecting and strengthening critical infrastructure systems in our society. We show that communities play a critical role in dismantling, given their inherent property of separating a network into strongly and weakly connected parts. The process of community-based dismantling depends on several design factors, including the choice of community detection method, community cut strategy, and inter-community node selection. We formalize the problem of community attacks to networks, identify critical design decisions for such methods, and perform a comprehensive empirical evaluation with respect to effectiveness and efficiency criteria on a set of more than 40 community-based network dismantling methods. We compare our results to state-of-the-art network dismantling, including collective influence, articulation points, as well as network decycling. We show that community-based network dismantling significantly outperforms existing techniques in terms of solution quality and computation time in the vast majority of real-world networks, while existing techniques mainly excel on model networks (ER, BA) mostly. We additionally show that the scalability of community-based dismantling opens new doors towards the efficient analysis of large real-world networks.

A comparative analysis of approaches to network-dismantling

Estimating, understanding, and improving the robustness of networks has many application areas such as bioinformatics, transportation, or computational linguistics. Accordingly, with the rise of network science for modeling complex systems, many methods for robustness estimation and network dismantling have been developed and applied to real-world problems. The state-of-the-art in this field is quite fuzzy, as results are published in various domain-specific venues and using different datasets. In this study, we report, to the best of our knowledge, on the analysis of the largest benchmark regarding network dismantling. We reimplemented and compared 13 competitors on 12 types of random networks, including ER, BA, and WS, with different network generation parameters. We find that network metrics, proposed more than 20 years ago, are often non-dominating competitors, while many recently proposed techniques perform well only on specific network types. Besides the solution quality, we also investigate the execution time. Moreover, we analyze the similarity of competitors, as induced by their node rankings. We compare and validate our results on real-world networks. Our study is aimed to be a reference for selecting a network dismantling method for a given network, considering accuracy requirements and run time constraints.

Dismantling efficiency and network fractality.

In network dismantling, a minimal set of nodes is identified whose removal breaks the network into small components of subextensive size. Because finding the optimal set of nodes is an NP-hard problem, several heuristic algorithms have been developed as alternative methods, for instance, the so-called belief propagation-based decimation (BPD) algorithm and the collective influence (CI) algorithm. Here, we test the performance of these algorithms and analyze them in terms of the fractality of the network. Networks are classified into two types: fractal and nonfractal networks. Real-world examples include the World Wide Web and the Internet at the autonomous system level, respectively. They have different ratios of long-range shortcuts to short-range ones. We find that the BPD algorithm works more efficiently than the CI algorithm no matter whether a network is fractal or not. On the other hand, the CI algorithm works better on nonfractal networks than on fractal networks. We construct diverse fractal and nonfractal model networks by controlling parameters such as the degree exponent, shortcut number, and system size and investigate how the performance of the two algorithms depends on structural features.

Compressing Networks with Super Nodes

Community detection is a commonly used technique for identifying groups in a network based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the network as a smaller network of ‘super nodes’, where each super node comprises one or more nodes of the original network. We can then use this super node representation as the input into standard community detection algorithms. To define the seeds, or centers, of our super nodes, we apply the ‘CoreHD’ ranking, a technique applied in network dismantling and decycling problems. We test our approach through the analysis of two common methods for community detection: modularity maximization with the Louvain algorithm and maximum likelihood optimization for fitting a stochastic block model. Our results highlight that applying community detection to the compressed network of super nodes is significantly faster while successfully producing partitions that are more aligned with the local network connectivity and more stable across multiple (stochastic) runs within and between community detection algorithms, yet still overlap well with the results obtained using the full network.

Optimal Dismantling of Interdependent Networks Based on Inverse Explosive Percolation

Seeking nodes whose removal can effectively dismantle networks is closely related to the robustness of networks under targeted attacks or malicious software. Modern systems, such as critical infrastructure networks and cyber-physical systems, however, become increasingly dependent on others, which can be encapsulated into the framework of interdependent networks. In this brief, we focus on the optimal dismantling of interdependent networks, and propose a novel algorithm, named inverse explosive percolation (IEP), to find the optimal removal nodes. The IEP proceeds by first identifying the nodes which make the least contribution to the giant mutual connected cluster of interdependent networks. When nodes have the same contribution, the one with the smallest overlapping degree is selected. We apply the IEP algorithm to interdependent networks composed of real-world power grids, Internet networks and artificial networks, and find IEP performs much better than the existing methods in various kinds of networks. Based on its efficiency, IEP can be applied to large-scale systems.

Fast and simple decycling and dismantling of networks.

Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple and considerably sub-optimal, on the one hand, and involved and accurate message-passing ones that evaluate single-node marginal probabilities, on the other hand. In this paper we propose a simple and extremely fast algorithm, CoreHD, which recursively removes nodes of the highest degree from the 2-core of the network. CoreHD performs much better than all existing simple algorithms. When applied on real-world networks, it achieves equally good solutions as those obtained by the state-of-art iterative message-passing algorithms at greatly reduced computational cost, suggesting that CoreHD should be the algorithm of choice for many practical purposes.

Network dismantling

We study the network dismantling problem, which consists of determining a minimal set of vertices in which removal leaves the network broken into connected components of subextensive size. For a large class of random graphs, this problem is tightly connected to the decycling problem (the removal of vertices, leaving the graph acyclic). Exploiting this connection and recent works on epidemic spreading, we present precise predictions for the minimal size of a dismantling set in a large random graph with a prescribed (light-tailed) degree distribution. Building on the statistical mechanics perspective, we propose a three-stage Min-Sum algorithm for efficiently dismantling networks, including heavy-tailed ones for which the dismantling and decycling problems are not equivalent. We also provide additional insights into the dismantling problem, concluding that it is an intrinsically collective problem and that optimal dismantling sets cannot be viewed as a collection of individually well-performing nodes.

Community Remembering

The dictatorship in Chile perpetrated massive human rights violations for 17 years, causing a rupture in social processes and engendering fear in the population. Data being gathered in an ongoing participatory action research study of the población (shantytown) La Pincoya show that while memory can be debilitating to most persons, it may empower others. Memories of the practices of the military regime continue to cause fear in some of the population, affecting community cohesion and participation in local organizations. This has led to the dismantling of social networks in the community, robbing members of their ability to be the protagonists of their own lives.

Gambling Addiction as a Pathology: Some Markers for Empowerment

Defined by researchers as “a silent epidemic” the gambling phenomenon is a social problem that is having negative impact on individuals, families and communities. Among these effects are seen a dismantling of community networks, weakening of family and social ties, psychiatric co-morbidity, suicides and lately more homelessness. Youth, women, elderly, deprived citizens and native communities constitute the social groups that seem to suffer more from gambling accessibility when compared to others. Without pretending to cover all these aspects, we intend, from a social critical perspective, to highlight some of the major psychosocial stakes of the gambling phenomenon. After a brief historical overview underlining the social construction of gambling as a pathology, we will address issues such as the social and ethical contradictions of governments when managing gambling and the heated debate around the disease model of addiction versus a multifactorial approach to this phenomenon. Finally, we propose markers...

Criminal Networks, Illegal Immigration and the Threat to Border Security

This paper considers some of the challenges posed to law enforcement agencies in post-modernity by the emergence of transnational criminal networks. Law enforcement, once very much local in character, must now reshape its structures and processes to meet the new and emerging risks presented. Though the paper uses the topic of illegal immigration to reveal something of the nature of such networks and the threat they pose, it also observes that fundamentally, transnational criminal networks are profit-driven and that, perhaps, it is misguided to think of these groups either as commodity-specific or process-specific. The paper concludes that law enforcement agencies need to meet the challenge that such networks present by managing their business with equal flexibility and resourcefulness. Though mechanisms to support that business are being developed, law enforcement agencies must not lose sight of the fact that it is successful outcomes, in the form of the dismantling and disruption of transnational criminal networks, rather than the new processes themselves (that simply underpin law enforcement's efforts) that are important.