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Chacoma A, Almeira N, Perotti JI, Billoni OV. Stochastic model for football's collective dynamics. Phys Rev E 2021; 104:024110. [PMID: 34525563 DOI: 10.1103/physreve.104.024110] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Accepted: 07/20/2021] [Indexed: 11/07/2022]
Abstract
In this paper, we study collective interaction dynamics emerging in the game of football (soccer). To do so, we surveyed a database containing body-sensor traces measured during three professional football matches, where we observed statistical patterns that we used to propose a stochastic model for the players' motion in the field. The model, which is based on linear interactions, captures to a good approximation the spatiotemporal dynamics of a football team. Our theoretical framework, therefore, can be an effective analytical tool to uncover the underlying cooperative mechanisms behind the complexity of football plays. Moreover, we showed that it can provide handy theoretical support for coaches to evaluate teams' and players' performances in both training sessions and competitive scenarios.
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Affiliation(s)
- A Chacoma
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
| | - N Almeira
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
| | - J I Perotti
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
| | - O V Billoni
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
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Martínez JH, Garrido D, Herrera-Diestra JL, Busquets J, Sevilla-Escoboza R, Buldú JM. Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective. ENTROPY 2020; 22:e22020172. [PMID: 33285947 PMCID: PMC7516593 DOI: 10.3390/e22020172] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 01/27/2020] [Accepted: 01/31/2020] [Indexed: 12/02/2022]
Abstract
We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017/2018 season. Second, we investigated how the player’s average location in the field is related to the amount of entropy of his passes. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.
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Affiliation(s)
- Johann H. Martínez
- Biomedical Engineering Department, Universidad de los Andes, 111711 Bogota, Colombia
- Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain
- Correspondence: (J.H.M.); (J.M.B.)
| | - David Garrido
- Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain
- Complex Systems Group, Rey Juan Carlos University, 28933 Madrid, Spain
- Laboratory of Biological Networks, Centre for Biomedical Technology (CTB-UPM), Universidad Politécnica de Madrid (UPM), 28223 Madrid, Spain
| | - José L. Herrera-Diestra
- ICTP—South American Institute for Fundamental Research, 01140-070 Sao Paulo, Brazil
- CeSiMo, Facultad de Ingeniería, Universidad de Los Andes, 5101 Merida, Venezuela
| | - Javier Busquets
- Department of Operations, Innovation and Data Science, ESADE Business School, 08034 Barcelona, Spain
| | | | - Javier M. Buldú
- Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain
- Complex Systems Group, Rey Juan Carlos University, 28933 Madrid, Spain
- Laboratory of Biological Networks, Centre for Biomedical Technology (CTB-UPM), Universidad Politécnica de Madrid (UPM), 28223 Madrid, Spain
- Institute of Unmanned System and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an 710072, China
- Correspondence: (J.H.M.); (J.M.B.)
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Buldú JM, Busquets J, Echegoyen I, Seirul Lo F. Defining a historic football team: Using Network Science to analyze Guardiola's F.C. Barcelona. Sci Rep 2019; 9:13602. [PMID: 31537882 PMCID: PMC6753100 DOI: 10.1038/s41598-019-49969-2] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Accepted: 09/03/2019] [Indexed: 12/03/2022] Open
Abstract
The application of Network Science to social systems has introduced new methodologies to analyze classical problems such as the emergence of epidemics, the arousal of cooperation between individuals or the propagation of information along social networks. More recently, the organization of football teams and their performance have been unveiled using metrics coming from Network Science, where a team is considered as a complex network whose nodes (i.e., players) interact with the aim of overcoming the opponent network. Here, we combine the use of different network metrics to extract the particular signature of the F.C. Barcelona coached by Guardiola, which has been considered one of the best teams along football history. We have first compared the network organization of Guardiola's team with their opponents along one season of the Spanish national league, identifying those metrics with statistically significant differences and relating them with the Guardiola's game. Next, we have focused on the temporal nature of football passing networks and calculated the evolution of all network properties along a match, instead of considering their average. In this way, we are able to identify those network metrics that enhance the probability of scoring/receiving a goal, showing that not all teams behave in the same way and how the organization Guardiola's F.C. Barcelona is different from the rest, including its clustering coefficient, shortest-path length, largest eigenvalue of the adjacency matrix, algebraic connectivity and centrality distribution.
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Affiliation(s)
- J M Buldú
- Complex System Group & GISC, Universidad Rey Juan Carlos, Madrid, Spain.
- Laboratory of Biological Networks, Center for Biomedical Technology, Universidad Politécnica de Madrid, Madrid, Spain.
- Institute of Unmanned System and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an, 710072, China.
| | | | - I Echegoyen
- Complex System Group & GISC, Universidad Rey Juan Carlos, Madrid, Spain
- Laboratory of Biological Networks, Center for Biomedical Technology, Universidad Politécnica de Madrid, Madrid, Spain
| | - F Seirul Lo
- Departamento de Metodología, F.C. Barcelona, Barcelona, Spain
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Functional brain networks reveal the existence of cognitive reserve and the interplay between network topology and dynamics. Sci Rep 2018; 8:10525. [PMID: 30002460 PMCID: PMC6043549 DOI: 10.1038/s41598-018-28747-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Accepted: 05/25/2018] [Indexed: 12/21/2022] Open
Abstract
We investigated how the organization of functional brain networks was related to cognitive reserve (CR) during a memory task in healthy aging. We obtained the magnetoencephalographic functional networks of 20 elders with a high or low CR level to analyse the differences at network features. We reported a negative correlation between synchronization of the whole network and CR, and observed differences both at the node and at the network level in: the average shortest path and the network outreach. Individuals with high CR required functional networks with lower links to successfully carry out the memory task. These results may indicate that those individuals with low CR level exhibited a dual pattern of compensation and network impairment, since their functioning was more energetically costly to perform the task as the high CR group. Additionally, we evaluated how the dynamical properties of the different brain regions were correlated to the network parameters obtaining that entropy was positively correlated with the strength and clustering coefficient, while complexity behaved conversely. Consequently, highly connected nodes of the functional networks showed a more stochastic and less complex signal. We consider that network approach may be a relevant tool to better understand brain functioning in aging.
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Valdez MA, Jaschke D, Vargas DL, Carr LD. Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks. PHYSICAL REVIEW LETTERS 2017; 119:225301. [PMID: 29286771 DOI: 10.1103/physrevlett.119.225301] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Indexed: 06/07/2023]
Abstract
We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the complexity of electroencephalogram or functional magnetic resonance imaging measurements of the brain. Using matrix product state methods, we show that network density, clustering, disparity, and Pearson's correlation obtain the critical point for both quantum Ising and Bose-Hubbard models to a high degree of accuracy in finite-size scaling for three classes of quantum phase transitions, Z_{2}, mean field superfluid to Mott insulator, and a Berzinskii-Kosterlitz-Thouless crossover.
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Affiliation(s)
- Marc Andrew Valdez
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Daniel Jaschke
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - David L Vargas
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Lincoln D Carr
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
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Hahn K, Massopust PR, Prigarin S. A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain. BMC Bioinformatics 2016; 17:87. [PMID: 26873589 PMCID: PMC4752807 DOI: 10.1186/s12859-016-0933-9] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2015] [Accepted: 01/29/2016] [Indexed: 12/15/2022] Open
Abstract
BACKGROUND Networks or graphs play an important role in the biological sciences. Protein interaction networks and metabolic networks support the understanding of basic cellular mechanisms. In the human brain, networks of functional or structural connectivity model the information-flow between cortex regions. In this context, measures of network properties are needed. We propose a new measure, Ndim, estimating the complexity of arbitrary networks. This measure is based on a fractal dimension, which is similar to recently introduced box-covering dimensions. However, box-covering dimensions are only applicable to fractal networks. The construction of these network-dimensions relies on concepts proposed to measure fractality or complexity of irregular sets in [Formula: see text]. RESULTS The network measure Ndim grows with the proliferation of increasing network connectivity and is essentially determined by the cardinality of a maximum k-clique, where k is the characteristic path length of the network. Numerical applications to lattice-graphs and to fractal and non-fractal graph models, together with formal proofs show, that Ndim estimates a dimension of complexity for arbitrary graphs. Box-covering dimensions for fractal graphs rely on a linear log-log plot of minimum numbers of covering subgraph boxes versus the box sizes. We demonstrate the affinity between Ndim and the fractal box-covering dimensions but also that Ndim extends the concept of a fractal dimension to networks with non-linear log-log plots. Comparisons of Ndim with topological measures of complexity (cost and efficiency) show that Ndim has larger informative power. Three different methods to apply Ndim to weighted networks are finally presented and exemplified by comparisons of functional brain connectivity of healthy and depressed subjects. CONCLUSION We introduce a new measure of complexity for networks. We show that Ndim has the properties of a dimension and overcomes several limitations of presently used topological and fractal complexity-measures. It allows the comparison of the complexity of networks of different type, e.g., between fractal graphs characterized by hub repulsion and small world graphs with strong hub attraction. The large informative power and a convenient computational CPU-time for moderately sized networks may make Ndim a valuable tool for the analysis of biological networks.
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Affiliation(s)
- Klaus Hahn
- Institute of Computational Biology, HMGU-German Research Center for Environmental Health, Ingolstädter Landstraße 1, Neuherberg, 85764, Germany.
| | - Peter R Massopust
- Institute of Computational Biology, HMGU-German Research Center for Environmental Health, Ingolstädter Landstraße 1, Neuherberg, 85764, Germany.
- Centre of Mathematics, Research Unit M6, Technische Universität München, Boltzmannstrasse 3, Garching bei München, 85747, Germany.
| | - Sergei Prigarin
- Novosibirsk State University, Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia.
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Sagarra O, Pérez Vicente CJ, Díaz-Guilera A. Statistical mechanics of multiedge networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062806. [PMID: 24483510 DOI: 10.1103/physreve.88.062806] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2013] [Indexed: 06/03/2023]
Abstract
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.
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Affiliation(s)
- O Sagarra
- Departament de Física Fonamental, Universitat de Barcelona, E-08028 Barcelona, Spain
| | - C J Pérez Vicente
- Departament de Física Fonamental, Universitat de Barcelona, E-08028 Barcelona, Spain
| | - A Díaz-Guilera
- Departament de Física Fonamental, Universitat de Barcelona, E-08028 Barcelona, Spain
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Chen G, Zhang HY, Xie C, Chen G, Zhang ZJ, Teng GJ, Li SJ. Modular reorganization of brain resting state networks and its independent validation in Alzheimer's disease patients. Front Hum Neurosci 2013; 7:456. [PMID: 23950743 PMCID: PMC3739061 DOI: 10.3389/fnhum.2013.00456] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2013] [Accepted: 07/22/2013] [Indexed: 12/05/2022] Open
Abstract
Previous studies have demonstrated disruption in structural and functional connectivity occurring in the Alzheimer's Disease (AD). However, it is not known how these disruptions alter brain network reorganization. With the modular analysis method of graph theory, and datasets acquired by the resting-state functional connectivity MRI (R-fMRI) method, we investigated and compared the brain organization patterns between the AD group and the cognitively normal control (CN) group. Our main finding is that the largest homotopic module (defined as the insula module) in the CN group was broken down to the pieces in the AD group. Specifically, it was discovered that the eight pairs of the bilateral regions (the opercular part of inferior frontal gyrus, area triangularis, insula, putamen, globus pallidus, transverse temporal gyri, superior temporal gyrus, and superior temporal pole) of the insula module had lost symmetric functional connection properties, and the corresponding gray matter concentration (GMC) was significant lower in AD group. We further quantified the functional connectivity changes with an index (index A) and structural changes with the GMC index in the insula module to demonstrate their great potential as AD biomarkers. We further validated these results with six additional independent datasets (271 subjects in six groups). Our results demonstrated specific underlying structural and functional reorganization from young to old, and for diseased subjects. Further, it is suggested that by combining the structural GMC analysis and functional modular analysis in the insula module, a new biomarker can be developed at the single-subject level.
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Affiliation(s)
- Guangyu Chen
- Department of Biophysics, Medical College of Wisconsin Milwaukee, WI, USA
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Reorganization of functional networks in mild cognitive impairment. PLoS One 2011; 6:e19584. [PMID: 21625430 PMCID: PMC3100302 DOI: 10.1371/journal.pone.0019584] [Citation(s) in RCA: 108] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2010] [Accepted: 04/01/2011] [Indexed: 11/25/2022] Open
Abstract
Whether the balance between integration and segregation of information in the brain is damaged in Mild Cognitive Impairment (MCI) subjects is still a matter of debate. Here we characterize the functional network architecture of MCI subjects by means of complex networks analysis. Magnetoencephalograms (MEG) time series obtained during a memory task were evaluated by synchronization likelihood (SL), to quantify the statistical dependence between MEG signals and to obtain the functional networks. Graphs from MCI subjects show an enhancement of the strength of connections, together with an increase in the outreach parameter, suggesting that memory processing in MCI subjects is associated with higher energy expenditure and a tendency toward random structure, which breaks the balance between integration and segregation. All features are reproduced by an evolutionary network model that simulates the degenerative process of a healthy functional network to that associated with MCI. Due to the high rate of conversion from MCI to Alzheimer Disease (AD), these results show that the analysis of functional networks could be an appropriate tool for the early detection of both MCI and AD.
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Generalizing unweighted network measures to capture the focus in interactions. SOCIAL NETWORK ANALYSIS AND MINING 2011. [DOI: 10.1007/s13278-011-0018-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Balenzuela P, Chernomoretz A, Fraiman D, Cifre I, Sitges C, Montoya P, Chialvo DR. Modular organization of brain resting state networks in chronic back pain patients. Front Neuroinform 2010; 4:116. [PMID: 21206760 PMCID: PMC3013486 DOI: 10.3389/fninf.2010.00116] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2010] [Accepted: 10/18/2010] [Indexed: 01/21/2023] Open
Abstract
Recent work on functional magnetic resonance imaging large-scale brain networks under resting conditions demonstrated its potential to evaluate the integrity of brain function under normal and pathological conditions. A similar approach is used in this work to study a group of chronic back pain patients and healthy controls to determine the impact of long enduring pain over brain dynamics. Correlation networks were constructed from the mutual partial correlations of brain activity's time series selected from ninety regions using a well validated brain parcellation atlas. The study of the resulting networks revealed an organization of up to six communities with similar modularity in both groups, but with important differences in the membership of key communities of frontal and temporal regions. The bulk of these findings were confirmed by a surprisingly naive analysis based on the pairwise correlations of the strongest and weakest correlated healthy regions. Beside confirming the brain effects of long enduring pain, these results provide a framework to study the effect of other chronic conditions over cortical function.
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Affiliation(s)
- Pablo Balenzuela
- Consejo Nacional de Investigaciones Científicas y Tecnológicas Buenos Aires, Argentina
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Baronchelli A, Pastor-Satorras R. Mean-field diffusive dynamics on weighted networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:011111. [PMID: 20866569 DOI: 10.1103/physreve.82.011111] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2009] [Revised: 02/11/2010] [Indexed: 05/29/2023]
Abstract
Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks. We also propose the concept of annealed weighted networks, in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process, pointing out a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions. Additionally, we show how to employ our formalism for more complex dynamics. Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for complex dynamics.
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Affiliation(s)
- Andrea Baronchelli
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain
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Lehnertz K, Bialonski S, Horstmann MT, Krug D, Rothkegel A, Staniek M, Wagner T. Synchronization phenomena in human epileptic brain networks. J Neurosci Methods 2009; 183:42-8. [DOI: 10.1016/j.jneumeth.2009.05.015] [Citation(s) in RCA: 166] [Impact Index Per Article: 11.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2009] [Revised: 05/19/2009] [Accepted: 05/20/2009] [Indexed: 01/21/2023]
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A dynamic network approach for the study of human phenotypes. PLoS Comput Biol 2009; 5:e1000353. [PMID: 19360091 PMCID: PMC2661364 DOI: 10.1371/journal.pcbi.1000353] [Citation(s) in RCA: 404] [Impact Index Per Article: 26.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2008] [Accepted: 03/09/2009] [Indexed: 12/11/2022] Open
Abstract
The use of networks to integrate different genetic, proteomic, and metabolic
datasets has been proposed as a viable path toward elucidating the origins of
specific diseases. Here we introduce a new phenotypic database summarizing
correlations obtained from the disease history of more than 30 million patients
in a Phenotypic Disease Network (PDN). We present evidence that the structure of
the PDN is relevant to the understanding of illness progression by showing that
(1) patients develop diseases close in the network to those they already have;
(2) the progression of disease along the links of the network is different for
patients of different genders and ethnicities; (3) patients diagnosed with
diseases which are more highly connected in the PDN tend to die sooner than
those affected by less connected diseases; and (4) diseases that tend to be
preceded by others in the PDN tend to be more connected than diseases that
precede other illnesses, and are associated with higher degrees of mortality.
Our findings show that disease progression can be represented and studied using
network methods, offering the potential to enhance our understanding of the
origin and evolution of human diseases. The dataset introduced here, released
concurrently with this publication, represents the largest relational phenotypic
resource publicly available to the research community. To help the understanding of physiological failures, diseases are defined as
specific sets of phenotypes affecting one or several physiological systems. Yet,
the complexity of biological systems implies that our working definitions of
diseases are careful discretizations of a complex phenotypic space. To reconcile
the discrete nature of diseases with the complexity of biological organisms, we
need to understand how diseases are connected, as connections between these
different discrete categories can be informative about the mechanisms causing
physiological failures. Here we introduce the Phenotypic Disease Network (PDN)
as a map summarizing phenotypic connections between diseases and show that
diseases progress preferentially along the links of this map. Furthermore, we
show that this progression is different for patients with different genders and
racial backgrounds and that patients affected by diseases that are connected to
many other diseases in the PDN tend to die sooner than those affected by less
connected diseases. Additionally, we have created a queryable online database
(http://hudine.neu.edu/) of the 18 different datasets generated
from the more than 31 million patients in this study. The disease associations
can be explored online or downloaded in bulk.
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Ahnert SE, Fink TMA. Clustering signatures classify directed networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036112. [PMID: 18851110 DOI: 10.1103/physreve.78.036112] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2007] [Revised: 06/04/2008] [Indexed: 05/26/2023]
Abstract
We use a clustering signature, based on a recently introduced generalization of the clustering coefficient to directed networks, to analyze 16 directed real-world networks of five different types: social networks, genetic transcription networks, word adjacency networks, food webs, and electric circuits. We show that these five classes of networks are cleanly separated in the space of clustering signatures due to the statistical properties of their local neighborhoods, demonstrating the usefulness of clustering signatures as a classifier of directed networks.
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Affiliation(s)
- S E Ahnert
- Theory of Condensed Matter, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
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Fagiolo G. Clustering in complex directed networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:026107. [PMID: 17930104 DOI: 10.1103/physreve.76.026107] [Citation(s) in RCA: 183] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2007] [Indexed: 05/25/2023]
Abstract
Many empirical networks display an inherent tendency to cluster, i.e., to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs, has been recently generalized to weighted, undirected networks. Here we extend the CC to the case of (binary and weighted) directed networks and we compute its expected value for random graphs. We distinguish between CCs that count all directed triangles in the graph (independently of the direction of their edges) and CCs that only consider particular types of directed triangles (e.g., cycles). The main concepts are illustrated by employing empirical data on world-trade flows.
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Affiliation(s)
- Giorgio Fagiolo
- Sant'Anna School of Advanced Studies, Laboratory of Economics and Management, Piazza Martiri della Libertà 33, I-56127 Pisa, Italy.
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