Initial Community Structure Research Articles

LeaDCD: Leadership concept-based method for community detection in social networks

Community discovery plays an essential role in analyzing and understanding the behavior and relationships of users in social networks. For this reason, various algorithms have been developed in the last decade for discovering the optimal community structure. In social networks, some individuals have special characteristics that make them well-known by others. These groups of users are called leaders and often have a significant impact on others, with an exceptional ability to build communities. In this paper, we propose an efficient method to detect communities in social networks using the concept of leadership (LeaDCD). The proposed algorithm mainly involves three phases. First, based on nodes' degree centrality and maximal cliques, some small groups of nodes (leaders) considered as seeds for communities are discovered. Next, unassigned nodes are added to the seeds through an expansion process to generate the initial community structure. Finally, small communities are merged to form the final community structure. To demonstrate the effectiveness of our proposal, we carried out comprehensive experiments on real-world and artificial graphs. The findings indicate that our algorithm outperforms other commonly used methods, demonstrating its high efficiency and reliability in discovering communities within social graphs.

A novel three-phase expansion algorithm for uncovering communities in social networks using local influence and similarity in embedding space

Community detection can help uncover and understand complex networks’ underlying patterns and structures. It involves identifying cohesive groups with similar entities while being separated from other groups. Social networks are a prime example of an area where community detection is particularly relevant, as it can provide insight into the behaviors of individuals. Several community detection methods have been proposed, each addressing the problem from different perspectives. However, the rise of vast and intricate networks from diverse domains has necessitated the development of community detection methods that can effectively handle large-scale graphs. This study introduces a novel three-phase expansion algorithm for community discovery based on nodes’ local information and similarity in embedding space. The proposed model consists of three steps. In the first stage, we generate an embedding space in which nodes are represented as vectors, and we extract nodes that greatly influence others and have an extraordinary ability to create communities using degree centrality measures. Then, based on cosine similarity in the embedding space, we group the most similar nodes to the influential ones in the same community and create an initial community structure. In the last phase, we extract the weak communities from the initial community structure generated in the second phase and merge them with the strong ones. We conduct extensive experiments on both real-world and synthetic networks to demonstrate the effectiveness of our proposal. The experimental results show that the proposed algorithm performs better than other widely used algorithms and is highly reliable and efficient in large-scale graphs.

Effects of swine manure dilution with lagoon effluent on microbial communities and odor formation in pit recharge systems

Pit recharge systems (PRS) control odor by managing organic solids in swine manure. However, there needs to be more understanding of PRS's effect on the microbiome composition and its impact on odor formation. A study was conducted to understand how recharge intervals used in PRS impact manure microbiome and odor formation. Bioreactors dynamically loaded simulated recharge intervals of 14, 10, and 4 days by diluting swine manure with lagoon effluent at varying ratios. Treatment ratios tested included 10:0 (control), 7:3 (typical Korean PRS), 5:5 (enhanced PRS #1), and 2:8 (enhanced PRS #2). Manure microbial membership, chemical concentrations, and odorant concentrations were used to identify the interactions between microbiota, manure, and odor. The initial microbial community structure was controlled by dilution ratio and manure barn source material. Firmicutes and Proteobacteria were the dominant microbial phyla in manure and lagoon effluent, respectively, and significantly decreased or increased with dilution. Key microbial species were Clostridium saudiense in manure and Pseudomonas caeni in lagoon effluent. Percentages of these species declined by 8.9% or increased by 17.6%, respectively, with each unit dilution. Microbial community composition was controlled by both treatment (i.e., manure dilution ratio and barn source material) and environmental factors (i.e., solids and pH). Microbiome composition was correlated with manure odor formation profiles, but this effect was inseparable from environmental factors, which explained over 75% of the variance in odor profiles. Consequently, monitoring solids and pH in recharge waters will significantly impact odor control in PRS.

Targeted remodeling of the human gut microbiome using Juemingzi (Senna seed extracts).

The genus Senna contains globally distributed plant species of which the leaves, roots, and seeds have multiple traditional medicinal and nutritional uses. Notable chemical compounds derived from Senna spp. include sennosides and emodin which have been tested for antimicrobial effects in addition to their known laxative functions. However, studies of the effects of the combined chemical components on intact human gut microbiome communities are lacking. This study evaluated the effects of Juemingzi (Senna sp.) extract on the human gut microbiome using SIFR® (Systemic Intestinal Fermentation Research) technology. After a 48-hour human fecal incubation, we measured total bacterial cell density and fermentation products including pH, gas production and concentrations of short chain fatty acids (SCFAs). The initial and post-incubation microbial community structure and functional potential were characterized using shotgun metagenomic sequencing. Juemingzi (Senna seed) extracts displayed strong, taxon-specific anti-microbial effects as indicated by significant reductions in cell density (40%) and intra-sample community diversity. Members of the Bacteroidota were nearly eliminated over the 48-hour incubation. While generally part of a healthy gut microbiome, specific species of Bacteroides can be pathogenic. The active persistence of the members of the Enterobacteriaceae and selected Actinomycetota despite the reduction in overall cell numbers was demonstrated by increased fermentative outputs including high concentrations of gas and acetate with correspondingly reduced pH. These large-scale shifts in microbial community structure indicate the need for further evaluation of dosages and potential administration with prebiotic or synbiotic supplements. Overall, the very specific effects of these extracts may offer the potential for targeted antimicrobial uses or as a tool in the targeted remodeling of the gut microbiome.

Community Detection Based on Markov Similarity Enhancement

Community detection can discover the cluster structure hidden in complex networks, which helps people predict network behavior and understand network functions. It is one of the current research hotspots. In this paper, we propose a Markov similarity enhancement method, which obtains the steady-state Markov similarity enhancement matrix through the Markov iterative state transition of the initial network. According to the Markov similarity index, the network is divided into initial community structure. Then, we merge the small communities into its closely connected communities to obtain the final community. On seven real networks and artificial networks with variable parameters, compared with other seven well-known community detection algorithms, numerical simulation experiments show that the proposed algorithm has a good community detection effect.

Response of soil microbial community to surfactant Sodium Dodecyl Sulfate (SDS) contamination in lake-terrestrial ecotone: Structural and functional changes

The most widely used surfactant in the world, sodium dodecyl sulfate (SDS), has an inhibitory effect on environmental microbes. Since the emergence of COVID-19, more SDS has been released into natural aquatic environment through lake–terrestrial ecotone, which has had a non-negligible impact on soil microbial activities and circulation of materials in lake–terrestrial ecotones. The lake–terrestrial ecotone is also a major site for the degradation and removal of SDS. Using simulation studies and high-throughput sequencing techniques, it could be possible to determine the concentration changes in SDS in soil and water in a lake–terrestrial ecotone, as well as the variations in diversity, species composition, and functional genes in soil microorganisms before and after SDS contamination. The results showed that (1) the crucial window for lacustrine bacteria to degrade SDS was between 6 and 9 days following contamination. The SDS adsorbed to soil particles required at least 18 days to be completely removed from water, while it was mostly removed after 12 days. (2) SDS affected the lake–terrestrial ecotone differently depending on the type of plants present. The microbial community was less impacted and the recovery time was shorter in lake–terrestrial ecotones with abundant aquatic microphyte. SDS boosted microbial diversity in regions with significant vegetative degradation. (3) A lake–terrestrial ecotone’s initial microbial community structure was considerably altered by SDS contamination, and Acinetobacter and Pseudomonas increased in prominence at various times. When SDS was added, the microbiome’s ability to fix nitrogen was compromised, and the number of genes involved in nitrogen and sulfate respiration increased. The abundance of human pathogenic genes also rose dramatically.

Transition from Ginseng Root Rot Disease-Conducive Soil to -Suppressive Soil Mediated by Pseudomonadaceae.

Ginseng is a popular medicinal herb with established therapeutic effects such as cardiovascular disease prevention, anticancer effects, and anti-inflammatory effects. However, the slow growth of ginseng due to soilborne pathogens has been a challenge for establishing new plantations. In this study, we investigated root rot disease associated with the microbiota in a ginseng monoculture model system. Our results showed that a collapse of the early microbiota community inhibiting root rot disease was observed before the disease became severe, and nitrogen fixation was necessary to support the initial microbiota community structure. Furthermore, changes in the nitrogen composition were essential for the suppression of pathogen activity in early monoculture soils. We hypothesize that Pseudomonadaceae, a population built up by aspartic acid, can inhibit the occurrence of root rot disease in ginseng and that specific management practices that maintain a healthy microbiome can be implemented to prevent and mitigate the disease. Our findings provide insights into the potential use of specific members of the microbiota for controlling root rot disease in ginseng cultivation. IMPORTANCE Understanding the initial soil microbiota and community shifts in a monoculture system is critical for developing disease-suppressive soils for crop production. The lack of resistance genes against soilborne pathogens in plants highlights the need for effective management strategies. Our investigation of root rot disease and initial microbiota community shifts in a ginseng monoculture model system provides valuable insight into the development of conducive soil into specific suppressive soil. With a thorough understanding of the microbiota in disease-conducive soil, we can work toward the development of disease-suppressive soil to prevent outbreaks and ensure sustainable crop production.

River discharge-related nutrient effects on North Sea coastal and offshore phytoplankton communities.

As a result of climate change, an increasing number of extreme weather events can be observed. Heavy precipitation events can increase river discharge which causes an abrupt increase of nutrient-rich freshwater into coastal zones. We investigated the potential consequences of nutrient-rich freshwater pulses on phytoplankton communities from three stations in the North Sea. After incubating the phytoplankton cultures with a gradient of nutrient-rich freshwater, we analyzed changes in community diversity, average cell size, growth rate and elemental stoichiometry. Pulses of nutrient-rich freshwater have caused an increase in the growth rate of the phytoplankton communities at two of the three stations and a decrease in cell size within the taxonomic groups of flagellates and diatoms at all stations, indicating a positive selection in favor of smaller taxa. In addition, we observed a decrease in the molar N:P ratio of the phytoplankton communities. Overall, the response of phytoplankton was highly dependent on the initial community structure at each sampling site. Our study demonstrates that the biomass and functional structure of North Sea phytoplankton communities could be altered by an abrupt increase in river discharge, which could have further consequences for higher trophic levels and short-term food web dynamics in the North Sea.

Be aware of the allele-specific bias and compositional effects in multi-template PCR.

High-throughput sequencing of amplicon libraries is the most widespread and one of the most effective ways to study the taxonomic structure of microbial communities, even despite growing accessibility of whole metagenome sequencing. Due to the targeted amplification, the method provides unparalleled resolution of communities, but at the same time perturbs initial community structure thereby reducing data robustness and compromising downstream analyses. Experimental research of the perturbations is largely limited to comparative studies on different PCR protocols without considering other sources of experimental variation related to characteristics of the initial microbial composition itself. Here we analyse these sources and demonstrate how dramatically they effect the relative abundances of taxa during the PCR cycles. We developed the mathematical model of the PCR amplification assuming the heterogeneity of amplification efficiencies and considering the compositional nature of data. We designed the experiment—five consecutive amplicon cycles (22–26) with 12 replicates for one real human stool microbial sample—and estimated the dynamics of the microbial community in line with the model. We found the high heterogeneity in amplicon efficiencies of taxa that leads to the non-linear and substantial (up to fivefold) changes in relative abundances during PCR. The analysis of possible sources of heterogeneity revealed the significant association between amplicon efficiencies and the energy of secondary structures of the DNA templates. The result of our work highlights non-trivial changes in the dynamics of real-life microbial communities due to their compositional nature. Obtained effects are specific not only for amplicon libraries, but also for any studies of metagenome dynamics.

An improved two-stage label propagation algorithm based on LeaderRank.

To solve the problems of poor stability and low modularity (Q) of community division results caused by the randomness of node selection and label update in the traditional label propagation algorithm, an improved two-stage label propagation algorithm based on LeaderRank was proposed in this study. In the first stage, the order of node updating was determined by the participation coefficient (PC). Then, a new similarity measure was defined to improve the label selection mechanism so as to solve the problem of label oscillation caused by multiple labels of the node with the most similarity to the node. Moreover, the influence of the nodes was comprehensively used to find the initial community structure. In the second stage, the rough communities obtained in the first stage were regarded as nodes, and their merging sequence was determined by the PC. Next, the non-weak community and the community with the largest number of connected edges were combined. Finally, the community structure was further optimized to improve the modularity so as to obtain the final partition result. Experiments were performed on nine classic realistic networks and 19 artificial datasets with different scales, complexities, and densities. The modularity and normalized mutual information (NMI) were used as evaluation indexes for comparing the improved algorithm with dozens of relevant classic algorithms. The results showed that the proposed algorithm yields superior performance, and the results of community partitioning obtained using the improved algorithm were stable and more accurate than those obtained using other algorithms. In addition, the proposed algorithm always performs well in nine large-scale artificial data sets with 6,000 to 50,000 nodes and three large realistic network datasets, which verifies its computational performance and utility in community detection for large-scale networks.

Chronic Environmental Perturbation Influences Microbial Community Assembly Patterns.

Acute environmental perturbations are reported to induce deterministic microbial community assembly, while it is hypothesized that chronic perturbations promote development of alternative stable states. Such acute or chronic perturbations strongly impact on the pre-adaptation capacity to the perturbation. To determine the importance of the level of microbial pre-adaptation and the community assembly processes following acute or chronic perturbations in the context of hydrocarbon contamination, a model system of pristine and polluted (hydrocarbon-contaminated) sediments was incubated in the absence or presence (discrete or repeated) of hydrocarbon amendment. The community structure of the pristine sediments changed significantly following acute perturbation, with selection of different phylotypes not initially detectable. Conversely, historically polluted sediments maintained the initial community structure, and the historical legacy effect of chronic pollution likely facilitated community stability. An alternative stable state was also reached in the pristine sediments following chronic perturbation, further demonstrating the existence of a legacy effect. Finally, ecosystem functional resilience was demonstrated through occurrence of hydrocarbon degradation by different communities in the tested sites, but the legacy effect of perturbation also strongly influenced the biotic response. This study therefore demonstrates the importance of perturbation chronicity on microbial community assembly processes and reveals ecosystem functional resilience following environmental perturbation.

ACSIMCD: A 2-phase framework for detecting meaningful communities in dynamic social networks

Detecting and analyzing community structure is a challenging topic in dynamic social network analysis. Although the number of methods in this area is on the rise, there are only a few algorithms that can discover meaningful communities based on different aspects of social networks. Indeed, social networks contain various information sources that can be used to analyze them. The most important part of this information is related to users’ topics of interest (content information) and users’ interactions (structure information). One promising solution to discover meaningful communities is to combine these two concepts. Based on this, we introduce ACSIMCD, a 2-phase framework for discovering and updating community structure without recomputing them from scratch at each snapshot. This article mainly includes two parts. In the first part, a static community detection algorithm which is called Content and Structure Information based Method for Community Detection (CSIMCD for short) is proposed to discover the initial community structure. The CSIMCD uses a hybrid approach founded on statistical and semantic measures to extract the users’ topics of interest. Accordingly, the original network is divided into several clusters (topical clusters) so that each one represents a distinct topic, then by performing a link analysis on each topical cluster, the communities are detected. In the second part, we propose ACSIMCD (Adaptive CSIMCD), an adaptive method for detecting and updating community structure in dynamic social networks. More precisely, the ACSIMCD explores the topics of interest of each changed node to identify the topical cluster it belongs to. After that, we update the community structure in this topical cluster, and we keep others as they are. We compare the ACSIMCD model with algorithms from different approaches including content-based methods on real-world networks. The experimental results showed that ACSIMCD produces a community structure of high quality from the perspective of links and interests compared with the classical methods, and that it is able to process network changes effectively in a reasonable time scale.

Shotgun metagenomic analysis of kombucha mutualistic community exposed to Mars‐like environment outside the International Space Station

Kombucha is a multispecies microbial ecosystem mainly composed of acetic acid bacteria and osmophilic acid-tolerant yeasts, which is used to produce a probiotic drink. Furthermore, Kombucha Mutualistic Community (KMC) has been recently proposed to be used during long space missions as both a living functional fermented product to improve astronauts' health and an efficient source of bacterial nanocellulose. In this study, we compared KMC structure and functions before and after samples were exposed to the space/Mars-like environment outside the International Space Station in order to investigate the changes related to their re-adaptation to Earth-like conditions by shotgun metagenomics, using both diversity and functional analyses of Community Ecology and Complex Networks approach. Our study revealed that the long-term exposure to space/Mars-like conditions on low Earth orbit may disorganize the KMC to such extent that it will not restore the initial community structure; however, KMC core microorganisms of the community were maintained. Nonetheless, there were no significant differences in the community functions, meaning that the KMC communities are ecologically resilient. Therefore, despite the extremely harsh conditions, key KMC species revived and provided the community with the genetic background needed to survive long periods of time under extraterrestrial conditions.

Sustained organic loading disturbance favors nitrite accumulation in bioreactors with variable resistance, recovery and resilience of nitrification and nitrifiers

Sustained disturbances are relevant for environmental biotechnology as they can lead to alternative stable states in a system that may not be reversible. Here, we tested the effect of a sustained organic loading alteration (food-to-biomass ratio, F:M, and carbon-to-nitrogen ratio, C:N) on activated sludge bioreactors, focusing on the stability of nitrification and nitrifiers. Two sets of replicate 5-L sequencing batch reactors were operated at different, low and high, F:M (0.19–0.36 mg COD/mg TSS/d) and C:N (3.5–6.3 mg COD/mg TKN) conditions for a period of 74 days, following 53 days of sludge acclimation. Recovery and resilience were tested during the last 14 days by operating all reactors at low F:M and C:N (henceforth termed F:M–C:N). Stable nitrite accumulation (77%) was achieved through high F:M–C:N loading with a concurrent reduction in the abundance of Nitrospira. Subsequently, only two of the three reactors experiencing a switch back from high to low F:M–C:N recovered the nitrite oxidation function, with an increase in Nitrobacter as the predominant NOB, without a recovery of Nitrospira. The AOB community was more diverse, resistant and resilient than the NOB community. We showed that functional recovery and resilience can vary across replicate reactors, and that nitrification recovery need not coincide with a return to the initial nitrifying community structure.

A Seed-Expanding Method Based on TOPSIS for Community Detection in Complex Networks

The centrality plays an important role in many community-detection algorithms, which depend on various kinds of centralities to identify seed vertices of communities first and then expand each of communities based on the seeds to get the resulting community structure. The traditional algorithms always use a single centrality measure to recognize seed vertices from the network, but each centrality measure has both pros and cons when being used in this circumstance; hence seed vertices identified using a single centrality measure might not be the best ones. In this paper, we propose a framework which integrates advantages of various centrality measures to identify the seed vertices from the network based on the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) multiattribute decision-making technology. We take each of the centrality measures involved as an attribute, rank vertices according to the scores which are calculated for them using TOPSIS, and then take vertices with top ranks as the seeds. To put this framework into practice, we concretize it in this paper by considering four centrality measures as attributes to identify the seed vertices of communities first, then expanding communities by iteratively inserting one unclassified vertex into the community to which its most similar neighbor belongs, and the similarity between them is the largest among all pairs of vertices. After that, we obtain the initial community structure. However, the amount of communities might be much more than they should be, and some communities might be too small to make sense. Therefore, we finally consider a postprocessing procedure to merge some initial communities into larger ones to acquire the resulting community structure. To test the effectiveness of the proposed framework and method, we have performed extensive experiments on both some synthetic networks and some real-world networks; the experimental results show that the proposed method can get better results, and the quality of the detected community structure is much higher than those of competitors.

Effects of initial microbial community structure on the performance of solid-state anaerobic digestion of corn stover

High organic loading can easily lead to the accumulation of volatile fatty acids (VFAs) during the early stage of solid-state anaerobic digestion (SS-AD). The accumulated VFAs inhibit the activity of methanogens resulting in digestion failure. This problem represents a major obstacle to the industrialization of SS-AD. A strategy to improve the initial microbial community structure was proposed to prevent acid inhibition in the early stage of SS-AD. To obtain inocula with different initial microbial community structures, the inoculum was treated with acetic acid to increase the abundance of acid-tolerant methanogens and then mixed with the untreated inoculum in different proportions. The effects of the initial microbial community structure on the performance of SS-AD of corn stover were investigated. The results showed that the concentrations of VFAs in the reactors inoculated with the acid-tolerant inoculum alone (treatment 100%) were significantly lower than those of the reactors inoculated with the original inoculum alone (treatment 0%) during the early stage of SS-AD. The peak values of the methane contents and daily methane yields of the reactors inoculated with the acid-resistant inoculum occurred on day six, which was four days earlier than in the reactors inoculated with the original inoculum alone. The results of this study verified that an appropriate initial microbial community structure prevented acid inhibition during the start-up stage and improved the performance of the SS-AD process.

Community recovery dynamics in yellow perch microbiome after gradual and constant metallic perturbations

BackgroundThe eco-evolutionary processes ruling post-disturbance microbial assembly remain poorly studied, particularly in host-microbiome systems. The community recovery depends not only on the type, duration, intensity, and gradient of disturbance, but also on the initial community structure, phylogenetic composition, legacy, and habitat (soil, water, host). In this study, yellow perch (Perca flavescens) juveniles were exposed over 90 days to constant and gradual sublethal doses of cadmium chloride. Afterward, the exposure of aquaria tank system to cadmium was ceased for 60 days. The skin, gut and water tank microbiomes in control and treatment groups, were characterized before, during and after the cadmium exposure using 16s rDNA libraries and high throughput sequencing technology (Illumina, Miseq).ResultsOur data exhibited long-term bioaccumulation of cadmium salts in the liver even after two months since ceasing the exposure. The gradient of cadmium disturbance had differential effects on the perch microbiota recovery, including increases in evenness, taxonomic composition shifts, as well as functional and phylogenetic divergence. The perch microbiome reached an alternative stable state in the skin and nearly complete recovery trajectories in the gut communities. The recovery of skin communities showed a significant proliferation of opportunistic fish pathogens (i.e., Flavobacterium). Our findings provide evidence that neutral processes were a much more significant contributor to microbial community turnover in control treatments than in those treated with cadmium, suggesting the role of selective processes in driving community recovery.ConclusionsThe short-term metallic disturbance of fish development has important long-term implications for host health. The recovery of microbial communities after metallic exposure depends on the magnitude of exposure (constant, gradual), and the nature of the ecological niche (water, skin, and gut). The skin and gut microbiota of fish exposed to constant concentrations of cadmium (CC) were closer to the control negative than those exposed to the gradual concentrations (CV). Overall, our results show that the microbial assembly during the community recovery were both orchestrated by neutral and deterministic processes.8KR8qv6CEcKmimx9at5UakVideo Abtract.

Detecting communities from networks using an improved self-organizing map

Community structure is one of the important features of complex networks. Researchers have derived a number of algorithms for detecting communities, some of them suffer from high complexity or need some prior knowledge, such as the size of community or number of communities. For some of them, the quality of the detected community structure cannot be guaranteed, even the results of some of them are nondeterministic. In this paper, we propose a Self-Organizing Map (SOM)-based method for detecting community structure from networks. We first preprocess the network by removing some nodes and their associated edges which have little contribution to the formation of communities, then we construct the extended attribute matrix from the preprocessed network, next we embed the detecting procedure in the training of SOM on the attribute matrix to acquire the initial community structure, and finally, we handle those removed nodes by inserting each of them into the community to which its only neighbor belongs, and fine-tune the initial community structure by merging some of the initial communities to improve the quality of the final result. The performance of the proposed method is evaluated on a variety of artificial networks and real-world networks, and experimental results show that our method takes full advantage of SOM model, it can automatically determine the number of communities embedded in the network, the quality of the detected community structure is steadily promising and superior to those of other comparison algorithms.

Effectively Detecting Communities by Adjusting Initial Structure via Cores

Community detection is helpful to understand useful information in real‐world networks by uncovering their natural structures. In this paper, we propose a simple but effective community detection algorithm, called ACC, which needs no heuristic search but has near‐linear time complexity. ACC defines a novel similarity which is different from most common similarity definitions by considering not only common neighbors of two adjacent nodes but also their mutual exclusive degree. According to this similarity, ACC groups nodes together to obtain the initial community structure in the first step. In the second step, ACC adjusts the initial community structure according to cores discovered through a new local density which is defined as the influence of a node on its neighbors. The third step expands communities to yield the final community structure. To comprehensively demonstrate the performance of ACC, we compare it with seven representative state‐of‐the‐art community detection algorithms, on small size networks with ground‐truth community structures and relatively big‐size networks without ground‐truth community structures. Experimental results show that ACC outperforms the seven compared algorithms in most cases.

Community detection via closure extension

Identifying community structure in networks plays an important role in understanding the network structure and analyzing the network features. Many state-of-the-art algorithms have been proposed to identify the community structure in networks. In this paper, we propose a novel method based on closure extension; it performs in two steps. The first step uses the similarity closure or correlation closure to find the initial community structure. In the second step, we merge the initial communities using Modularity [Formula: see text]. The proposed method does not need any prior information such as the number or sizes of communities, and it is able to obtain the same resulting communities in multiple runs. Moreover, it is noteworthy that our method has low computational complexity because of considering only local information of network. Some real-world and synthetic graphs are used to test the performance of the proposed method. The results demonstrate that our method can detect deterministic and informative community structure in most cases.