Largest Connected Component Research Articles

Robustness of Real-World Networks after Weight Thresholding with Strong Link Removal

Weight thresholding (WT) is a method intended to decrease the number of links within weighted networks that may otherwise be excessively dense for network science applications. WT aims to remove links to simplify the network by holding most of the features of the original network. Here, we test the robustness and the efficacy of the node attack strategies on real-world networks subjected to WT that remove links of higher weight (strong links). We measure the network robustness along node removal with the largest connected component (LCC). We find that the real-world networks under study are generally robust when subjected to WT. Nonetheless, WT with strong link removal changes the efficacy of the attack strategies and the rank of node centralities. Also, WT with strong link removal may trigger a more significant change in the node centrality rank than WT by removing weak links. Network science research with the aim to find important/influential nodes in the network has to consider that simplifying the network with WT methodologies may change the node centrality.

Random Walks-Based Node Centralities to Attack Complex Networks

Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. Different research studies have proposed many node centralities based on the network structure for ranking nodes to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks and is an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node centralities for network dismantling with effective node removal strategies from the literature, namely betweenness, closeness, degree, and k-shell node removal, for synthetic and real-world networks. We evaluate the dismantling of the network by using the size of the largest connected component (LCC). We find that the degree nodes attack is the best strategy overall, and the new node removal strategies based on RW show the highest efficacy in regard to peculiar network topology. Specifically, RW strategy based on covering time emerges as the most effective strategy for a synthetic lattice network and a real-world road network. Our results may help researchers select the best node attack strategies in a specific network class and build more robust network structures.

Examining indicators of complex network vulnerability across diverse attack scenarios

Complex networks capture the structure, dynamics, and relationships among entities in real-world networked systems, encompassing domains like communications, society, chemistry, biology, ecology, politics, etc. Analysis of complex networks lends insight into the critical nodes, key pathways, and potential points of failure that may impact the connectivity and operational integrity of the underlying system. In this work, we investigate the topological properties or indicators, such as shortest path length, modularity, efficiency, graph density, diameter, assortativity, and clustering coefficient, that determine the vulnerability to (or robustness against) diverse attack scenarios. Specifically, we examine how node- and link-based network growth or depletion based on specific attack criteria affect their robustness gauged in terms of the largest connected component (LCC) size and diameter. We employ partial least squares discriminant analysis to quantify the individual contribution of the indicators on LCC preservation while accounting for the collinearity stemming from the possible correlation between indicators. Our analysis of 14 complex network datasets and 5 attack models invariably reveals high modularity and disassortativity to be prime indicators of vulnerability, corroborating prior works that report disassortative modular networks to be particularly susceptible to targeted attacks. We conclude with a discussion as well as an illustrative example of the application of this work in fending off strategic attacks on critical infrastructures through models that adaptively and distributively achieve network robustness.

Forecasting real-world complex networks’ robustness to node attack using network structure indexes

In this study, we simulate the degree and betweenness node attack over a large set of 200 real-world networks from different areas of science. We perform an initial node attack approach, where the node centrality rank is computed at the beginning of the simulation, and it is not updated along the node removal process. We quantify the network damage by tracing the largest connected component (LCC) and evaluate the network robustness with the “percolation threshold qc,” i.e., the fraction of nodes removed, for which the size of the LCC is quasi-zero. We correlate qc with 20 network structural indicators (NSIs) from the literature using single linear regression (SLR), multiple linear regression (MLR) models, and the Pearson correlation coefficient test. The NSIs cover most of the essential structural features proposed in network science to describe real-world networks. We find that the Estrada heterogeneity (EH) index, evaluating the degree difference of connected nodes, best predicts qc. The EH index measures the network node degree heterogeneity based on the difference of functions of node degrees for all pairs of linked nodes. We find that the qc value decreases as a function of the EH index, unveiling that heterogeneous real-world networks with a higher variance in the degree of connected nodes are more vulnerable to node attacks.

Persistent homology analysis of type 2 diabetes genome-wide association studies in protein-protein interaction networks.

Genome-wide association studies (GWAS) involving increasing sample sizes have identified hundreds of genetic variants associated with complex diseases, such as type 2 diabetes (T2D); however, it is unclear how GWAS hits form unique topological structures in protein-protein interaction (PPI) networks. Using persistent homology, this study explores the evolution and persistence of the topological features of T2D GWAS hits in the PPI network with increasing p-value thresholds. We define an n-dimensional persistent disease module as a higher-order generalization of the largest connected component (LCC). The 0-dimensional persistent T2D disease module is the LCC of the T2D GWAS hits, which is significantly detected in the PPI network (196 nodes and 235 edges, P0.05). In the 1-dimensional homology group analysis, all 18 1-dimensional holes (loops) of the T2D GWAS hits persist over all p-value thresholds. The 1-dimensional persistent T2D disease module comprising these 18 persistent 1-dimensional holes is significantly larger than that expected by chance (59 nodes and 83 edges, P0.001), indicating a significant topological structure in the PPI network. Our computational topology framework potentially possesses broad applicability to other complex phenotypes in identifying topological features that play an important role in disease pathobiology.

PeerRemove: An adaptive node removal strategy for P2P botnet based on deep reinforcement learning

Botnets have become one of the major intrusion threats to cybersecurity. P2P botnets have high concealment and resilience because of their distributed structure, which are difficult to be completely dismantled and destroyed. Existing methods based on traffic statistics and vulnerability tracing cannot effectively solve the problem of P2P botnet disintegration. Although P2P networks emphasize that each node is peer-to-peer, the difference in processing power, resource distribution, and node bandwidth can lead to a certain heterogeneity. The critical nodes bridge the underlying bot nodes and the upper control server. Traditional methods for ranking the importance of nodes mainly relies on classical graph-theoretic feature statistics method, such as degree, betweenness, clustering coefficient, feature vector centrality, PageRank, etc. In this paper, botnet defense strategies are investigated from the perspective of complex network graph theory, and graph embedding and deep reinforcement learning combination optimization methods are adopted to handle the critical nodes identification problem of P2P botnets. Then, a novel adaptive node removal model called PeerRemove is proposed. The model uses Structure2vec graph embedding to characterize the network structure information as a low-dimensional embedding space, and it uses n-step Q-learning to train the model to learn complex topological patterns to find the critical nodes that effectively disintegrate the network. To evaluate the effectiveness of the proposed method, the Area Under the Curve (AUC) of the Largest Connected Component (LCC) size during node removal is used as an evaluation indicator, and six different types real or synthetic P2P botnets are selected, namely Sality, ZeroAccess, NSIS, Mozi, Gnutella, and Peer sampling service. Experiments are conducted on many real and model networks with node sizes reaching thousands and tens of thousands, and our method is compared with five classical static or dynamic node attack methods of HAD, PageRank, CI, BPD, and HPRA. The experimental results show that the overall AUC curve of the PeerRemove method is lower than that of the benchmark method, which can minimize botnet resiliency at a small cost. The proposed method is superior to the existing node removal methods and shows good robustness and feasibility. To demonstrate the generality of this method, it is tested on a centralized topological dataset and good experimental results are obtained.

Network Connectivity Under a Probabilistic Node Failure Model

Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against failures. Most of the available studies assume that the node removal task is always successful. Yet, we argue that this assumption is unrealistic. Indeed, the removal process should take into account also the strength of the targeted node itself, to simulate the failure scenarios in a more effective and realistic fashion. Unlike previous literature, herein a {\em probabilistic node failure model} is proposed, in which nodes may fail with a particular probability, considering two variants, namely: {\em Uniform} (in which the nodes survival-to-failure probability is fixed) and {\em Best Connected} (BC) (where the nodes survival probability is proportional to their degree). To evaluate our method, we consider five popular centrality metrics carrying out an experimental, comparative analysis to evaluate them in terms of {\em effectiveness} and {\em coverage}, on four real-world graphs. By effectiveness and coverage we mean the ability of selecting nodes whose removal decreases graph connectivity the most. Specifically, the graph spectral radius reduction works as a proxy indicator of effectiveness, and the reduction of the largest connected component (LCC) size is a parameter to assess coverage. The metric that caused the biggest drop has been then compared with the Benchmark analysis (i.e, the non-probabilistic degree centrality node removal process) to compare the two approaches. The main finding has been that significant differences emerged through this comparison with a deviation range that varies from 2\% up to 80\% regardless of the dataset used that highlight the existence of a gap between the common practice with a more realistic approach.

Research on the Destruction Resistance of Giant Urban Rail Transit Network from the Perspective of Vulnerability

Giant urban rail transit (GURT) systems have been formed in many metropolises and play a critical role in addressing serious traffic congestion. Unfortunately, as a dynamic and complex system, the vulnerability of GURT networks under various failure scenarios will be more prominent as the network expansion continues. Thus, it is imperative to explore the complex structural characteristics of the network and improve the ability to deal with the disturbance of emergencies. In this study, the destruction resistance of GURT networks with scale growth is illustrated from a vulnerability perspective. Specifically, taking Shanghai rail transit (SHRT) system as an example, the network topology model is constructed using the Space L method, and the network structure characteristics are analyzed based on the complex network theory. In addition, five attack strategies are developed to represent random and targeted attacks during the simulation of network failure, and two metrics are determined to evaluate the network vulnerability. Some meaningful results have been obtained: (i) The Shanghai rail transit planning network (SHRTPN) has increased the network efficiency by more than 10% over the Shanghai rail transit operating network (SHRTON) and has effectively enhanced the network destruction resistance. (ii) The SHRT network is a small-world network and shows significant vulnerability under the targeted attacks. The failure of only 3% high betweenness stations in SHRTON can lead to a 66.2% decrease in the network efficiency and a 75.8% decrease in the largest connected component (LCC) ratio. (iii) Attacking stations will cause more severe network failures than attacking edges, and it is necessary to focus on preventing catastrophic network failure caused by the critical station’s failure breaking the threshold. Finally, the strategies for improving the destruction resistance of GURT networks are proposed. The findings of this research can provide an essential reference for the rational planning, safety protection, and sustainable construction of GURT systems.

Network-based response module comprised of gene expression biomarkers predicts response to infliximab at treatment initiation in ulcerative colitis

This cross-cohort study aimed to (1) determine a network-based molecular signature that predicts the likelihood of inadequate response to the tumor necrosis factor-ɑ inhibitor (TNFi) therapy, infliximab, in ulcerative colitis (UC) patients, and (2) address biomarker irreproducibility across different cohort studies. Whole-transcriptome microarray data were derived from biopsies of affected colon tissue from 2 cohorts of infliximab-treated UC patients (training N=24 and validation N=22). Response was defined as endoscopic and histologic healing at 4-6 weeks and 8 weeks, respectively. From the training cohort, genes with RNA expression that significantly correlated with clinical response outcomes were mapped onto the Human Interactome network map of protein-protein interactions to identify a largest connected component (LCC) of proteins indicative of infliximab response status in UC. Expression levels of transcripts within the LCC were fed into a probabilistic neural network model to generate a classifier that predicts inadequate response to infliximab. A classifier predictive of inadequate response to infliximab was generated and tested in a cross-cohort, blinded fashion; the AUC was 0.83 and inadequate response was predicted with a 100% positive predictive value and 64% sensitivity. Genes separately identified from the 2 cohorts that correlated with response to infliximab appeared distinct but mapped onto the same network region of the Human Interactome, reflecting a common underlying biology of response among UC patients. Cross-cohort validation of a classifier predictive of infliximab response status in UC patients indicates that a molecular signature of non-response to TNFi therapies is present in patients' baseline gene expression data. The goal is to develop a diagnostic test that predicts which patients will have an inadequate response to targeted therapies and define new targets and pathways for therapeutic development.

Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi–Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that when model networks present absent or low modular structure ID strategy is more effective than IB to decrease the LCC. Conversely, in the case the model network present higher modularity, the IB strategy becomes the most effective to fragment the LCC. In addition, networks with higher modularity present a signature of a 1st order percolation transition and a decrease of the LCC with one or several abrupt changes when nodes are removed, for both strategies; differently, networks with non-modular structure or low modularity show a 2nd order percolation transition networks when nodes are removed. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the network robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks for both the node attack strategies, especially for the IB strategy (p-value < 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

Identifying important nodes for temporal networks based on the ASAM model

The identification of important nodes in a temporal network is of great significance for the analysis and control of the information dissemination process. In this work, the multi-layer coupled network analysis method is employed to identify important nodes in a temporal network. First, to overcome the problem of a fixed constant being unable to reflect differences in the inter-layer coupling relationship, and by combining a node’s own neighbors and common neighbors of nodes in two-time layers, a new Enhanced Similarity Index (ESI) is proposed to measure the inter-layer coupling relationship. Secondly, the attenuation factor is introduced to more accurately describe the inter-layer coupling relationship. Finally, an Attenuation-Based Supra-Adjacency Matrix (ASAM) temporal network modeling method based on the attenuation of the inter-layer coupling strength is proposed. The importance of nodes in the temporal network is evaluated by calculating the eigenvector centrality of the nodes in each time layer in the temporal network. It is found that after deleting a certain percentage of the important nodes identified by the ASAM method, the temporal Largest Connected Component (LCC) of the network becomes smaller, and the network performance is improved as compared with the SAM and SSAM methods. The results indicate that the important nodes identified by the ASAM are at the core of the network and have a greater impact on the network structure and functions. This demonstrates that the proposed ASAM model can more effectively identify important nodes in the temporal network, and has significant application value in this research field.

Identification and Quantification of Node Criticality through EWM\u2013TOPSIS: A Study of Hong Kong\u2019s MTR System

Public transport networks (PTNs) are critical in populated and rapidly densifying cities such as Hong Kong, Beijing, Shanghai, Mumbai, and Tokyo. Public transportation plays an indispensable role in urban resilience with an integrated, complex, and dynamically changeable network structure. Consequently, identifying and quantifying node criticality in complex PTNs is of great practical significance to improve network robustness from damage. Despite the proposition of various node criticality criteria to address this problem, few succeeded in more comprehensive aspects. Therefore, this paper presents an efficient and thorough ranking method, that is, entropy weight method (EWM)–technology for order preference by similarity to an ideal solution (TOPSIS), named EWM–TOPSIS, to evaluate node criticality by taking into account various node features in complex networks. Then we demonstrate it on the Mass Transit Railway (MTR) in Hong Kong by removing and recovering the top k critical nodes in descending order to compare the effectiveness of degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), and the proposed EWM–TOPSIS method. Four evaluation indicators, that is, the frequency of nodes with the same ranking (F), the global network efficiency (E), the size of the largest connected component (LCC), and the average path length (APL), are computed to compare the performance of the four methods and measure network robustness under different designed attack and recovery strategies. The results demonstrate that the EWM–TOPSIS method has more obvious advantages than the others, especially in the early stage.

Modeling the Consequences of Social Distancing Over Epidemics Spreading in Complex Social Networks: From Link Removal Analysis to SARS-CoV-2 Prevention

In this perspective, we describe how the link removal (LR) analysis in social complex networks may be a promising tool to model non-pharmaceutical interventions (NPIs) and social distancing to prevent epidemics spreading. First, we show how the extent of the epidemic spreading and NPIs effectiveness over complex social networks may be evaluated with a static indicator, that is, the classic largest connected component (LCC). Then we explain how coupling the LR analysis and type SIR epidemiological models (EM) provide further information by including the temporal dynamics of the epidemic spreading. This is a promising approach to investigate important aspects of the recent NPIs applied by government to contain SARS-CoV-2, such as modeling the effect of the social distancing severity and timing over different network topologies. Further, implementing different link removal strategies to halt epidemics spreading provides information to individuate more effective NPIs, representing an important tool to offer a rationale sustaining policies to prevent SARS-CoV-2 and similar epidemics.

Identifying critical metro stations in multiplex network based on D–S evidence theory

Public transport networks (PTNs) undertake large amount of passenger demand in the urban transport system. Particularly, stations in metro networks with high significance in structure and function are more likely to contribute to passenger transport. Once these stations are under functional failure, it is easy to lead to the collapse of network connectivity. Thus, identifying critical nodes in PTNs is of practical significance for the public transport planning and operation. This study proposes an identification method for the critical nodes in multiplex network by considering the interaction between metro and bus networks. First, metro and bus networks are constructed by L-space and P-space methods, respectively. Then, ridership is extracted to describe the connection between nodes as the weights of links, and the metro-bus multiplex network is then constructed. Furthermore, the identification method in Multiplex Network based on Dempster–Shafer evidence theory (MNDS) is proposed to fuse the significance of nodes in sub-networks, and the critical nodes in the multiplex network are identified. Finally, the PTNs in Shenzhen City, China, is used as a case to demonstrate the feasibility of MNDS. By attacking critical nodes, a comparison is conducted and compared with two traditional identification methods (Weighted Closeness Centrality and Technique for Order Preference by Similarity to Ideal Solution) using two indicators, global efficiency (GE) and the size of the largest connected component (LCC). The results indicate the critical nodes identified by MNDS are of greater significance than those identified by the other two methods. This study provides a feasible method for critical nodes identification in urban public transport system, which can be applied to public transport operation and planning.

Automatic brain extraction from MRI of human head scans using Helmholtz free energy principle and morphological operations

In this article, two novel methods are proposed to detect the brain boundary in a magnetic resonance image (MRI) by making an analogy between Helmholtz free energy (HFE) principle in thermodynamics and the intensity of pixels in an image. In the first method, an intensity transformation equation is derived using HFE. This transformation is applied to pixels in each slice of the MRI of human head and is used to detect boundaries of all objects present in it. To identify the brain portion among these objects, a sequence of two dimensional (2D) morphological operations and the largest connected component (LCC) analysis are done. These operations produced a mask for the brain using which the brain is extracted from the T1-W MRI slices. However, the LCC process failed in some cases to identify the brain region correctly. To address this issue, a second method which makes use of information in the adjacent slices is developed. This extended scheme performed well in extracting the brain portion from each slice of a MRI volume. Experiments are conducted by applying this schemes on 38 volumes of MRI of human head scans collected from the Internet Brain Segmentation Repository (IBSR). The proposed methods produced competitive or better results than the existing popular methods Brain Extraction Tool (BET), Brain Surface Extractor (BSE) and other similar recent methods.

Modelling photosystem I as a complex interacting network.

In this paper, we model the excitation energy transfer (EET) of photosystem I (PSI) of the common pea plant Pisum sativum as a complex interacting network. The magnitude of the link energy transfer between nodes/chromophores is computed by Forster resonant energy transfer (FRET) using the pairwise physical distances between chromophores from the PDB 5L8R (Protein Data Bank). We measure the global PSI network EET efficiency adopting well-known network theory indicators: the network efficiency (Eff) and the largest connected component (LCC). We also account the number of connected nodes/chromophores to P700 (CN), a new ad hoc measure we introduce here to indicate how many nodes in the network can actually transfer energy to the P700 reaction centre. We find that when progressively removing the weak links of lower EET, the Eff decreases, while the EET paths integrity (LCC and CN) is still preserved. This finding would show that the PSI is a resilient system owning a large window of functioning feasibility and it is completely impaired only when removing most of the network links. From the study of different types of chromophore, we propose different primary functions within the PSI system: chlorophyll a (CLA) molecules are the central nodes in the EET process, while other chromophore types have different primary functions. Furthermore, we perform nodes removal simulations to understand how the nodes/chromophores malfunctioning may affect PSI functioning. We discover that the removal of the CLA triggers the fastest decrease in the Eff, confirming that CAL is the main contributors to the high EET efficiency. Our outcomes open new perspectives of research, such comparing the PSI energy transfer efficiency of different natural and agricultural plant species and investigating the light-harvesting mechanisms of artificial photosynthesis both in plant agriculture and in the field of solar energy applications.

Disrupting resilient criminal networks through data analysis: The case of Sicilian Mafia.

Compared to other types of social networks, criminal networks present particularly hard challenges, due to their strong resilience to disruption, which poses severe hurdles to Law-Enforcement Agencies (LEAs). Herein, we borrow methods and tools from Social Network Analysis (SNA) to (i) unveil the structure and organization of Sicilian Mafia gangs, based on two real-world datasets, and (ii) gain insights as to how to efficiently reduce the Largest Connected Component (LCC) of two networks derived from them. Mafia networks have peculiar features in terms of the links distribution and strength, which makes them very different from other social networks, and extremely robust to exogenous perturbations. Analysts also face difficulties in collecting reliable datasets that accurately describe the gangs’ internal structure and their relationships with the external world, which is why earlier studies are largely qualitative, elusive and incomplete. An added value of our work is the generation of two real-world datasets, based on raw data extracted from juridical acts, relating to a Mafia organization that operated in Sicily during the first decade of 2000s. We created two different networks, capturing phone calls and physical meetings, respectively. Our analysis simulated different intervention procedures: (i) arresting one criminal at a time (sequential node removal); and (ii) police raids (node block removal). In both the sequential, and the node block removal intervention procedures, the Betweenness centrality was the most effective strategy in prioritizing the nodes to be removed. For instance, when targeting the top 5% nodes with the largest Betweenness centrality, our simulations suggest a reduction of up to 70% in the size of the LCC. We also identified that, due the peculiar type of interactions in criminal networks (namely, the distribution of the interactions’ frequency), no significant differences exist between weighted and unweighted network analysis. Our work has significant practical applications for perturbing the operations of criminal and terrorist networks.

Link and Node Removal in Real Social Networks: A Review

We review the main results from the literature on the consequences of link and node removal in real social networks We restrict our review to only those works that adopted the two most common measures of network robustness, i e , the largest connected component (LCC) and network efficiency (Eff) We consider both binary and weighted network approaches We show that the study of the response of social networks subjected to link/node removal turns out to be extremely useful for managing a number of real problems For instance, we show that the consequences of the imposition of social distancing in many states to control the spread of COVID-19 could be analyzed within the framework of social network analysis Our mini-review outlines that in social networks, it is necessary to consider the weight of links between persons to perform reliable analyses Finally, we propose promising lines for future research in social network science

Liver Segmentation on a Variety of Computed Tomography (CT) Images Based on Convolutional Neural Networks Combined with Connected Components

Liver Segmentation on a Variety of Computed Tomography (CT) Images Based on Convolutional Neural Networks Combined with Connected Components

Robustness in Multilayer Networks Under Strategical and Random Attacks

Many real-world complex systems are modelled by multilayer networks (MLNs) which are inter-connected and inter-dependent in nature. For example, Transport networks, Power grid networks, Biological networks etc. In these networks, damage to any network layer may affect the functionality of other network layers or the entire system of multilayer network. For example, in the Transport networks, damage to Road networks may affect the Railway network as well as Air-Transport networks. Therefore, the robustness of these networks is not only an important characteristics, but also it is a challenging area of research. In the present research work, we study the robustness behavior of synthetic MLNs under random attacks as well as targeted attack by removing the specified fraction of nodes from each network layer and compare the results with single layer networks. For both kinds of attacks, it is revealed that the single layer networks are more vulnerable towards failure as compared to the MLNs. We also study the robustness in the case of MLN where network layers contain more than one connected components. By keeping the network layers intact (not removing the nodes), we remove the inter-layer edges sequentially. It is found that before the removal of last inter-layer edge, MLN contains approximately 95% of nodes in largest connected component (LCC)in the best case and approximately 73% of nodes in (LCC) in the worst case under strategical attacks.