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Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks

Renaud Lambiotte, Jean-Charles Delvenne, Mauricio Barahona
2014 IEEE Transactions on Network Science and Engineering  
Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph.  ...  The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure.  ...  Rosvall and C. T. Bergstrom, "Maps of random walks on complex networks reveal community structure," Proceedings of the National Academy of Sciences USA, vol.  ... 
doi:10.1109/tnse.2015.2391998 fatcat:zmfpfsocsbfq3btj4sn6ixgwvi

Multiscale Information Propagation in Emergent Functional Networks

Arsham Ghavasieh, Manlio De De Domenico
2021 Entropy  
Here, we introduce the multiscale emergent functional state, which can be represented as a network where links encode the flow exchange between the nodes, calculated using diffusion processes on top of  ...  Our results suggest that the topological complexity of fungal networks guarantees the existence of functional modules at different scales keeping the information entropy, and functional diversity, high  ...  Data Availability Statement: The data are publicly available from the cited references. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e23101369 pmid:34682093 pmcid:PMC8534377 fatcat:uqj25m24djbebnun74h55gez34

Encoding dynamics for multiscale community detection: Markov time sweeping for the map equation

Michael T. Schaub, Renaud Lambiotte, Mauricio Barahona
2012 Physical Review E  
matrix of the Markov process.  ...  Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an information-theoretic description of the process of coding inter- and intra-community transitions of a random walker in the network at stationarity  ...  This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State  ... 
doi:10.1103/physreve.86.026112 pmid:23005830 fatcat:3fpxsse4qreb3g67c4qkofkkf4

Urban Analytics: Multiplexed and Dynamic Community Networks [article]

Weisi Guo, Guillem Mosquera Donate, Stephen Law, Samuel Johnson, Maria Liakata, Alan Wilson
2018 arXiv   pre-print
The better understanding of the structural dynamics and multiplexed relationships can provide useful information to inform both urban planning policies and shape the design of socially coupled urban infrastructure  ...  In this paper, we review how increasingly available heterogeneous mobile big data sets can be leveraged to detect the community interaction structure using natural language processing and machine learning  ...  Interestingly, the first two processes can be shown to be dual to the later, i.e. equivalent to Markov chain modelling the diffusion of random walks across the network.  ... 
arXiv:1706.05535v4 fatcat:xlhu2522jjf5xpswfqii6m3jmm

Markov Dynamics as a Zooming Lens for Multiscale Community Detection: Non Clique-Like Communities and the Field-of-View Limit

Michael T. Schaub, Jean-Charles Delvenne, Sophia N. Yaliraki, Mauricio Barahona, Olaf Sporns
2012 PLoS ONE  
In recent years, there has been a surge of interest in community detection algorithms for complex networks.  ...  We show how by adopting a dynamical perspective towards community detection (Delvenne et al. (2010) PNAS:107: 12755-12760; Lambiotte et al. (2008) arXiv:0812.1770), in which the evolution of a Markov process  ...  the creation of the figures and graphs of the protein examples.  ... 
doi:10.1371/journal.pone.0032210 pmid:22384178 pmcid:PMC3288079 fatcat:zcvxnac7x5afjmjawv3libsjfa

Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity

RICHARD F. BETZEL, ALESSANDRA GRIFFA, ANDREA AVENA-KOENIGSBERGER, JOAQUÍN GOÑI, JEAN-PHILIPPE THIRAN, PATRIC HAGMANN, OLAF SPORNS
2013 Network Science  
In this report we used the partition stability framework, which defines communities in terms of a Markov process (random walk), to infer the connectome's multi-scale community structure.  ...  This result suggests a mapping between communities in structural networks, models of communication processes, and brain function.  ...  As this process evolves, a random walker makes progressively longer walks and explores more distant parts of the network.  ... 
doi:10.1017/nws.2013.19 fatcat:f3h2zoz6sngn3cwwnpqpe52sjm

Persistence of information flow: a multiscale characterization of human brain

Barbara Benigni, Arsham Ghavasieh, Alessandra Corso, Valeria d'Andrea, Manlio De Domenico
2021 Network Neuroscience  
We find that the spectral entropy of empirical data lies between two generative models, indicating an interpolation between modular and geometry-driven structural features.  ...  Neuroimaging techniques allow for the indirect measurement of information flows among brain areas and, consequently, for reconstructing connectomes analyzed through the lens of network science.  ...  Li-Wei Kuo and the MR NeuroImaging Lab (National Health Research Institutes, Taiwan) for kindly providing access to some of the empirical datasets used in this study.  ... 
doi:10.1162/netn_a_00203 pmid:34746629 pmcid:PMC8567833 fatcat:araytw6ovbhlfgeuthxrcolvzq

Modular Brain Networks

Olaf Sporns, Richard F. Betzel
2016 Annual Review of Psychology  
brain networks and briefly considers their potential functional roles in brain evolution, wiring minimization, and the emergence of functional specialization and complex dynamics. osporns@indiana.edu  ...  The development of new technologies for mapping structural and functional brain connectivity has led to the creation of comprehensive network maps of neuronal circuits and systems.  ...  O.S. was supported by the JS McDonnell Foundation (22002082) and the National Institutes of Health (R01 AT009036-01).  ... 
doi:10.1146/annurev-psych-122414-033634 pmid:26393868 pmcid:PMC4782188 fatcat:iktzb65cbjbwjib2ig3lag2rme

Selection of Significant Community Structure Based on Network Partition-based Cluster

Qingju Jiao, Yuanyuan Jin
2019 Journal Europeen des Systemes Automatises  
Experiments on selection of benchmark and real networks demonstrate that the new method for selecting significant partitions is very effectively.  ...  Module (or community) structure detection, which has been successfully applied to many fields, is vital step for understand network dynamic and complex systems.  ...  ACKNOWLEDGMENTS The authors acknowledge the supports from the National Language Committee scientific research projects of China (No.  ... 
doi:10.18280/jesa.520105 fatcat:d2ydgzzq6fgsfaky5zmcoxey3m

The Stability of a Graph Partition: A Dynamics-Based Framework for Community Detection [chapter]

Jean-Charles Delvenne, Michael T. Schaub, Sophia N. Yaliraki, Mauricio Barahona
2013 Modeling and Simulation in Science, Engineering and Technology  
Naturally, the study of real-world systems leads to highly complex networks and a current challenge is to extract intelligible, simplified descriptions from the network in terms of relevant subgraphs,  ...  Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed  ...  D. acknowledges support from the grant "Actions de recherche concertées-Large Graphs and Networks" of the Communauté Française de Belgique, the EULER project (  ... 
doi:10.1007/978-1-4614-6729-8_11 fatcat:iu6btcknozcrrhnt2yobv5dacm

Graph Wavelets for Multiscale Community Mining

Nicolas Tremblay, Pierre Borgnat
2014 IEEE Transactions on Signal Processing  
The effectiveness of the method is discussed first on multiscale graph benchmarks, then on real data of social networks and on models for signal processing on graphs.  ...  We develop a signal processing approach to the multiscale detection of communities in networks, that is of groups of nodes well connected together.  ...  ACKNOWLEDGMENT The authors would like to thank the three anonymous reviewers for their constructive comments, which greatly helped to improve the paper, R. Hamon for fruitful discussions, and A.  ... 
doi:10.1109/tsp.2014.2345355 fatcat:ehcbr5o3hfgvbn7sg6w7dfquui

Multi-scale Modularity in Complex Networks [article]

Renaud Lambiotte
2010 arXiv   pre-print
We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales.  ...  characteristic number of modules which might not be compatible with the modular organization of the system.  ...  Fortunato and D. Meunier for fruitful discussions, E. Landuyt for proof-reading and J.-L. Guillaume for providing the C++ code of the Louvain method for modularity optimization 5 [19] .  ... 
arXiv:1004.4268v1 fatcat:ns53jmujoffybaiwccmzrptf2u

Multiscale mobility patterns and the restriction of human mobility under lockdown [article]

Dominik Schindler, Jonathan Clarke, Mauricio Barahona
2022 arXiv   pre-print
A special emphasis lies on dynamical perspectives of network analysis and multi-scale community detection with Markov Stability analysis is performed to identify signatures for the mobility contraction  ...  The analysis of the UK mobility network reveals a pronounced decline of human mobility under COVID-19 and suggests that local community structure has been strengthened under lockdown.  ...  Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks. IEEE Transactions on Network Science and Engineering 1, 76–90 (July 2014). 25. Bacik, K. A. et al.  ... 
arXiv:2201.06323v1 fatcat:jy6u5c4crbevjiclfsvs5smywm

How choosing random-walk model and network representation matters for flow-based community detection in hypergraphs

Anton Eriksson, Daniel Edler, Alexis Rojas, Manlio de Domenico, Martin Rosvall
2021 Communications Physics  
We define unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random-walk model change the number, size, depth, and overlap of identified  ...  For different hypergraph data and research questions, which combination of random-walk model and network representation is best?  ...  The source code is available on GitHub (http://github.com/mapequation/mappinghypergraphs). Acknowledgements  ... 
doi:10.1038/s42005-021-00634-z fatcat:hyjou6il2jg7rhv44fxsp4miue

Network Geometry [article]

Marian Boguna, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Angeles Serrano
2020 arXiv   pre-print
Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks.  ...  and challenges in this novel frontier in the study of complexity.  ...  processes evolving on the top of complex networks.  ... 
arXiv:2001.03241v2 fatcat:n3kqsgmpxffr5klzoihs525mrm
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