Community Structure In Networks Research Articles

Community hiding: Completely escape from community detection

Community detection algorithms play an important role in revealing and analyzing complex network structures. However, when these algorithms are put into practice, privacy concerns often arise, especially when community nodes wish to safeguard their identities from exposure. This interaction between network analysis and privacy issues leads to what we refer to as the “community hiding problem.” In the context of concealing specific target communities, popular methods primarily focus on preventing community detection algorithms from accurately identifying the entire original community, resulting in partial concealment. This study formally addresses the challenge of achieving complete concealment of target communities. We introduce key metrics such as escape scores, dispersion scores, and hiding scores to precisely define the problem. Additionally, we design a metric, denoted as M-value, to evaluate the effectiveness of concealing target communities from multiple perspectives. To tackle this challenge, we employ a genetic algorithm that leverages previous knowledge to maximize the concealment of the target community while minimizing changes to link connections. We validate our approach through extensive experiments with various real-world datasets, demonstrating that our algorithm outperforms several state-of-the-art baseline algorithms across multiple metrics. Visual representations of our method confirm its ability to effectively hide target communities while minimally affecting the broader network's community structure, strengthening the inherent effectiveness of our community hiding approach. Furthermore, we assess the adaptability of our modified network with different community detection algorithms, consistently demonstrating effective concealment even when these algorithms are extended. This emphasizes the robustness and generality of our proposed approach in various algorithmic scenarios.

The equivalences of community detection methods for bipartite networks

Abstract Investigating the community structures of bipartite networks is a frequent topic of discussion in the ecological and social fields. The most widely used methods, as proposed by numerous academics from varying perspectives, include spectral graph partitioning, modularity, nonnegative matrix factorization, and stochastic block model. In this paper, we demonstrate three equivalences among these four methods. One, both Dhillon spectral graph partitioning and Barber modularity clustering are equivalent to solving for the matrix's left and right singular vectors after relaxing the discrete constraints. Two, the nonnegative matrix factorization clustering is equivalent to the Dhillon spectral graph partitioning. Three, The bipartite stochastic block model is equivalent to the constraint-based NMF that uses K-L divergence as its cost function. These equivalences, obtained through rigorous mathematical derivations, will aid in the future development of efficient algorithms for community detection in bipartite networks.

Product Promotion Strategies for Influencers in Social Network Associations

The development of the Internet has given birth to a new type of promotion mode, and the selection of promotion agents has become a hot issue. The influence index of the agent itself and the type of its association structure become the key factors affecting the degree of product promotion. In this study, we analyze different types of influencers and their community structure in social networks, study the influence of influencers' community structure and influence on information dissemination, and try to find out the agent selection strategy to obtain the highest promotion efficiency under the lowest budget. Based on these findings, this paper proposes an agent selection strategy for product promotion that integrates influencer type and association structure. The strategy suggests that firms first identify the social network structure of their target market and then select the combination of influencers that maximizes the effect of information dissemination. The findings of this study provide a new perspective and methodology for enterprises to promote their products in social networks, which helps them to utilize social network resources more effectively and enhance the effectiveness and efficiency of product promotion.

Distributed Pseudo-Likelihood Method for Community Detection in Large-Scale Networks

This paper proposes a distributed pseudo-likelihood method (DPL) to conveniently identify the community structure of large-scale networks. Specifically, we first propose a block-wise splitting method to divide large-scale network data into several subnetworks and distribute them among multiple workers. For simplicity, we assume the classical stochastic block model. Then, the DPL algorithm is iteratively implemented for the distributed optimization of the sum of the local pseudo-likelihood functions. At each iteration, the worker updates its local community labels and communicates with the master. The master then broadcasts the combined estimator to each worker for the new iterative steps. Based on the distributed system, DPL significantly reduces the computational complexity of the traditional pseudo-likelihood method using a single machine. Furthermore, to ensure statistical accuracy, we theoretically discuss the requirements of the worker sample size. Moreover, we extend the DPL method to estimate degree-corrected stochastic block models. The superior performance of the proposed distributed algorithm is demonstrated through extensive numerical studies and real data analysis.

Motif-based community detection in heterogeneous multilayer networks

Multilayer networks composed of intralayer edges and interlayer edges are an important type of complex networks. Considering the heterogeneity of nodes and edges, it is necessary to design more reasonable and diverse community detection methods for multilayer networks. Existing research on community detection in multilayer networks mainly focuses on multiplexing networks (where the nodes are homogeneous and the edges are heterogeneous), but few studies have focused on heterogeneous multilayer networks where both nodes and edges represent different semantics. In this paper, we studied community detection on heterogeneous multilayer networks and proposed a motif-based detection algorithm. First, the communities and motifs of multilayer networks are defined, especially the interlayer motifs. Then, the modularity of multilayer networks based on these motifs is designed, and the community structure of the multilayer network is detected by maximizing the modularity of multilayer networks. Finally, we verify the effectiveness of the detection algorithm on synthetic networks. In the experiments on synthetic networks, comparing with the classical community detection algorithms (without considering interlayer heterogeneity), the motif-based modularity community detection algorithm can obtain better results under different evaluation indexes, and we found that there exists a certain relationship between motifs and communities. In addition, the proposed algorithm is applied in the empirical network, which shows its practicability in the real world. This study provides a solution for the investigation of heterogeneous information in multilayer networks.

Collective cognition based analysis of community structure discovery algorithms

Social network topology can shape collective cognition and group behavior. Different social network topologies can facilitate various forms of collective cognition, leading to diverse collective cognition and group function. We analyzed the characteristics of contract networks and compared the performance of community structure discovery algorithms in social networks, using modularity as the assessment index. By examining the speed and effectiveness of these algorithms, we found that the Louvain algorithm and Girvan–Newman algorithm are suitable for discovering the network structure of sparse social networks. Experimental results have shown that the Louvain algorithm outperforms the Girvan–Newman algorithm on sparse networks across multiple scales. Finally, we learned a close relationship between collective cognition and community structure in contract networks, particularly influenced by the central nodes within these communities.

Identifying influential nodes based on the disassortativity and community structure of complex network

The complex networks exhibit significant heterogeneity in node connections, resulting in a few nodes playing critical roles in various scenarios, including decision-making, disease control, and population immunity. Therefore, accurately identifying these influential nodes that play crucial roles in networks is very important. Many methods have been proposed in different fields to solve this issue. This paper focuses on the different types of disassortativity existing in networks and innovatively introduces the concept of disassortativity of the node, namely, the inconsistency between the degree of a node and the degrees of its neighboring nodes, and proposes a measure of disassortativity of the node (DoN) by a step function. Furthermore, the paper analyzes and indicates that in many real-world network applications, such as online social networks, the influence of nodes within the network is often associated with disassortativity of the node and the community boundary structure of the network. Thus, the influential metric of node based on disassortativity and community structure (mDC) is proposed. Extensive experiments are conducted in synthetic and real networks, and the performance of the DoN and mDC is validated through network robustness experiments and immune experiment of disease infection. Experimental and analytical results demonstrate that compared to other state-of-the-art centrality measures, the proposed methods (DoN and mDC) exhibits superior identification performance and efficiency, particularly in non-disassortative networks and networks with clear community structures. Furthermore, we find that the DoN and mDC exhibit high stability to network noise and inaccuracies of the network data.

A multi-node attack scheme based on community partitioning in large scale infrastructure networks

Node attack plays a vital role in evaluating the reliability of large scale infrastructure networks, which has attracted intensive research interests. Unfortunately, most of them focus on single node attack. Multi-node attack based on MBA (Module based Adaptive) is a promising research vector with great potential in improving efficiency. However, MBA-based node attack typically needs to repetitively consider community structures of large networks during the entire node attack process, which brings significant loss in network reliability and causes computational overheads. In light of this, we propose a novel scheme based on MBA to implement multi-node attack, which adopts the Multilevel community partitioning algorithm to overcome the above limitations. We evaluate our scheme on two artificial synthetic networks and four real-world networks with comparison to four widely used node attack schemes, and demonstrate the non-negligible superiority of our scheme over all benchmarks. Especially in the US Powergrid, our scheme can always achieve robustness around 10 times that of other schemes when deleting the same percentage of nodes. To the best of our knowledge, we are the first to achieve an MBA-based node attack scheme that only needs to execute the community partitioning algorithm once during the entire node deletion process.

Finding community structure in Bayesian networks by heuristic K-standard deviation method

When constructing a Bayesian network for high-dimensional data, due to the complex relationships among distinct nodes, the difficulty in detecting the community structure will directly restrict the feasibility of the divide-and-conquer learning algorithm. This study attempts to solve this problem from the shortest path perspective and proposes the heuristic K-standard deviation algorithm. Firstly, we design a novel heuristic function and drive the A* algorithm to find the shortest paths between nodes in the Bayesian network. In addition, the new heuristic function is theoretically proved to be admissible and consistent. Experiments on different synthetic datasets and benchmark Bayesian networks verify that the proposed heuristic K-standard deviation algorithm generally gets better clustering performance than other representative algorithms and improves the efficiency and accuracy of the conventional Bayesian network structure learning algorithms, especially for high-dimensional data.

Multi-constraint non-negative matrix factorization for community detection: orthogonal regular sparse constraint non-negative matrix factorization

AbstractCommunity detection is an important method to analyze the characteristics and structure of community networks, which can excavate the potential links between nodes and further discover subgroups from complex networks. However, most of the existing methods only unilaterally consider the direct link topology without comprehensively considering the internal and external characteristics of the community as well as the result itself, which fails to maximize the access to the network information, thus affecting the effectiveness of community detection. To compensate for this deficiency, we propose a new community detection method based on multi-constraint non-negative matrix factorization, named orthogonal regular sparse constraint non-negative matrix factorization (ORSNMF). Based on the network topology, the ORSNMF algorithm models the differences of the outside of the community, the similarities of the nodes inside the community, and the sparseness of the community membership matrices at the same time, which together guides the iterative learning process to better reflect the underlying information and inherent attributes of the community structure in order to improve the correct rate of dividing subgroups. An algorithm with convergence guarantee is also proposed to solve the model, and finally a large number of comparative experiments are conducted, and the results show that the algorithm has good results.

Application of K-Core analysis based on complex network community structure to rolling bearing fault diagnosis

A complex network is a method to analyze nonlinear time series on multiple temporal and spatial scales. K-core analysis of several typical nonlinear series was studied, and then based on this, a fast algorithm method was employed to divide the community structure. According to the definition of k-core, the rolling bearings complex network was divided into different cores at the router level, and the main characteristic quantities such as degree distribution and clustering coefficient of every k-core can be analyzed. The results show that there is a corresponding relationship between the characteristic parameters and the community structure of the bearing. The analysis results show that compared with the traditional method, the method of complex network community structure and k-core analysis has a better diagnosis effect.

Community cohesion looseness in gene networks reveals individualized drug targets and resistance.

Community cohesion plays a critical role in the determination of an individual's health in social science. Intriguingly, a community structure of gene networks indicates that the concept of community cohesion could be applied between the genes as well to overcome the limitations of single gene-based biomarkers for precision oncology. Here, we develop community cohesion scores which precisely quantify the community ability to retain the interactions between the genes and their cellular functions in each individualized gene network. Using breast cancer as a proof-of-concept study, we measure the community cohesion score profiles of 950 case samples and predict the individualized therapeutic targets in 2-fold. First, we prioritize them by finding druggable genes present in the community with the most and relatively decreased scores in each individual. Then, we pinpoint more individualized therapeutic targets by discovering the genes which greatly contribute to the community cohesion looseness in each individualized gene network. Compared with the previous approaches, the community cohesion scores show at least four times higher performance in predicting effective individualized chemotherapy targets based on drug sensitivity data. Furthermore, the community cohesion scores successfully discover the known breast cancer subtypes and we suggest new targeted therapy targets for triple negative breast cancer (e.g. KIT and GABRP). Lastly, we demonstrate that the community cohesion scores can predict tamoxifen responses in ER+ breast cancer and suggest potential combination therapies (e.g. NAMPT and RXRA inhibitors) to reduce endocrine therapy resistance based on individualized characteristics. Our method opens new perspectives for the biomarker development in precision oncology.

Adversarial Socialbots Modeling Based on Structural Information Principles

The importance of effective detection is underscored by the fact that socialbots imitate human behavior to propagate misinformation, leading to an ongoing competition between socialbots and detectors. Despite the rapid advancement of reactive detectors, the exploration of adversarial socialbot modeling remains incomplete, significantly hindering the development of proactive detectors. To address this issue, we propose a mathematical Structural Information principles-based Adversarial Socialbots Modeling framework, namely SIASM, to enable more accurate and effective modeling of adversarial behaviors. First, a heterogeneous graph is presented to integrate various users and rich activities in the original social network and measure its dynamic uncertainty as structural entropy. By minimizing the high-dimensional structural entropy, a hierarchical community structure of the social network is generated and referred to as the optimal encoding tree. Secondly, a novel method is designed to quantify influence by utilizing the assigned structural entropy, which helps reduce the computational cost of SIASM by filtering out uninfluential users. Besides, a new conditional structural entropy is defined between the socialbot and other users to guide the follower selection for network influence maximization. Extensive and comparative experiments on both homogeneous and heterogeneous social networks demonstrate that, compared with state-of-the-art baselines, the proposed SIASM framework yields substantial performance improvements in terms of network influence (up to 16.32%) and sustainable stealthiness (up to 16.29%) when evaluated against a robust detector with 90% accuracy.

Remediation potential of an immobilized microbial consortium with corn straw as a carrier in polycyclic aromatic hydrocarbons contaminated soil

Polycyclic aromatic hydrocarbons (PAHs) are widespread in soils and threaten human health seriously. The immobilized microorganisms (IM) technique is an effective and environmentally sound approach for remediating PAH-contaminated soil. However, the knowledge of the remedial efficiency and the way IM operates using natural organic materials as carriers in complex soil environments is limited. In this study, we loaded a functional microbial consortium on corn straw to analyze the effect of IM on PAH concentration and explore the potential remediation mechanisms of IM in PAH-contaminated soil. The findings revealed that the removal rate of total PAHs in the soil was 88.25% with the application of IM after 20 days, which was 39.25% higher than the control treatment, suggesting that IM could more easily degrade PAHs in soil. The findings from high-throughput sequencing and quantitative PCR revealed that the addition of IM altered the bacterial community structure and key components of the bacterial network, enhanced cooperative relationships among bacteria, and increased the abundance of bacteria and functional gene copies such as nidA and nahAc in the soil, ultimately facilitating the degradation of PAHs in the soil. This study enhances our understanding of the potential applications of IM for the treatment of PAH-contaminated soil.

A generalized hypothesis test for community structure in networks

AbstractResearchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibit statistically meaningful community structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world datasets.

Epilepsy-related functional brain network alterations are already present at an early age in the GAERS rat model of genetic absence epilepsy.

Genetic Absence Epilepsy Rats from Strasbourg (GAERS) represent a model of genetic generalized epilepsy. The present longitudinal study in GAERS and age-matched non-epileptic controls (NEC) aimed to characterize the epileptic brain network using two functional measures, resting state-functional magnetic resonance imaging (rs-fMRI) and manganese-enhanced MRI (MEMRI) combined with morphometry, and to investigate potential brain network alterations, following long-term seizure activity. Repeated rs-fMRI measurements at 9.4 T between 3 and 8 months of age were combined with MEMRI at the final time point of the study. We used graph theory analysis to infer community structure and global and local network parameters from rs-fMRI data and compared them to brain region-wise manganese accumulation patterns and deformation-based morphometry (DBM). Functional connectivity (FC) was generally higher in GAERS when compared to NEC. Global network parameters and community structure were similar in NEC and GAERS, suggesting efficiently functioning networks in both strains. No progressive FC changes were observed in epileptic animals. Network-based statistics (NBS) revealed stronger FC within the cortical community, including regions of association and sensorimotor cortex, and with basal ganglia and limbic regions in GAERS, irrespective of age. Higher manganese accumulation in GAERS than in NEC was observed at 8 months of age, consistent with higher overall rs-FC, particularly in sensorimotor cortex and association cortex regions. Functional measures showed less similarity in subcortical regions. Whole brain volumes of 8 months-old GAERS were higher when compared to age-matched NEC, and DBM revealed increased volumes of several association and sensorimotor cortex regions and of the thalamus. rs-fMRI, MEMRI, and volumetric data collectively suggest the significance of cortical networks in GAERS, which correlates with an increased fronto-central connectivity in childhood absence epilepsy (CAE). Our findings also verify involvement of basal ganglia and limbic regions. Epilepsy-related network alterations are already present in juvenile animals. Consequently, this early condition seems to play a greater role in dynamic brain function than chronic absence seizures.

Plant-pollinator network architecture does not impact intraspecific microbiome variability.

Variation in how individuals interact with food resources can directly impact, and be affected by, their microbial interactions due to the potential for transmission. The degree to which this transmission occurs, however, may depend on the structure of forager networks, which determine the community-scale transmission opportunities. In particular, how the community-scale opportunity for transfer balances individual-scale barriers to transmission is unclear. Examining the bee-flower and bee-microbial interactions of over 1000 individual bees, we tested (1) the degree to which individual floral visits predicted microbiome composition and (2) whether plant-bee networks with increased opportunity for microbial transmission homogenized the microbiomes of bees within that network. The pollen community composition carried by bees was associated with microbiome composition at some sites, suggesting that microbial transmission at flowers occurred. Contrary to our predictions, however, microbiome variability did not differ based on transfer opportunity: bee microbiomes in asymmetric networks with high opportunity for microbial transfer were similarly variable compared to microbiomes in networks with more evenly distributed links. These findings suggest that microbial transmission at flowers is frequent enough to be observed at the community level, but that community network structure did not substantially change the dynamics of this transmission, perhaps due to filtering processes in host guts.

Long-Horizon Associative Learning Explains Human Sensitivity to Statistical and Network Structures in Auditory Sequences.

Networks are a useful mathematical tool for capturing the complexity of the world. In a previous behavioral study, we showed that human adults were sensitive to the high-level network structure underlying auditory sequences, even when presented with incomplete information. Their performance was best explained by a mathematical model compatible with associative learning principles, based on the integration of the transition probabilities between adjacent and nonadjacent elements with a memory decay. In the present study, we explored the neural correlates of this hypothesis via magnetoencephalography (MEG). Participants (N = 23, 16 females) passively listened to sequences of tones organized in a sparse community network structure comprising two communities. An early difference (∼150 ms) was observed in the brain responses to tone transitions with similar transition probability but occurring either within or between communities. This result implies a rapid and automatic encoding of the sequence structure. Using time-resolved decoding, we estimated the duration and overlap of the representation of each tone. The decoding performance exhibited exponential decay, resulting in a significant overlap between the representations of successive tones. Based on this extended decay profile, we estimated a long-horizon associative learning novelty index for each transition and found a correlation of this measure with the MEG signal. Overall, our study sheds light on the neural mechanisms underlying human sensitivity to network structures and highlights the potential role of Hebbian-like mechanisms in supporting learning at various temporal scales.

Effects of protection and temperature variation on temporal stability in a marine reserve network.

Understanding the drivers of ecosystem stability has been a key focus of modern ecology as the impacts of the Anthropocene become more prevalent and extreme. Marine protected areas (MPAs) are tools used globally to promote biodiversity and mediate anthropogenic impacts. However, assessing the stability of natural ecosystems and responses to management actions is inherently challenging due to the complex dynamics of communities with many interdependent taxa. Using a 12-year time series of subtidal community structure in an MPA network in the Channel Islands (United States), we estimated species interaction strength (competition and predation), prey species synchrony, and temporal stability in trophic networks, as well as temporal variation in sea surface temperature to explore the causal drivers of temporal stability at community and metacommunity scales. At the community scale, only trophic networks in MPAs at Santa Rosa Island showed greater temporal stability than reference sites, likely driven by reduced prey synchrony. Across islands, competition was sometimes greater and predation always greater in MPAs compared with reference sites. Increases in interaction strength resulted in lower temporal stability of trophic networks. Although MPAs reduced prey synchrony at the metacommunity scale, reductions were insufficient to stabilize trophic networks. In contrast, temporal variation in sea surface temperature had strong positive direct effects on stability at the regional scale and indirect effects at the local scale through reductions in species interaction strength. Although MPAs can be effective management strategies for protecting certain species or locations, our findings for this MPA network suggest that temperature variation has a stronger influence on metacommunity temporal stability by mediating species interactions and promoting a mosaic of spatiotemporal variation in community structure of trophic networks. By capturing the full spectrum of environmental variation in network planning, MPAs will have the greatest capacity to promote ecosystem stability in response to climate change.

Effects of Combined Stress of High Density Polyethylene Microplastics and Chlorimuron-ethyl on Soybean Growth and Rhizosphere Bacterial Community

With the vigorous development of agriculture in China， plastic mulch film and pesticides are widely used in agricultural production. However， the accumulation of microplastics （formed by the degradation of plastic mulch film） and pesticides in soil has also caused many environmental problems. At present， the environmental biological effects of microplastics or pesticides have been reported， but there are few studies on the combined effects on crop growth and the rhizosphere soil bacterial community. Therefore， in this study， the high density polyethylene microplastics （HDPE， 500 mesh） were designed to be co-treated with sulfonylurea herbicide chlorimuron-ethyl to study their effects on soybean growth. In addition， the effects of the combined stress of HDPE and chlorimuron-ethyl on soybean rhizosphere soil bacterial community diversity， structure composition， microbial community network， and soil function were investigated using high-throughput sequencing technology， interaction network， and PICRUSt2 function analysis to clarify the combined toxicity of HDPE and chlorimuron-ethyl to soybean. The results showed that the half-life of chlorimuron-ethyl in soil was prolonged by the 1% HDPE treatment （from 11.5 d to 14.3 d）， and the combined stress of HDPE and chlorimuron-ethyl had more obvious inhibition effects on soybean growth than that of the single pollutant or control. The HiSeq 2 500 sequencing showed that the rhizosphere bacterial community of soybean was composed of 20 phyla and 312 genera under combined stress， the number of phyla and genera was significantly less than that of the control and single pollutant treatment， and the relative abundances of bacteria with potential biological control and plant growth-promoting characteristics （such as Nocardioides and Sphingomonas） were reduced. Alpha diversity analysis showed that the combined stress significantly reduced the richness and diversity of the soybean rhizosphere bacterial community， and Beta diversity analysis showed that the combined stress significantly changed the structure of the bacterial community. The dominant flora of the rhizosphere bacterial community were regulated， and the abundances of secondary functional layers such as amino acid metabolism， energy metabolism， and lipid metabolism were reduced under combined stress by the analysis of LEfSe and PICRUSt2. It was inferred from the network analysis that the combined stress of HDPE and chlorimuron-ethyl reduced the total number of connections and network density of soil bacteria， simplified the network structure， and changed the important flora species to maintain the stability of the network. The results above indicated that the combined stress of HDPE and chlorimuron-ethyl significantly affected the growth of soybean and changed the rhizosphere bacterial community structure， soil function， and network structure. Compared with that of the single pollutant treatment， the potential risk of combined stress was greater. The results of this study can provide guidance for evaluating the ecological risks of polyethylene microplastics and chlorimuron-ethyl and for the remediation of contaminated soil.