Measuring intrinsic significance of community structure

2019 ◽  
Vol 30 (09) ◽  
pp. 1950068
Author(s):  
Jiarong Xie ◽  
Mingwei Du ◽  
Zengru Di ◽  
Huaiwei Zhu ◽  
Ying Fan ◽  
...  
Keyword(s):  
Community Structure ◽  
Metabolic Networks ◽  
Optimal Number ◽  
Protein Interaction Networks ◽  
Matrix Perturbation ◽  
Community Structures ◽  
C Elegans ◽  
Matrix Perturbation Theory ◽  
The Matrix ◽  
Clustering Problems

The significance of communities is an important inherent property of the community structure. It measures the degree of reliability of the community structure identified by the algorithm. Real networks obtained from complex systems always contain error links. Moreover, most of the community detecting algorithms usually involve random factors. Thus evaluating the significance of community structure is very important. In this paper, using the matrix perturbation theory, we propose a normalized index to efficiently evaluate the significance of community structure without detecting communities. Furthermore, we find that the peaks of this index can be used to determine the optimal number of communities and identify hierarchical community structure, which are two challenging problems in many community detecting algorithms. Lastly, the index is applied to 16 typical real networks, and we find that significant community structures exist in many social networks and in the C. elegans neural network. Comparatively insignificant community structures are identified in protein-interaction networks and metabolic networks. Our method can be generalized to broad clustering problems in data mining.

Urban community structure detection based on the OD of traffic analysis zones

2019 ◽  
Vol 33 (13) ◽  
pp. 1950164
Author(s):  
Qing-Feng Dong ◽  
Dian-Kun Chen ◽  
Ting Wang
Keyword(s):  
Community Structure ◽  
Quantitative Methods ◽  
Urban Community ◽  
Spatial Location ◽  
Traffic Analysis ◽  
Association Mining ◽  
Community Structures ◽  
City Community ◽  
Traffic Characteristics ◽  
Structure Detection

At present, the detection of urban community structures is mainly based on existing administrative divisions, and is performed using qualitative methods. The lack of quantitative methods makes it difficult to judge the rationality of urban community divisions. In this study, we used complex network association mining methods to detect a city community structure by using the Origin-Destinations (OD) at traffic analysis zone (TAZ) level, and successively assigned all the TAZs into different communities. Based on the community results, we calculated the community core degree of each TAZ within every community, and then calculated the Traffic Core Degree and Location Core Degree indicators of the community based on OD passenger flow and spatial location relationship between communities. Finally, we analyzed the correlation among three indicators to ensure the rationality of the community structure. We used the city of Zhengzhou in 2016 as an example case study. For Zhengzhou, we detected a total of six communities. We found a relatively low correlation between Traffic Core Degree and Location Core Degree. Within each group, the correlation between community core degree and Traffic Core Degree was higher than that between community core degree and Location Core Degree, indicating that the urban community structure is more reasonably based on traffic characteristics. The development of a quantitative approach for determining reasonable city community structures has important implications for transportation planning and industrial layout.

Community Detection in Political Discussions on Twitter

2016 ◽  
Vol 35 (2) ◽  
pp. 244-261 ◽  
Author(s):  
Frederic Guerrero-Solé
Keyword(s):  
Community Structure ◽  
Community Detection ◽  
Reliable Method ◽  
Community Structures ◽  
Network Community ◽  
High Polarization

In November 9, 2014, the Catalan government called Catalan people to participate in a straw poll about the independence of Catalonia from Spain. This article analyzes the use of Twitter between November 8 and 10, 2014. Drawing on a methodology developed by Guerrero-Solé, Corominas-Murtra, and Lopez-Gonzalez, this work examines the structure of the retweet overlap network (RON), formed by those users whose communities of retweeters have nonzero overlapping, to detect the community structure of the network. The results show a high polarization of the resulting network and prove that the RON is a reliable method to determinate network community structures and users’ political leaning in political discussions.

scholarly journals High-throughput amplicon sequencing reveals the spatiotemporal effects, abiotic and biotic shaping factors for the microbial communities in tropical mangrove sediments in Sanya, China

2020 ◽  
Author(s):  
Wu Qu ◽  
Boliang Gao ◽  
Jie Wu ◽  
Min Jin ◽  
Jianxin Wang ◽  
...  
Keyword(s):  
Community Structure ◽  
Microbial Community ◽  
Microbial Communities ◽  
Fungal Community ◽  
Amplicon Sequencing ◽  
Biotic Factors ◽  
Community Structures ◽  
Mangrove Sediments ◽  
Element Cycling ◽  
Microbial Community Structures

Abstract Background Microbial roles in element cycling and nutrient providing are crucial for mangrove ecosystems and serve as important regulators for climate change in Earth ecosystem. However, some key information about the spatiotemporal influences and abiotic and biotic shaping factors for the microbial communities in mangrove sediments remains lacking. Methods In this work, 22 sediment samples were collected from multiple spatiotemporal dimensions, including three locations, two depths, and four seasons, and the bacterial, archaeal, and fungal community structures in these samples were studied using amplicon sequencing. Results The microbial community structures were varied in the samples from different depths and locations based on the results of LDA effect size analysis, principal coordinate analysis, the analysis of similarities, and permutational multivariate ANOVA. However, these microbial community structures were stable among the seasonal samples. Linear fitting models and Mantel test showed that among the 13 environmental factors measured in this study, the sediment particle size (PS) was the key abiotic shaping factor for the bacterial, archaeal, or fungal community structure. Besides PS, salinity and humidity were also significant impact factors according to the canonical correlation analysis (p ≤ 0.05). Co-occurrence networks demonstrated that the bacteria assigned into phyla Ignavibacteriae, Proteobacteria, Bacteroidetes, Chloroflexi, and Acidobacteria were the key biotic factors for shaping the bacterial community in mangrove sediments. Conclusions This work showed the variability on spatial dimensions and the stability on temporal dimension for the bacterial, archaeal, or fungal microbial community structure, indicating that the tropical mangrove sediments are versatile but stable environments. PS served as the key abiotic factor could indirectly participate in material circulation in mangroves by influencing microbial community structures, along with salinity and humidity. The bacteria as key biotic factors were found with the abilities of photosynthesis, polysaccharide degradation, or nitrogen fixation, which were potential indicators for monitoring mangrove health, as well as crucial participants in the storage of mangrove blue carbons and mitigation of climate warming. This study expanded the knowledge of mangroves for the spatiotemporal variation, distribution, and regulation of the microbial community structures, thus further elucidating the microbial roles in mangrove management and climate regulation.

Ideal flow of Markov Chain

2018 ◽  
Vol 10 (06) ◽  
pp. 1850073
Author(s):  
Kardi Teknomo
Keyword(s):  
Transition Probability ◽  
Transition Probability Matrix ◽  
Scaling Factor ◽  
Matrix Perturbation ◽  
Flow Network ◽  
Ideal Flow ◽  
The Matrix ◽  
Strongly Connected ◽  
Flow Equilibrium ◽  
Matrix Perturbation Analysis

Ideal flow network is a strongly connected network with flow, where the flows are in steady state and conserved. The matrix of ideal flow is premagic, where vector, the sum of rows, is equal to the transposed vector containing the sum of columns. The premagic property guarantees the flow conservation in all nodes. The scaling factor as the sum of node probabilities of all nodes is equal to the total flow of an ideal flow network. The same scaling factor can also be applied to create the identical ideal flow network, which has from the same transition probability matrix. Perturbation analysis of the elements of the stationary node probability vector shows an insight that the limiting distribution or the stationary distribution is also the flow-equilibrium distribution. The process is reversible that the Markov probability matrix can be obtained from the invariant state distribution through linear algebra of ideal flow matrix. Finally, we show that recursive transformation [Formula: see text] to represent [Formula: see text]-vertices path-tracing also preserved the properties of ideal flow, which is irreducible and premagic.

A Probabilistic Analysis for Static and Dynamic Frequency of Blade With Uncertain Boundary Conditions

2005 ◽  
Author(s):  
Z. Q. Wang ◽  
L. Q. An ◽  
Z. Z. Peng
Keyword(s):  
Boundary Condition ◽  
Probabilistic Analysis ◽  
Natural Frequencies ◽  
Perturbation Technique ◽  
Ritz Method ◽  
Joint Stiffness ◽  
Matrix Perturbation ◽  
Sensitivity Matrix ◽  
The Matrix ◽  
Uncertain Boundary

A probabilistic analysis method is developed for frequencies analysis of turbine blade with uncertain boundary condition at the root of blade. The Ritz method is used to derive the eigenvalues equation of the rotating blade with uncertain root boundary condition. The matrix perturbation technique is employed for the probabilistic analysis to obtain the deterministic part of natural frequencies and vibration modes, the sensitivity matrix, the covariance matrix and the coefficient of variance (COV) for the natural frequencies. The effects of variations in the expectation and the variance of joint stiffness on the expectation and the variance of the natural frequencies are investigated.

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