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Role extraction for digraphs via neighborhood pattern similarity

Physical Review E 2022年第5期106卷 054301-054301页

作者： Giovanni Barbarino Vanni Noferini Paul Van Dooren Université catholique de Louvain Department of Mathematical Engineering Av. Lemaitre 4 B-1348 Louvain-la-Neuve Belgium

We analyze the recovery of different roles in a network modeled by a directed graph, based on the so-called Neighborhood Pattern Similarity approach. Our analysis uses results from random matrix theory to show that, when assuming that the graph is generated as a particular stochastic block model with Bernoulli probability distributions for the different blocks, then the recovery is asymptotically correct when the graph has a sufficiently large dimension. Under these assumptions there is a sufficient gap between the dominant and dominated eigenvalues of the similarity matrix, which guarantees the asymptotic correct identification of the number of different roles. We also comment on the connections with the literature on stochastic block models, including the case of probabilities of order log(n)/n where n is the graph size. We provide numerical experiments to assess the effectiveness of the method when applied to practical networks of finite size.

关键词： Clustering community structure Block models community detection algorithms

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Local topological moves determine global diffusion properties of hyperbolic higher-order networks

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Physical Review E 2021年第5期104卷 054302-054302页

作者： Ana P. Millán Reza Ghorbanchian Nicolò Defenu Federico Battiston Ginestra Bianconi Amsterdam UMC Vrije Universiteit Amsterdam Department of Clinical Neurophysiology and MEG Center Amsterdam Neuroscience De Boelelaan 1117 Amsterdam The Netherlands School of Mathematical Sciences Queen Mary University of London Mile End Road E1 4NS London United Kingdom Institute for Theoretical Physics ETH Zürich Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland Department of Network and Data Science Central European University 1100 Vienna Austria The Alan Turing Institute British Library 96 Euston Road NW1 2DB London United Kingdom

From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that network topology and geometry has on the emerging dynamical properties of higher-order networks is yet to be clarified. In this perspective, the spectral dimension plays a key role since it determines the effective dimension for diffusion processes on a network. Despite its relevance, a theoretical understanding of which mechanisms lead to a finite spectral dimension, and how this can be controlled, still represents a challenge and is the object of intense research. Here, we introduce two nonequilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the intertwined appearance of small-world behavior, δ-hyperbolicity, and community structure. We show that different topological moves, determining the nonequilibrium growth of the higher-order hyperbolic network models, induce tuneable values of the spectral dimension, showing a rich phenomenology which is not displayed in random graph ensembles. In particular, we observe that, if the topological moves used to construct the higher-order network increase the area/volume ratio, then the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the area/volume ratio. Our work reveals a new link between the geometry of a network and its diffusion properties, contributing to a better understanding of the complex interplay between network structure and dynamics.

关键词： Growth processes Network diffusion Network evolution Network structure Random walks Topological tools Scale free & inhomogeneous networks Small-world networks Stochastic networks Surface growth Triangular network community detection algorithms Evolving network models Monte Carlo methods Network Models Preferential attachment models Small-world model

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Stochastic graph Voronoi tessellation reveals community structure

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Physical Review E 2017年第2期95卷 022306-022306页

作者： Zsolt I. Lázár István Papp Levente Varga Ferenc Járai-Szabó Dávid Deritei Mária Ercsey-Ravasz Faculty of Physics Babeş-Bolyai University Cluj-Napoca Romania Department of Network Science Central European University Hungary Romanian Institute of Science and Technology Cluj-Napoca Romania

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called Voronoi cohesion which describes the probability for sharing the same Voronoi cell, when randomly choosing g centers in the network. This measure provides information based on the global context (the network in its entirety), a type of information that is not carried by other similarity measures. We explore the mathematical background of this phenomenon and several of its potential applications. A special focus is laid on the possibilities and limitations pertaining to the exploitation of the phenomenon for community detection purposes.

关键词： community structure Stochastic processes community detection algorithms

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Unwinding the hairball graph: Pruning algorithms for weighted complex networks

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Physical Review E 2016年第1期93卷 012304-012304页

作者： Navid Dianati []The Lazer Lab Northeastern University Boston Massachusetts 02115 USA and Institute for Quantitative Social Sciences Harvard University Cambridge Massachusetts 02138 USA

Empirical networks of weighted dyadic relations often contain “noisy” edges that alter the global characteristics of the network and obfuscate the most important structures therein. Graph pruning is the process of identifying the most significant edges according to a generative null model and extracting the subgraph consisting of those edges. Here, we focus on integer-weighted graphs commonly arising when weights count the occurrences of an “event” relating the nodes. We introduce a simple and intuitive null model related to the configuration model of network generation and derive two significance filters from it: the marginal likelihood filter (MLF) and the global likelihood filter (GLF). The former is a fast algorithm assigning a significance score to each edge based on the marginal distribution of edge weights, whereas the latter is an ensemble approach which takes into account the correlations among edges. We apply these filters to the network of air traffic volume between US airports and recover a geographically faithful representation of the graph. Furthermore, compared with thresholding based on edge weight, we show that our filters extract a larger and significantly sparser giant component.

关键词： Complex systems Transportation networks community detection algorithms

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Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model

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Physical Review E 2024年第6期109卷 064309-064309页

作者： Zhana Kuncheva Ognyan Kounchev Data Science and Engineering Optima Partners London UK WC1X 8HN Bulgarian Academy of Sciences Sofia 1113 Bulgaria

We study the behavior of the eigenvectors associated with the smallest eigenvalues of the Laplacian matrix of temporal networks. We consider the multilayer representation of temporal networks, i.e., a set of networks linked through ordinal interconnected layers. We analyze the Laplacian matrix, known as supra-Laplacian, constructed through the supraadjacency matrix associated with the multilayer formulation of temporal networks, using a constant block Jacobi model which has closed-form solution. To do this, we assume that the interlayer weights are perturbations of the Kronecker sum of the separate adjacency matrices forming the temporal network. Thus we investigate the properties of the eigenvectors associated with the smallest eigenvalues (close to zero) of the supra-Laplacian matrix. Using arguments of perturbation theory, we show that these eigenvectors can be approximated by linear combinations of the zero eigenvectors of the individual time layers. This finding is crucial in reconsidering and generalizing the role of the Fielder vector in supra-Laplacian matrices.

关键词： Clustering community structure Network evolution Erdos-Renyi graph Interconnected & interdependent networks Multilayer & multiplex networks Weighted networks Block models community detection algorithms Diffusion & random walks

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Item and domain network structures of the Resilience Scale for Adults in 675 university students

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EPIDEMIOLOGY AND PSYCHIATRIC SCIENCES 2020年 29卷 e33-e33页

作者： Briganti, G. Linkowski, P. Univ Libre Bruxelles Sch Publ Hlth Dept Clin Epidemiol & Biostat Route Lennik 808 B-1070 Brussels Belgium Ecole Super Sante Dept Pathophysiol Pl Chateau 3 CH-1014 Lausanne Switzerland

Aims. The Resilience Scale for Adults (RSA) is a questionnaire that measures protective factors of mental health. The aim of this paper is to perform a network analysis of the RSA in a dataset composed of 675 French-speaking Belgian university students, to identify potential targets for intervention to improve protective factors in individuals. Methods. We estimated a network structure for the 33-item questionnaire and for the six domains of resilience: perception of self, planned future, social competence, structured style, family cohesion and social competence. Node predictability (shared variance with surrounding nodes in the network) was used to assess the connectivity of items. An exploratory graph analysis (EGA) was performed to detect communities in the network: the number of communities detected being different than the original number of factors proposed in the scale, we estimated a new network with the resulting structure and verified the validity of the new construct which was proposed. We provide the anonymised dataset and code in external online materials (10.17632/64db36w8kf.2) to ensure complete reproducibility of the results. Results. The network composed of items from the RSA is overall positively connected with strongest connections arising among items from the same domain. The domain network reports several connections, both positive and negative. The EGA reported the existence of four communities that we propose as an additional network structure. Node predictability estimates show that connectedness varies among the items and domains of the RSA. Conclusions. Network analysis is a useful tool to explore resilience and identify targets for clinical intervention. In this study, the four domains acting as components of the additional four-domain network structure may be potential targets to improve an individual's resilience. Further studies may endeavour to replicate our findings in different samples.

关键词： Behaviour community detection algorithms psychometrics

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Electron bunch profile reconstruction based on phase-constrained iterative algorithm

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Physical Review Accelerators and Beams 2016年第3期19卷 032801-032801页

作者： F. Bakkali Taheri I. V. Konoplev G. Doucas P. Baddoo R. Bartolini J. Cowley S. M. Hooker John Adams Institute Department of Physics University of Oxford Denys Wilkinson Building Keble Road Oxford OX1 3RH United Kingdom

The phase retrieval problem occurs in a number of areas in physics and is the subject of continuing investigation. The one-dimensional case, e.g., the reconstruction of the temporal profile of a charged particle bunch, is particularly challenging and important for particle accelerators. Accurate knowledge of the longitudinal (time) profile of the bunch is important in the context of linear colliders, wakefield accelerators and for the next generation of light sources, including x-ray SASE FELs. Frequently applied methods, e.g., minimal phase retrieval or other iterative algorithms, are reliable if the Blaschke phase contribution is negligible. This, however, is neither known a priori nor can it be assumed to apply to an arbitrary bunch profile. We present a novel approach which gives reproducible, most-probable and stable reconstructions for bunch profiles (both artificial and experimental) that would otherwise remain unresolved by the existing techniques.

关键词： community detection algorithms

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A study of research topic visualization using network structure analysis

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Journal of Educational Media and Library Science 2013年第4期50卷 565-596页

作者： Lin, Sung-Chien Department of Information and Communications Shih Hsin University Taipei Taiwan

The Pathfinder network (PFNet) method and the community detection algorithms both are methods which have been widely applied to visual presentation and analysis of research topics. The PFNet method can delete a large amount of insignificant links in networks but also retains the structural characteristics of the original networks, while the community detection algorithms are able to partition networks into a set of cohesive subgroups. However, each of the methods has its deficiencies. The PFNet method cannot automatically find out critical subgroups in input networks and the community detection algorithms do not guarantee nodes in the same subgroup able to be mapped in neighboring area. The integration of these two methods provides a way to alleviate the above problems: The output network from the PFNet method is partitioned using community detection algorithm. In addition, this study also suggests that the use of high frequency terms within papers in subgroups as the labels of research topics to make the analysis and interpretation of results easier. This study takes the field of Information Communication as an analytic case to study the application of the integrated methods, and the data of master theses of the related graduated schools are collected to be used for the analysis. The results show that it is effective to integrate the PFNet method and the community detection algorithms to discover subgroups representing important research topics from the network which is constructed upon the relations between papers in the examined field. The terms with high occurring frequency in subgroups are very relevant to the problems, method, theorems and technologies in the field of Information Communications and its fundamental disciplines, and therefore, they are suitable as the representatives of research topics.

关键词： Analysis of research topics community detection algorithms Information visualization Path-finder Networks

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Detecting brain network communities: Considering the role of information flow and its different temporal scales

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NEUROIMAGE 2021年 225卷 117431-117431页

作者： Sanchez-Rodriguez, Lazaro M. Iturria-Medina, Yasser Mouches, Pauline Sotero, Roberto C. Univ Calgary Dept Radiol 3330 Hosp Dr NW Calgary AB T2N 4N1 Canada Univ Calgary Hotchkiss Brain Inst 3330 Hosp Dr NW Calgary AB T2N 4N1 Canada McGill Univ Montreal Neurol Inst Dept Neurol & Neurosurg Montreal PQ Canada McGill Univ McConnel Brain Imaging Ctr Montreal Neurol Inst Montreal PQ Canada McGill Univ Ludmer Ctr Neuroinformat & Mental Hlth Montreal PQ Canada Univ Calgary Biomed Engn Grad Program Calgary AB Canada

The identification of community structure in graphs continues to attract great interest in several fields. Network neuroscience is particularly concerned with this problem considering the key roles communities play in brain processes and functionality. Most methods used for community detection in brain graphs are based on the maximization of a parameter-dependent modularity function that often obscures the physical meaning and hierarchical organization of the partitions of network nodes. In this work, we present a new method able to detect communities at different scales in a natural, unrestricted way. First, to obtain an estimation of the information flow in the network we release random walkers to freely move over it. The activity of the walkers is separated into oscillatory modes by using empirical mode decomposition. After grouping nodes by their co-occurrence at each time scale, k-modes clustering returns the desired partitions. Our algorithm was first tested on benchmark graphs with favorable performance. Next, it was applied to real and simulated anatomical and/or functional connectomes in the macaque and human brains. We found a clear hierarchical repertoire of community structures in both the anatomical and the functional networks. The observed partitions range from the evident division in two hemispheres -in which all processes are managed globally- to specialized communities seemingly shaped by physical proximity and shared function. Additionally, the spatial scales of a network's community structure (characterized by a measure we term within-communities path length) appear inversely proportional to the oscillatory modes' average frequencies. The proportionality constant may constitute a network-specific propagation velocity for the information flow. Our results stimulate the research of hierarchical community organization in terms of temporal scales of information flow in the brain network.

关键词： community detection algorithms Brain networks Random walkers Empirical mode decomposition k-modes clustering

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Fragility of spectral clustering for networks with an overlapping structure

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Physical Review Research 2020年第4期2卷 043101-043101页

作者： Chihiro Noguchi Tatsuro Kawamoto Artificial Intelligence Research Center National Institute of Advanced Industrial Science and Technology 2-3-26 Aomi Koto-ku Tokyo Japan

Overlapping communities are commonly observed in real-world networks. This is a motivation to develop overlapping community detection methods, because methods for nonoverlapping communities may not perform well. However, deterioration mechanism of the detection methods used for nonoverlapping communities have rarely been investigated theoretically. Here, we analyze accuracy of spectral clustering, which does not consider overlapping structures, by using the replica method from statistical physics. Our analysis on an overlapping stochastic block model reveals how the structural information is lost from the leading eigenvector because of the overlapping structure.

关键词： Clustering community structure Random graphs Block models community detection algorithms Overlapping communities Replica methods Replica theory

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