Community Structure In Networks Research Articles

Evidence of community structure in phonological networks of multiple languages.

Thousands of phonological word forms known to a speaker can be organised as a lexical network using the tools of network science. In these networks, nodes represent words and edges are placed between phonological neighbours. Previous work has shown that phonological networks of various languages have similar macrolevel network properties. The present study aimed to investigate if phonological networks of different languages also have similar mesolevel properties, specifically, the presence of robust community structure. Prior community detection analyses revealed robust community structure for English. Community detection analyses conducted on French, German, Dutch, and Spanish networks indicate that all networks showed strong evidence of community structure-mesolevel clustering of word forms whereby larger communities tended to contain shorter, frequent words with many phonological neighbours. Words of the same community tended to share similar phonotactic structures. Results suggest that the organisation of phonological word forms in language are governed by similar principles that could have important implications for lexical processing. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Supplemental Material for Evidence of Community Structure in Phonological Networks of Multiple Languages

Supplemental Material for Evidence of Community Structure in Phonological Networks of Multiple Languages

Com_Tracker: a two-phases framework for detecting and tracking community evolution in dynamic social networks

Purpose This paper aims to introduce a novel modularity-based framework, Com_Tracker, designed to detect and track community structures in dynamic social networks without recomputing them from scratch at each snapshot. Despite extensive research in this area, existing approaches either require repetitive computations or fail to capture key community behavioral events, both of which limit the ability to generate timely and actionable insights. Efficiently tracking community structures is crucial for real-time decision-making in rapidly evolving networks, while capturing behavioral events is necessary for understanding deeper community dynamics. This study addresses these limitations by proposing a more efficient and adaptive solution. It aims to answer the following questions: How can we efficiently track community structures without recomputation? How can we detect significant community events over time? Design/methodology/approach Com_Tracker models dynamic social networks as a sequence of snapshots. First, it detects the community structure of the initial snapshot using a static community detection algorithm. Then, for each subsequent time step, Com_Tracker updates the community structure based on the previous snapshot, allowing it to track communities and detect their changes over time. The locus-based adjacency encoding scheme is adopted, and Pearson’s correlation guides the construction of neighboring solutions. Findings Experiments conducted on various networks demonstrate that Com_Tracker effectively detects community structures and tracks their evolution in dynamic social networks. The results highlight its potential for real-time tracking and provide promising performance outcomes. Practical implications Com_Tracker offers valuable insights into community evolution, helping practitioners across fields such as resource management, public security, marketing and public health. By understanding how communities evolve, decision-makers can better allocate resources, enhance targeted strategies and predict future community behaviors, improving overall responsiveness to changes in network dynamics. Originality/value Com_Tracker addresses critical gaps in existing research by combining the strengths of modularity maximization with efficient tracking of community changes. Unlike previous methods that either recompute structures or fail to capture behavioral events, Com_Tracker provides an incremental, adaptive framework capable of detecting both community evolution and behavioral changes, enhancing real-world applicability in dynamic environments.

Identification of dynamic networks community by fusing deep learning and evolutionary clustering

Community detection is a critical component of network analysis and a hot topic in social computing. Detecting community structure in dynamic networks has important theoretical and practical implications for understanding the intrinsic function of networks and predicting network behavior. However, the majority of existing dynamic community detection methods adopt shallow models, which have limited ability to excavate complex non-linear structures and tend to generate undesirable community structures. In order to obtain an accurate and robust community structure in dynamic networks, we are inspired by network representation learning and utilize the deep learning to detect evolving communities in dynamic networks. In this paper, we propose a novel dynamic community detection method by fusing Deep Learning and Evolutionary Clustering (DLEC). This work attempts to combine deep learning and evolutionary clustering into a unified framework. First, we propose a matrix construction strategy to fully reveal the inherent community structures via the underlying community memberships. Then, we develop a novel multi-layer deep autoencoder framework that consists of multiple non-linear functions to extract the latent deep representation of the dynamic network. Based on the evolutionary clustering framework, a graph regularization term is introduced to ensure the smoothness of the community evolution. Finally, we employ the K-means clustering algorithm on the low-dimensional network space to obtain the community structure. Extensive experimental results on synthetic and real-world networks show that the proposed DLEC algorithm can effectively detect high-quality communities in dynamic networks.

Rhizosphere microbial community assembly as influenced by reductive soil disinfestation to resist successive cropping obstacle.

Reductive soil disinfestation (RSD), which involves creating anaerobic conditions and incorporating large amounts of organic materials into the soil, has been identified as a reliable strategy for reducing soilborne diseases in successive cropping systems. However, limited research exists on the connections between soil microorganism composition and plant diseases under various types of organic material applications. This study aimed to evaluate the effects of distinct RSD strategies (control without soil amendment; RSD with 1500 kg ha-1 molasses powder; RSD with 3000 kg ha-1 molasses powder; RSD with 3000 kg ha-1 molasses powder and 37.5-41.3 kg ha-1 microbial agent) on the plant disease index, bacterial community composition and network structure in rhizosphere soil. RSD treatments significantly reduced the occurrence of black shank disease in tobacco and increased soil bacterial diversity. High amounts of molasses powder in RSD treatments further enhanced disease inhibition and reduced fungal abundance and Shannon index. RSD also increased the relative abundance of bacterial phylum Firmicutes and fungal phylum Ascomycota, while decreasing the relative abundance of bacterial phyla Chloroflexi and Acidobacteriota and fungal phylum Basidiomycota in rhizosphere soil. A multiple regression model identified bacterial positive cohesion as the primary factor influencing the plant disease index, with a greater impact than bacterial negative cohesion and community stability. The competition among beneficial bacteria for creating a healthy rhizosphere environment is likely a key factor in the success of RSD in reducing plant disease risk. RSD, especially with higher rates of molasses powder, is a viable strategy for controlling black shank disease in tobacco and promoting soil health by fostering beneficial microbial communities. This study provides guidelines for soil management and plant disease prevention. © 2024 Society of Chemical Industry.

Characterization of Industrial Carbon Emission Dynamics and Network Structure Evolution in China

Given that industry is the major source of carbon emissions, clarifying the carbon transfer regularity triggered by industry production linkage is of great importance in realizing the synergistic development of industry to reduce pollution and carbon emissions. Based on the perspective of responsibility allocation, the study accounted for the industry carbon emissions and constructed a carbon transfer weighted directed network model and applied the social network analysis method to explore the structure of the industry carbon transfer network and its evolution characteristics from 2005 to 2020. The results showed that： ① The overall carbon emissions of industries from 2005 to 2020 presented a rapid growth trend and large differences occurred in emissions between industries. ② The scale of the carbon transfer network was expanding rapidly and the characteristics of the small-world network were significant. ③ The community structure of the carbon transfer network was obvious, including four optimal associations： high carbon emission, carbon transmission, carbon endogenous, and high spillover. ④ The construction industry and the metal smelting and rolling processing industry were the core of the carbon transfer network structure, with strong network control. In view of the above characteristics, we proposed countermeasures and suggestions in terms of implementing the allocation of carbon emission reduction responsibilities and differentiated emission reduction measures for associations as well as focusing on the management of core nodes of the network, with the intent of providing cross-sectoral synergistic emission reduction ideas for the development of sustainable low-carbon transformation in China's industry sector.

Enhancing robustness of community structure in networks against attacks with gray information

In recent years, network science has received significant attention and application. As an important mesoscale structure of networks, community structure reveals the inherent modular structure and potential functionality of networks. Therefore, maintaining the community structure during attacks is crucial. Existing studies on community robustness primarily focus on two attack behaviors: malicious attacks and random failures. However, little is known on the community robustness in the more practical situations where the attackers have limited ability to access precise network information, leading to gray information attack behaviors. Hence, in this paper, we investigate the robustness of network communities under gray information attacks and the enhancing algorithms. Following the community robustness measure for the sequential attacks, we establish a unified evaluation framework for attacks with gray information by introducing a gray attack coefficient, which treats the usual random failures and malicious attacks as the two special situations in the proposed framework. Several enhancing algorithms with local search strategy are exquisitely devised. The efficacy of our framework and algorithms which significantly improve the community robustness against gray attacks is demonstrated by the experimental results on a variety of real-world networks. Our findings have important implications not only in enhancing the community robustness of existing networks but also in designing robust ones from the scratch, which paves the way to further understand and seek strategies and solutions for network community robustness with gray information.

Urbanization reduces the stability of soil microbial community by reshaping the diversity and network complexity

Rapid urbanization considerably alters soil environment, biodiversity, and stability of terrestrial ecosystems. Soil microbial community, a key component of global biodiversity, plays a pivotal role in ecosystem stability and is highly vulnerable to urbanization. However, effects of urbanization on the diversity, stability, and network structure of soil microbial community remain poorly understood. Herein, we investigated the diversity and stability of soil microbial communities, including bacteria, fungi, and protists, across three regions with different levels of urbanization—urban, suburb, and ecoregion—using high-throughput sequencing techniques. Our results revealed that urbanization led to a notable decrease in the alpha diversity of soil microbial community, causing a significant reduction in soil stability, as assessed by the average variation degree (AVD). The loss of stability was linked to the diminished alpha diversity of the soil fungal and protistan communities, along with weakened interactions among bacteria, fungi, and protists. Notably, the majority of keystone species identified through network analysis were classified as bacteria (Proteobacteria) and displayed a strong positive correlation with the environmental factors influencing AVD. This highlights that the variability of bacteria and the immutability of fungi and protists are important to sustain soil microbial stability. Furthermore, structural equation models indicated that protistan diversity primarily drove soil microbial stability across all regions studied. In the suburban and ecoregion areas, soil microbial stability was directly influenced by the soil properties, bacterial diversity, and keystone species, as well as indirectly affected by heavy metals. These results underscore how urbanization can reduce the stability of soil microbial community via declined diversity and network complexity, whereas the establishment of ecoregions maybe contribute to preserve the diversity and stability of soil microbial community.

Dynamic Silos: Increased Modularity and Decreased Stability in Intraorganizational Communication Networks During the COVID-19 Pandemic

Workplace communications around the world were drastically altered by the COVID-19 pandemic, related work-from-home orders, and the rise of remote work. To understand these shifts, we analyzed aggregated, anonymized metadata from over 360 billion emails within 4,361 organizations worldwide. By comparing month-to-month and year-over-year metrics, we examined changes in network community structures over the 24 months before and after COVID-19. We also examined shifts across multiple communication media (email, instant message, video call, and calendaring software) within a single global organization and compared them with communications shifts that were driven by changes in formal organizational structure. We found that in 2020, organizations around the world became more siloed than in 2019, evidenced by increased modularity. This shift was concurrent with decreased stability within silos. Collectively, our analyses indicate that following the onset of COVID-19, employees’ communications began to shift more dynamically between subcommunities (teams, workgroups, or functional areas). At the same time, once in a subcommunity, they limited their communication to other members of that community. We term these network changes dynamic silos. We provide initial insights into the meaning and implications of dynamic silos for the future of work. This paper was accepted by Lamar Pierce, organizations. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.02797 .

Local core expanding-based label diffusion and local deep embedding for fast community detection algorithm in social networks

Community detection is a key task in social network analysis, as it reveals the underlying structure and function of the network. Various global and local techniques exist for uncovering community structures in social networks wherein diffusion-based algorithms are proposed as novel methods for local community detection, particularly suited for large-scale networks. The efficacy of diffusion processes and initial detection is paramount in the successful identification of community structures within social networks. This effectiveness hinges significantly on the meticulous selection of the label diffuser core, which serves as the foundation for propagating labels through the network, and the precise labeling of boundary nodes. Addressing the constraints of current community detection algorithms, notably their time complexity and efficiency, this paper proposes a novel local community detection algorithm that combines core expansion with label diffusion, and deep embedding techniques. In the proposed method, a new centrality measure is introduced for appropriate core selection to facilitate precise label diffusion in the initial phase. Subsequently, a deep embedding technique is employed for updating labels of boundary and core nodes using the GraphSage embedding method. Finally, a rapid merging step is executed to amalgamate initially proximate communities into finalized community structures in large-scale social networks. We evaluate our algorithm on 14 real-world and 4 synthetic networks and show that it outperforms existing methods in terms of NMI, F-measure, ARI, and modularity. According to numerical results, the proposed method shows approximately 1.04 %, 1.03 %, and 1.12 % improvement in F-measure, NMI, and ARI measures respectively, compared to the second-best method, LBLD, in the networks with ground-truth. In addition, our method is able to accurately identify communities in large-scale networks such as Orkut, YouTube, and LiveJournal, where it ranks among the top-performing methods. Our approach exhibits the best performance in terms of ARI compared to other algorithms under comparison.

Persistence, changes and robustness of nest webs along a latitudinal gradient in the Canadian boreal forest

IntroductionIn eastern Canada, the boreal forest is associated with an important latitudinal shift in forest composition and structure, which occurs in the transition between the mixed southern boreal forest and the coniferous northern boreal forest. Along this transition, upland mixedwood stands with large deciduous trees (important for cavity-dependent vertebrate species) are gradually replaced by forests with smaller conifer trees, primarily black spruce (Picea mariana). Concomitantly, the availability of lowland forests flooded by the American beaver (Castor canadensis), which can provide adequate conditions for tree-cavity users, is also decreasing.MethodsWe hypothesized that this latitudinal gradient would bring important changes in the functional diversity and network structure of vertebrate cavity-using communities. Along this latitudinal gradient we used a nest web approach to analyze the structure and robustness of networks of cavity users in upland forests and in lowland forests flooded by beavers.ResultsDespite their low availability in the northern forest region, we found that mixedwood stands persisted throughout the boreal forest in being the main drivers of nest webs network structure of upland forests whereas old black spruce stands contribution was low. In lowland forests, beaver ponds harbored nest webs with a rich and complex structure in both forest regions. Species removal simulations revealed that across our latitudinal gradient upland and lowland forest nest webs responded differently. In upland forests, the removal of trembling aspen and the Pileated Woodpecker (Dryocopus pileatus) caused the highest proportions of secondary extinctions, showing low robustness of nest webs given that these two species were highly connected to the other species. Contrastingly, nest webs in beaver ponds were more robust mainly because excavator species used a higher diversity of tree species despite the removal of the Northern Flicker (Colaptes auratus) which induced numerous secondary extinctions. The Pileated Woodpecker remained the pivotal species across the two forest regions in upland forests whereas the Northern Flicker became the main large cavity provider in beaver ponds across the latitudinal gradient.DiscussionWe discuss how mixedwood forests and beaver ponds, which are key habitat types for the cavity-using vertebrate community across our latitudinal gradient, should be maintained and protected in landscapes under industrial timber harvesting.

Endophytic and epiphytic metabarcoding reveals fungal communities on cashew phyllosphere in Kenya.

Plants intimately coexist with diverse taxonomically structured microbial communities that influence host health and productivity. The coexistence of plant microbes in the phyllosphere benefits biodiversity maintenance, ecosystem function, and community stability. However, differences in community composition and network structures of phyllosphere epiphytic and endophytic fungi are widely unknown. Using Illumina Miseq sequencing of internal transcribed spacer (ITS) and 28S rRNA gene amplicons, we characterised the epiphytic and endophytic fungal communities associated with cashew phyllosphere (leaf, flower and fruit) from Kwale, Kilifi and Lamu counties in Kenya. The ITS and 28S rRNA gene sequences were clustered into 267 and 108 operational taxonomic units (OTUs) at 97% sequence similarity for both the epiphytes and endophytes. Phylum Ascomycota was abundant followed by Basidiomycota, while class Saccharomycetes was most dominant followed by Dothideomycetes. The major non-ascomycete fungi were associated only with class Tremellales. The fungal communities detected had notable ecological functions as saprotrophs and pathotrophs in class Saccharomyectes and Dothideomycetes. The community composition of epiphytic and endophytic fungi significantly differed between the phyllosphere organs which was statistically confirmed by the Analysis of Similarity test (ANOSIM Statistic R: 0.3273, for 28S rRNA gene and ANOSIM Statistic R: 0.3034 for ITS). The network analysis revealed that epiphytic and endophytic structures were more specialized, modular and had less connectance. Our results comprehensively describe the phyllosphere cashew-associated fungal community and serve as a foundation for understanding the host-specific microbial community structures among cashew trees.

Network structure and taxonomic composition of tritrophic communities of Fagaceae, cynipid gallwasps and parasitoids in Sichuan, China

Abstract A key question in insect community ecology is whether parasitoid assemblages are structured by the food plants of their herbivore hosts. Tritrophic communities centred on oak‐feeding cynipid gallwasps are one of the best‐studied tritrophic insect communities. Previous work suggests that host plant identity is a much stronger predictor of oak–cynipid interactions than of cynipid–parasitoid interactions. However, these relationships have not been formally quantified. We reason that the potential for ‘bottom‐up’ effects should increase with host plant phylogenetic diversity. We, therefore, generated quantified interaction network data for previously unstudied tritrophic cynipid communities in Sichuan, China, where, in addition to Quercus, cynipid host plants include Castanea, Castanopsis and Lithocarpus. We characterise these communities taxonomically and compare the extent to which host plant taxonomy predicts plant–herbivore and plant–parasitoid associations. We sampled 42,620 cynipid galls of 176 morphotypes from 23 host plant species, yielding over 4500 specimens of 64 parasitoid morphospecies. Many parasitoids were identifiable to chalcidoid taxa present in other Holarctic oak cynipid communities, with the addition of Cynipencyrtus (Cynipencyrtidae). As elsewhere, Sichuan parasitoid assemblages were dominated by generalists. Gallwasp–plant interaction networks were significantly more modular than parasitoid–plant association networks. Gallwasps were significantly more specialised to host plants (i.e. had higher mean d' values) than parasitoids. Parasitoid assemblages nevertheless showed significant plant‐associated beta diversity, with a dominant turnover component. We summarise parallels between our study and other Fagaceae‐associated cynipid communities and discuss our findings in light of the processes thought to structure tritrophic interactions centred on endophytic insect herbivores.

Evaluating disease surveillance strategies for early outbreak detection in contact networks with varying community structure

Disease surveillance systems allow public health agencies to respond to emerging diseases before they become widespread. Developing such systems requires identifying optimal ways to monitor in the context of an epidemic outbreak; this problem is known as sensor selection. Contact networks represent the dynamics of interaction in a population and are used to model how a disease spreads in a population and to explore strategies of sensor selection. We evaluated five sensor selection strategies on their ability to provide an early warning of a COVID-like outbreak in synthetic contact networks encapsulated in four network scenarios. Three of these scenarios assessed different aspects of community structure. The fourth scenario employed a contact network representing the population and interactions of 6.8 million people in New York City, constructed from an agent-based simulation using census and transportation data. This scenario exemplifies how sensor selection strategies may perform in a real-world, urban context. Our findings suggest that the choice of the optimal strategy depends heavily on the community structure of the network. Strategies that select highly connected nodes or maximize network coverage are the optimal surveillance strategy for outbreak detection in many network community structures. However, a naive implementation of these strategies may fail to provide an early warning at all—including in the New York City scenario. Moreover, these methods are impractical for real-world use as they require knowledge of the underlying contact network. Instead, a selection strategy that starts with a set of random nodes and then performs a random walk through a chain of neighbors reliably provides early warnings without requiring prior knowledge of the network. We find this method, called “random chain”, to be the most pragmatic for implementation in a real-world disease surveillance context.

Integrating topology and content equally in non-negative matrix factorization for community detection

Non-negative matrix factorization (NMF) is widely used in analyzing the community structure of complex networks. However, most of the current related efforts only focus on the network structural topology, while neglecting the node content. Although there have been efforts to integrate topology and content, inefficient strategies balancing their contributions can also lead to unsatisfactory results. In this work, we treat topology and content equally and propose two novel NMF-based methods to finely balance topology and content to improve the performance of community detection. We first propose a double encoder–decoder-based NMF (DEDNMF) method that employs two NMF-based encoder–decoders to integrate topology and content adaptively. Experimental results show that DEDNMF outperforms the baseline methods with average improvements of 50.69% and 46.93% in terms of normalized mutual information (NMI) and adjusted rand index (ARI) on all experimental networks, respectively. Moreover, we propose a double-decoder-based NMF (DDNMF) method that uses only two decoders for both topology and content, imposing sparsity constraints on NMF. Experimental results show that DDNMF outperforms the baseline methods with average improvements of 72.11% and 77.00% in terms of NMI and ARI on all experimental networks. Experimental results also show that the proposed two methods have good convergence and robustness.

The spatio-temporal accumulation of 6 PPD-Q in greenbelt soils and its effects on soil microbial communities

6 PPD-Q (6 PPD-Quinone) is an ozone-induced byproduct derived from the degradation of N-(1,3-dimethylbutyl)-N′-phenyl-p-phenylenediamine (6 PPD), commonly found in road dust resulting from tire wear. However, the extent of 6 PPD-Q pollution in urban soil remains unclear. This study investigates the spatial and temporal accumulation patterns of 6 PPD-Q in greenbelt soils in Ningbo, and explores the correlation between 6 PPD-Q accumulation and soil microbial community composition and functions. Our findings indicate that 6 PPD-Q is present (ranging from 0.85 to 12.58 μg/kg) in soil samples collected from both sides of urban traffic arteries. Soil fungi exhibit higher sensitivity to 6 PPD-Q accumulation compared to bacteria, and associated fungi (Basidiomycota) may be potential biomarkers for environmental 6 PPD-Q contamination. Co-occurrence network analysis reveals that the bacterial microbial network in summer exhibits greater stability and resilience in response to 6 PPD-Q inputs than in winter. However, 6 PPD-Q accumulation disrupts the network structure of fungal communities to some extent, leading to reduced diversity in fungal microbial communities. Long-term accumulation of 6 PPD-Q weakens the nitrogen and phosphorus cycling potential within urban soil, while the enhancement of carbon cycling may further promote 6 PPD-Q degradation in urban soil. Taken together, this study provides new insights into the ecological risks of 6 PPD-Q in urban soils.

Effects of climate change on plant-pollinator interactions and its multitrophic consequences

AbstractThere is wide consensus that climate change will seriously impact flowering plants and their pollinators. Shifts in flowering phenology and insect emergence as well as changes in the functional traits involved can cause alterations in plant-pollinator interactions, pollination success and plant reproductive output. Effects of rising temperatures, advanced snowmelt and altered precipitation patterns are expected to be particularly severe in alpine habitats due to the constrained season and upper range margins. Yet, our understanding of the magnitude and consequences of such changes in life history events and functional diversity in high elevation environments is incomplete.This special issue collects novel insights into the effects of climate change on plant-pollinator interactions in individual plant species and on network structure of entire plant and pollinator communities in alpine ecosystems. Using simulated changes of earlier snowmelt, natural gradients of variation in temperature, precipitation and snowmelt, or a long-term monitoring approach, these studies illustrate how plant species, plant communities, and pollinators respond to variation in environmental conditions associated with scenarios of ongoing climate change.The collection of papers presented here clearly demonstrates how spatial or temporal variation in the environmental climatic context affects flower abundances and plant community composition, and the consequences of these changes for pollinator visitation, pollination network structure, pollen transfer dynamics, or seed production. As changes in the availability of flowers, fruits, and seeds are likely to impact on other trophic levels, the time is ripe and pressing for a holistic multitrophic view of the effects of climate change on biotic interactions in alpine ecological communities.

Negative binomial community network vector autoregression for multivariate integer-valued time series

Modeling multivariate integer-valued time series with appropriate methods is currently a popular research topic. In this paper, we propose a multivariate integer-valued autoregressive time series model based on a fixed network community structure. We use the negative binomial distribution as the conditional marginal distribution and a copula to construct the conditional joint distribution. The newly proposed model introduces the heterogeneity of nodes. Stability conditions are provided for both fixed and increasing dimensions. We estimate the parameters of the proposed model by maximizing the quasi-likelihood function with known and unknown community membership matrices, respectively. Corresponding asymptotic properties of parameter estimates are also provided. A simulation study is conducted to demonstrate the asymptotic behavior of the proposed model, and two real datasets are employed to compare the proposed model with other competitive models.

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.

Extremists of a feather flock together? Community structures, transitivity, and patterns of homophily in the US Islamist co-offending network.

Prior research suggests that members of terrorist groups prioritize forming network ties based on trust to improve their organizational and operational security. The homophily principle, which postulates that individuals tend to form relationships based on shared characteristics, can be a key mechanism through which people identify trustworthy associates. Next to homophily, the mechanism of establishing interconnected relationships through transitivity is also well-known to serve this purpose and shape community structures in social networks. We analyze the community structures of the Islamist co-offending network in the United States, which is highly violent, to assess whether homophily and transitivity determine which extremists form co-offending ties. We rely on a new database on the individual attributes and the co-offending relationships of 494 Islamist offenders radicalized in the United States between 1993 and 2020. Using community detection algorithms, we show that the US Islamist co-offending network is highly clustered, modular, and includes many small but only a few large communities. Furthermore, results from exponential random graph modeling show that transitive relationships as well as spatial proximity, ideological affiliation, and shared socio-cultural characteristics drive co-offending among US Islamist extremists. Overall, these findings demonstrate that the processes of homophily and transitivity shape violent social networks.