Networks with communities and clustering

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[1]  M. Serrano,et al.  Percolation and epidemic thresholds in clustered networks. , 2006, Physical review letters.

[2]  Kellen Petersen August.  Real Analysis , 2009 .

[3]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  R. Pastor-Satorras,et al.  Generation of uncorrelated random scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Alessandro Vespignani,et al.  Absence of epidemic threshold in scale-free networks with degree correlations. , 2002, Physical review letters.

[6]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[7]  Marián Boguñá,et al.  Clustering in complex networks. I. General formalism. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Falk Schreiber,et al.  MAVisto: a tool for the exploration of network motifs , 2005, Bioinform..

[9]  Catherine S. Greenhill,et al.  The switch Markov chain for sampling irregular graphs and digraphs , 2017, Theor. Comput. Sci..

[10]  A. Martin-Löf,et al.  Generating Simple Random Graphs with Prescribed Degree Distribution , 2006, 1509.06985.

[11]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Nikolaos Fountoulakis,et al.  The probability of connectivity in a hyperbolic model of complex networks , 2016, Random Struct. Algorithms.

[14]  Fan Chung Graham,et al.  On the Spectra of General Random Graphs , 2011, Electron. J. Comb..

[15]  Edward R. Scheinerman,et al.  On Random Intersection Graphs: The Subgraph Problem , 1999, Combinatorics, Probability and Computing.

[16]  Joshua R. Wang,et al.  Finding Four-Node Subgraphs in Triangle Time , 2015, SODA.

[17]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[18]  Fan Chung Graham,et al.  Concentration Inequalities and Martingale Inequalities: A Survey , 2006, Internet Math..

[19]  Remco van der Hofstad,et al.  Heavy-tailed configuration models at criticality , 2016, 1612.00650.

[20]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[21]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[22]  Jérôme Kunegis,et al.  KONECT: the Koblenz network collection , 2013, WWW.

[23]  Jure Leskovec,et al.  {SNAP Datasets}: {Stanford} Large Network Dataset Collection , 2014 .

[24]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[25]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[26]  Jure Leskovec,et al.  Higher-order clustering in networks , 2017, Physical review. E.

[27]  Wiseman,et al.  Lack of self-averaging in critical disordered systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Nikolaos Fountoulakis,et al.  Percolation on Sparse Random Graphs with Given Degree Sequence , 2007, Internet Math..

[29]  Deryk Osthus,et al.  Popularity based random graph models leading to a scale-free degree sequence , 2004, Discret. Math..

[30]  Antoine Allard,et al.  The geometric nature of weights in real complex networks , 2016, Nature Communications.

[31]  S. Shen-Orr,et al.  Superfamilies of Evolved and Designed Networks , 2004, Science.

[32]  Remco van der Hofstad,et al.  Switch chain mixing times and triangle counts in simple random graphs with given degrees , 2018, J. Complex Networks.

[33]  Anthony Bonato,et al.  A Spatial Web Graph Model with Local Influence Regions , 2007, Internet Math..

[34]  Marián Boguñá,et al.  Sustaining the Internet with Hyperbolic Mapping , 2010, Nature communications.

[35]  M E J Newman,et al.  Random graphs with clustering. , 2009, Physical review letters.

[36]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[37]  K. Kaski,et al.  Intensity and coherence of motifs in weighted complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[39]  A. Vázquez.  Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Luciano Pietronero,et al.  Absence of self-averaging and of homogeneity in the large-scale galaxy distribution , 2008, 0805.1132.

[41]  Valentas Kurauskas,et al.  Assortativity and clustering of sparse random intersection graphs , 2012, 1209.4675.

[42]  Yiming Yang,et al.  Introducing the Enron Corpus , 2004, CEAS.

[43]  Béla Bollobás,et al.  Mathematical results on scale‐free random graphs , 2005 .

[44]  J. Kertész,et al.  Structural transitions in scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[46]  Béla Bollobás,et al.  An old approach to the giant component problem , 2012, J. Comb. Theory, Ser. B.

[47]  Preetam Ghosh,et al.  Long-range degree correlations in complex networks , 2015 .

[48]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Remco van der Hofstad,et al.  Critical epidemics, random graphs, and Brownian motion with a parabolic drift , 2010, Advances in Applied Probability.

[50]  Ilkka Norros,et al.  On a conditionally Poissonian graph process , 2006, Advances in Applied Probability.

[51]  Liudmila Ostroumova,et al.  Global Clustering Coefficient in Scale-Free Networks , 2014, WAW.

[52]  Amin Saberi,et al.  Asymptotic behavior and distributional limits of preferential attachment graphs , 2014, 1401.2792.

[53]  Stefania Ottaviano,et al.  Epidemic outbreaks in two-scale community networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[55]  Nicolas Broutin,et al.  Scaling limits of random graph models at criticality: Universality and the basin of attraction of the Erdős-Rényi random graph , 2014, 1411.3417.

[56]  Pol Colomer-de-Simon,et al.  Deciphering the global organization of clustering in real complex networks , 2013, Scientific Reports.

[57]  Ilkka Norros,et al.  Large Cliques in a Power-Law Random Graph , 2009, Journal of Applied Probability.

[58]  Remco van der Hofstad,et al.  Critical window for the configuration model: finite third moment degrees , 2016, 1605.02868.

[59]  Oliver Riordan,et al.  The Phase Transition in the Configuration Model , 2011, Combinatorics, Probability and Computing.

[60]  David Aldous,et al.  Brownian excursions, critical random graphs and the multiplicative coalescent , 1997 .

[61]  Svante Janson,et al.  A new approach to the giant component problem , 2007, Random Struct. Algorithms.

[62]  Ulrik Brandes,et al.  What is network science? , 2013, Network Science.

[63]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[64]  R. Hofstad,et al.  Universality for critical heavy-tailed network models: Metric structure of maximal components , 2017, Electronic Journal of Probability.

[65]  Remco van der Hofstad,et al.  Novel scaling limits for critical inhomogeneous random graphs , 2009, 0909.1472.

[66]  Shankar Bhamidi,et al.  Continuum limit of critical inhomogeneous random graphs , 2014, 1404.4118.

[67]  Piet Van Mieghem,et al.  Distances in random graphs with finite variance degrees , 2005, Random Struct. Algorithms.

[68]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[69]  Johan van Leeuwaarden,et al.  Giant component sizes in scale-free networks with power-law degrees and cutoffs , 2015, ArXiv.

[70]  Krishna P. Gummadi,et al.  On the evolution of user interaction in Facebook , 2009, WOSN '09.

[71]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[72]  Peter Bailey,et al.  Engineering a multi-purpose test collection for Web retrieval experiments , 2003, Inf. Process. Manag..

[73]  Bruce A. Reed,et al.  The Size of the Giant Component of a Random Graph with a Given Degree Sequence , 1998, Combinatorics, Probability and Computing.

[74]  Jure Leskovec,et al.  Defining and evaluating network communities based on ground-truth , 2012, Knowledge and Information Systems.

[75]  F. Chung,et al.  The average distances in random graphs with given expected degrees , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[76]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[77]  Chiara Orsini,et al.  Quantifying randomness in real networks , 2015, Nature Communications.

[78]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[79]  Aaron Clauset,et al.  Scale-free networks are rare , 2018, Nature Communications.

[80]  Harris,et al.  Absence of Self-Averaging and Universal Fluctuations in Random Systems near Critical Points. , 1996, Physical review letters.

[81]  L. Russo.  On the critical percolation probabilities , 1981 .

[82]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[83]  Pu Gao,et al.  Uniform generation of random graphs with power-law degree sequences , 2017, SODA.

[84]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[85]  F. Ball,et al.  Analysis of a stochastic SIR epidemic on a random network incorporating household structure. , 2010, Mathematical biosciences.

[86]  Svante Janson.  The Probability That a Random Multigraph is Simple , 2009, Comb. Probab. Comput..

[87]  Jure Leskovec,et al.  Higher-order organization of complex networks , 2016, Science.

[88]  János Kertész,et al.  Clustering in complex networks , 2004 .

[89]  R. Arratia,et al.  How likely is an i.i.d. degree sequence to be graphical , 2005, math/0504096.

[90]  Victor M. Preciado,et al.  Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees , 2015, IEEE Transactions on Network Science and Engineering.

[91]  N. Litvak,et al.  Limit theorems for assortativity and clustering in the configuration model with scale-free degrees , 2017 .

[92]  S. N. Dorogovtsev.  Clustering of correlated networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[93]  Emilie Coupechoux,et al.  How Clustering Affects Epidemics in Random Networks , 2012, Advances in Applied Probability.

[94]  Z N Oltvai,et al.  Evolutionary conservation of motif constituents in the yeast protein interaction network , 2003, Nature Genetics.

[95]  Angel Sánchez,et al.  Mesoscopic Structure Conditions the Emergence of Cooperation on Social Networks , 2006, PloS one.

[96]  L. Stone,et al.  Generating uniformly distributed random networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[97]  Jure Leskovec,et al.  Empirical comparison of algorithms for network community detection , 2010, WWW '10.

[98]  M. Newman,et al.  On the uniform generation of random graphs with prescribed degree sequences , 2003, cond-mat/0312028.

[99]  Liudmila Ostroumova,et al.  Generalized Preferential Attachment: Tunable Power-Law Degree Distribution and Clustering Coefficient , 2012, WAW.

[100]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[101]  Yuval Shavitt,et al.  RAGE - A rapid graphlet enumerator for large networks , 2012, Comput. Networks.

[102]  Chao Gao,et al.  Testing Network Structure Using Relations Between Small Subgraph Probabilities , 2017, ArXiv.

[103]  Charalampos E. Tsourakakis.  Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[104]  Ove Frank,et al.  MOMENT PROPERTIES OF SUBGRAPH COUNTS IN STOCHASTIC GRAPHS , 1979 .

[105]  Alessandro Vespignani,et al.  Large-scale topological and dynamical properties of the Internet. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[106]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[107]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[108]  Béla Bollobás,et al.  The phase transition in inhomogeneous random graphs , 2007, Random Struct. Algorithms.

[109]  Piotr Sankowski,et al.  Algorithmic Complexity of Power Law Networks , 2015, SODA.

[110]  Kristina Lerman,et al.  Degree Correlations Amplify the Growth of Cascades in Networks , 2018, Physical review. E.

[111]  Peter Morters,et al.  Spatial preferential attachment networks: Power laws and clustering coefficients , 2012, 1210.3830.

[112]  S. Hakimi.  On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph. I , 1962 .

[113]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[114]  S. Taheri,et al.  Distributed maximal independent set on inhomogeneous random graphs , 2017, 2017 2nd Conference on Swarm Intelligence and Evolutionary Computation (CSIEC).

[115]  Adrien Joseph,et al.  The component sizes of a critical random graph with given degree sequence , 2010, 1012.2352.

[116]  Liudmila Ostroumova,et al.  Local Clustering Coefficient in Generalized Preferential Attachment Models , 2015, WAW.

[117]  K. Sneppen,et al.  Detection of topological patterns in complex networks: correlation profile of the internet , 2002, cond-mat/0205379.

[118]  Y. Moreno,et al.  Resilience to damage of graphs with degree correlations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[119]  Remco van der Hofstad,et al.  Universality for first passage percolation on sparse random graphs , 2012, 1210.6839.

[120]  S. N. Dorogovtsev,et al.  Pseudofractal scale-free web. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[121]  R. Pastor-Satorras,et al.  Class of correlated random networks with hidden variables. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[122]  Marián Boguñá,et al.  Clustering in complex networks. II. Percolation properties. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[123]  Christos Faloutsos,et al.  Dynamics of large networks , 2008 .

[124]  Lisa Singh,et al.  Exploring community structure in biological networks with random graphs , 2013, BMC Bioinformatics.

[125]  Tobias Friedrich,et al.  Cliques in hyperbolic random graphs , 2015, INFOCOM.

[126]  Massimo Ostilli.  Fluctuation analysis in complex networks modeled by hidden-variable models: necessity of a large cutoff in hidden-variable models. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[127]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[128]  Svante Janson,et al.  On percolation in random graphs with given vertex degrees , 2008, 0804.1656.

[129]  Sebastian Wernicke,et al.  FANMOD: a tool for fast network motif detection , 2006, Bioinform..

[130]  Guido Caldarelli,et al.  Hyperbolicity Measures "Democracy" in Real-World Networks , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[131]  V. Eguíluz,et al.  Growing scale-free networks with small-world behavior. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[132]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[133]  Nikolaos Fountoulakis,et al.  On the Largest Component of a Hyperbolic Model of Complex Networks , 2015, Electron. J. Comb..

[134]  Remco van der Hofstad,et al.  Random Graphs and Complex Networks , 2016, Cambridge Series in Statistical and Probabilistic Mathematics.

[135]  James P Gleeson,et al.  Cascades on correlated and modular random networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[136]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[137]  M. Newman,et al.  Statistical mechanics of networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[138]  Moupriya Das,et al.  Self-Averaging Fluctuations in the Chaoticity of Simple Fluids. , 2017, Physical review letters.

[139]  Jakub W. Pachocki,et al.  Scalable Motif-aware Graph Clustering , 2016, WWW.

[140]  Tobias Friedrich,et al.  Parameterized clique on inhomogeneous random graphs , 2015, Discret. Appl. Math..

[141]  Jerzy Szymanski.  Concentration of vertex degrees in a scale-free random graph process , 2005, Random Struct. Algorithms.

[142]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[143]  Alessandro Vespignani,et al.  Correlations in complex networks , 2007 .

[144]  Svante Janson,et al.  Susceptibility in Inhomogeneous Random Graphs , 2009, Electron. J. Comb..

[145]  Pim van der Hoorn,et al.  Upper Bounds for Number of Removed Edges in the Erased Configuration Model , 2015, WAW.

[146]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[147]  Stephanie Forrest,et al.  Email networks and the spread of computer viruses. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[148]  R. Pastor-Satorras,et al.  Langevin approach for the dynamics of the contact process on annealed scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[149]  D. Bu,et al.  Topological structure analysis of the protein-protein interaction network in budding yeast. , 2003, Nucleic acids research.

[150]  Antoine Allard,et al.  The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013 , 2015, Scientific Reports.

[151]  Wen-Xu Wang,et al.  Collective synchronization induced by epidemic dynamics on complex networks with communities. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[152]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[153]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[154]  Pim van der Hoorn,et al.  Average nearest neighbor degrees in scale-free networks , 2017, Internet Math..

[155]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[156]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[157]  Nikolaos Fountoulakis,et al.  University of Birmingham Clustering and the hyperbolic geometry of complex networks , 2015 .

[158]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[159]  M. Newman,et al.  Origin of degree correlations in the Internet and other networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[160]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[161]  U. Alon.  Network motifs: theory and experimental approaches , 2007, Nature Reviews Genetics.

[162]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[163]  Filippo Menczer,et al.  Virality Prediction and Community Structure in Social Networks , 2013, Scientific Reports.

[164]  Remco van der Hofstad,et al.  Distances in Random Graphs with Finite Mean and Infinite Variance Degrees , 2005, math/0502581.

[165]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[166]  Diego Garlaschelli,et al.  Analytical maximum-likelihood method to detect patterns in real networks , 2011, 1103.0701.

[167]  S. Redner.  How popular is your paper? An empirical study of the citation distribution , 1998, cond-mat/9804163.

[168]  Liudmila Ostroumova,et al.  General results on preferential attachment and clustering coefficient , 2017, Optim. Lett..

[169]  G. Caldarelli,et al.  Assortative model for social networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[170]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[171]  Remco van der Hofstad,et al.  Universality for the Distance in Finite Variance Random Graphs , 2006 .

[172]  Kevin E. Bassler,et al.  Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence , 2010, PloS one.

[173]  Ralph Keusch,et al.  Sampling Geometric Inhomogeneous Random Graphs in Linear Time , 2017, ESA.

[174]  Nicole Eggemann,et al.  The clustering coefficient of a scale-free random graph , 2008, Discret. Appl. Math..

[175]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[176]  Willemien Kets,et al.  RANDOM INTERSECTION GRAPHS WITH TUNABLE DEGREE DISTRIBUTION AND CLUSTERING , 2009, Probability in the Engineering and Informational Sciences.

[177]  Bambi Hu,et al.  Epidemic spreading in community networks , 2005 .

[178]  A. Arenas,et al.  Models of social networks based on social distance attachment. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[179]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[180]  P. Trapman,et al.  On analytical approaches to epidemics on networks. , 2007, Theoretical population biology.

[181]  Leonid Pastur,et al.  Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model , 1991 .

[182]  Mason A. Porter,et al.  Communities in Networks , 2009, ArXiv.

[183]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[184]  G. I. Kustova,et al.  From the author , 2019, Automatic Documentation and Mathematical Linguistics.

[185]  Christiane Fellbaum,et al.  Book Reviews: WordNet: An Electronic Lexical Database , 1999, CL.

[186]  Tatyana S. Turova,et al.  Diffusion approximation for the components in critical inhomogeneous random graphs of rank 1. , 2009, Random Struct. Algorithms.

[187]  Uri Alon,et al.  Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs , 2004, Bioinform..

[188]  Nelly Litvak,et al.  Uncovering disassortativity in large scale-free networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[189]  Svante Janson,et al.  A simple solution to the k-core problem , 2007, Random Struct. Algorithms.

[190]  Luca Gugelmann,et al.  Random Hyperbolic Graphs: Degree Sequence and Clustering , 2012, ArXiv.

[191]  Fan Chung Graham,et al.  The Spectra of Random Graphs with Given Expected Degrees , 2004, Internet Math..

[192]  F. Schreiber,et al.  MODA: an efficient algorithm for network motif discovery in biological networks. , 2009, Genes & genetic systems.

[193]  Sergey Melnik,et al.  How clustering affects the bond percolation threshold in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[194]  Christos Faloutsos,et al.  R-MAT: A Recursive Model for Graph Mining , 2004, SDM.

[195]  P. Groeneboom.  Brownian motion with a parabolic drift and airy functions , 1989 .

[196]  Remco van der Hofstad,et al.  Degree-Degree Dependencies in Random Graphs with Heavy-Tailed Degrees , 2014, Internet Math..

[197]  Guilin Qi,et al.  Zhishi.me - Weaving Chinese Linking Open Data , 2011, SEMWEB.

[198]  Mark E. J. Newman,et al.  Random graphs containing arbitrary distributions of subgraphs , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[199]  Amin Vahdat,et al.  Hyperbolic Geometry of Complex Networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[200]  Frank Ball,et al.  Threshold behaviour and final outcome of an epidemic on a random network with household structure , 2008, Advances in Applied Probability.

[201]  Wei Huang,et al.  Epidemic spreading in scale-free networks with community structure , 2007 .

[202]  Marián Boguñá,et al.  Network Cosmology , 2012, Scientific Reports.

[203]  Béla Bollobás,et al.  A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs , 1980, Eur. J. Comb..

[204]  Jure Leskovec,et al.  Friendship and mobility: user movement in location-based social networks , 2011, KDD.

[205]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[206]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[207]  Johan van Leeuwaarden,et al.  Scaling limits for critical inhomogeneous random graphs with finite third moments , 2009, 0907.4279.

[208]  Stéphane Robin,et al.  Network motifs : mean and variance for the count , 2006 .

[209]  Pol Colomer-de-Simon,et al.  Clustering of random scale-free networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[210]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[211]  Marcel Salathé,et al.  Dynamics and Control of Diseases in Networks with Community Structure , 2010, PLoS Comput. Biol..

[212]  Matthieu Latapy,et al.  Efficient and simple generation of random simple connected graphs with prescribed degree sequence , 2005, J. Complex Networks.

[213]  Joshua A. Grochow,et al.  Network Motif Discovery Using Subgraph Enumeration and Symmetry-Breaking , 2007, RECOMB.

[214]  Franck Picard,et al.  Assessing the Exceptionality of Network Motifs , 2007, J. Comput. Biol..

[215]  James P Gleeson,et al.  Bond percolation on a class of clustered random networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[216]  P. Van Mieghem,et al.  Influence of assortativity and degree-preserving rewiring on the spectra of networks , 2010 .

[217]  Martin Rosvall,et al.  Maps of random walks on complex networks reveal community structure , 2007, Proceedings of the National Academy of Sciences.

[218]  L. Prokhorenkova,et al.  Local clustering coefficients in preferential attachment models , 2016 .

[219]  Yuval Peres,et al.  Critical percolation on random regular graphs , 2007, Random Struct. Algorithms.

[220]  Eytan Domany,et al.  Finite-Size Scaling and Lack of Self-Averaging in Critical Disordered Systems , 1998 .

[221]  Zonghua Liu,et al.  How community structure influences epidemic spread in social networks , 2008 .

[222]  Mindaugas Bloznelis,et al.  Degree and clustering coefficient in sparse random intersection graphs , 2013, 1303.3388.

[223]  Remco van der Hofstad,et al.  Diameters in Preferential Attachment Models , 2007, 0705.4153.

[224]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[225]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[226]  Thomas Bläsius,et al.  Efficient Shortest Paths in Scale-Free Networks with Underlying Hyperbolic Geometry , 2018, ICALP.

[227]  Tobias Friedrich,et al.  On the average-case complexity of parameterized clique , 2015, Theor. Comput. Sci..