Complex Networks

21 Oct 2024 11:28

Having written a whole pop-sci article about these things (see below), I won't explain them at all here. This notebook is more of a placeholder than usual.

Stuff I should learn more about: structural complexity measures for graphs and ensembles of random graphs; Gibbs measures for equilibrium ensembles of graphs; Markovian graphs. Why does it seem like the edges are the important random variables, rather than the nodes?

Data analysis in general and community discovery in particular get their own notebooks. So does the connection between network topology and synchronization. The "homophily or influence?" problem. . Graph sampling algorithms, i.e., procedures for efficiently generating graphs with specified properties. Spectral properties.

Reka Albert and Albert-László Barabási, "Statistical Mechanics of Complex Networks," Reviews of Modern Physics 74 (2002): 47, cond-mat/0106096
Alain Barrat, Marc Barthelemy and Alessandro Vespignani, Dynamical Processes on Complex Networks
Rick Durrett, Random Graph Dynamics
Mark E. J. Newman
- "The structure and function of complex networks," cond-mat/0303516
- Networks: An Introduction [A.k.a. "the big black book"]
Mark Newman, Albert-László Barabási, and Duncan Watts (eds.), "The Structure and Dynamics of Networks [Collects many of the most important papers from the pre-history of the 1950s up through the early 2000s]
Duncan Watts
- Small Worlds
- "The 'New' Science of Networks", Annual Review of Sociology 30 (2004): 243--270

Lada A. Adamic, R. M. Lukose, A. R. Puniyani and Bernardo A. Huberman, "Search in Power-Law Networks," cs.NI/0103016
Yael Artzy-Randrup, Sarel J. Fleishman, Nir Ben-Tal and Lewi Stone, "Comment on 'Network Motifs: Simple Building Blocks of Complex Networks' and 'Superfamilies of Evolved and Designed Networks'", Science 305 (2004): 1107
M. Argollo de Menezes and A.-L. Barabási, "Fluctuations in network dynamics", Physical Review Letters 92 (2004): 028701, cond-mat/0306304
Fan Chung and Linyuan Lu, Complex Graphs and Networks
Aaron Clauset and Cristopher Moore, "How Do Networks Become Navigable?", cond-mat/0309415
Santo Fortunato, Alessandro Flammini, Filippo Menczer, "Scale-free network growth by ranking", cond-mat/0602081
Geoffrey Grimmett, Probability on Graphs: Random Processes on Graphs and Lattices
Vamsi Kalapala, Vishal Sanwalani, Aaron Clauset, and Cristopher Moore, "Scale Invariance in Road Networks", physics/0510198 = Physical Review E 73 (2006): 026130
Eben Kenah and James Robins, "Second look at the spread of epidemics on networks", q-bio.QM/0610057
Raya Khanin and Ernst Wit, "How Scale-Free Are Biological Networks?", Journal of Computational Biology 13 (2006): 810--818 [Ans.: not very scale-free at all.]
Evelyn Fox Keller, "Revisiting 'scale-free' networks", BioEssays 27 (2005): 1060--1068
Judith Kleinfeld, "Could It Be a Big World After All? What the Milgram Papers in the Yale Archive Reveal About the Original Small World Study" [Six degrees of separation, for the general population, is quite unsupported empirically. Of course it works for other kinds of networks, e.g., people in a common profession, or participating in a common institution; but that's different. Preprint.]
Arnon Levy and William Bechtel, "Abstraction and the Organization of Mechanisms", Philosophy of Science 80 (2013): 241--261
Adrián López García de Lomana, Qasim K. Beg, G. de Fabritiis and Jordi Villà-Freixa, "Statistical Analysis of Global Connectivity and Activity Distributions in Cellular Networks", Journal of Computational Biology 17 (2010): 869--878, arxiv:1004.3138
Cristopher Moore, Gourab Ghoshal and Mark E. J. Newman, "Exact solutions for models of evolving networks with addition and deletion of nodes", cond-mat/0604069 = Physical Review E 74 (2006): 036121 [The most amusing result is that in a network where new nodes form links by preferential attachment, but the size of addition and deletion of nodes exactly balance, the degree distribution follows a stretched exponential (Weibull) distribution, rather than a power law. This suggests, as they note, that the current exponent for the web should increase as its growth-rate slows. "A sufficiently large exponent would make the distribution indistinguishable experimentally from an exponential or stretched exponential distribution, although we do not realistically anticipate seeing behaivor of this type any time in the near future."]
Mark E. J. Newman
- "Analysis of weighted networks", cond-mat/0407503
- "Assortative mixing in networks," cond-mat/0205405
- "Clustering and Preferential Attachment in Growing Networks," cond-mat/0104029
- "Ego-centered networks and the ripple effect," cond-mat/0111070
- "Exact solutions of epidemic models on networks," cond-mat/0201433
- "Properties of highly clustered networks," cond-mat/0303183
- "Random graphs as models of networks," cond-mat/0202208
- "The spread of epidemic disease on networks," cond-mat/0205009
Robin Pemantle and Brian Skyrms, "Network formation by reinforcement learning: the long and medium run", math.PR/0404106 = Mathematical Social Sciences 48 (2004): 315--327
David M. Pennock et al., "Winners don't take all: Characterizing the competition for links on the web", Proceedings of the National Academy of Sciences 99 (2002): 5207--5211
Bo Söderberg, "A General Formalism for Inhomogeneous Random Graphs", cond-mat/0211063 [A re-invention of block models, but a clear one]
Ricard V. Sole, Romualdo Pastor-Satorras, Eric Smith and Thomas B. Kepler, "A model of large-scale proteome evolution," Advances in Complex Systems 5 (2002): 43ff = cond-mat/0207311
R. Vilela Mendes, "Tools for Network Dynamics", International Journal of Bifurcations and Chaos 15 (2005): 1185--1213 [There is, admittedly, something of a bias here towards tools devised by Vilela Mendes and collaborators, but I daresay I'd do the same were I to write such a piece. More importantly, they're good stuff.]
Duncan J. Watts, Peter S. Dodds and Mark E. J. Newman, "Identity and Search in Social Networks," Science 296 (2002): 1302--1305, cond-mat/0205383
Duncan Watts and Steven Strogatz, "Collective Dynamics of 'Small-World' Networks," Nature 393 (1998): 440--442

Kartik Anand and Ginestra Bianconi, "Entropy measures for networks: Toward an information theory of complex topologies", Physical Review E 80 (2009): 045102 = arxiv:0907.1514 [Basic calculations comparing the log of the number of graphs compatible with given macroscopic properties (the Boltzmann entropy; weirdly called the Gibbs entropy here) with the Shannon entropy of the distribution of graphs where those properties hold in the mean (which is the actual Gibbs entropy in statistical mechanics). These are not equivalent, which evidently causes some distress to the authors; no mention of the literature on ensemble in-equivalence and its roots (see e.g. the references here) or to the vast literature on exponential families of random graphs (i.e., ensembles of maximum Shannon entropy).]

CRS, "Growth, Form, Function, Crashes," Santa Fe Institute Bulletin 15:2 (2000) [On-line]
CRS, "Networks and Netwars"

Juan A. Acebrón, Sergi Lozano, and Alex Arenas, "Amplified Signal Response in Scale-Free Networks by Collaborative Signaling", Physical Review Letters 99 (2007): 128701
Reka Albert, Istvan Albert and Gary L. Nakarad, "Structural Vulnerability of the North American Power Grid", cond-mat/0401084
David J. Aldous, "A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance", cond-mat/0304701
Alberto Aleta and Yamir Moreno, "Multilayer Networks in a Nutshell", Annual Review of Condensed Matter Physics 10 (2019): 45--62
Giacomo Aletti, Irene Crimaldi, Andrea Ghiglietti, "Networks of reinforced stochastic processes: a complete description of the first-order asymptotics", arxiv:2206.07514
Eivind Almaas and A.-L. Barabási, "Power laws in biological networks", q-bio.MN/0401010
Nahuel Almeira, Orlando Vito Billoni, Juan Ignacio Perotti, "Scaling of percolation transitions on Erdös-Rényi networks under centrality-based attacks", arxiv:1907.13190
Tanya Araujo, R. Vilela Mendes and Joao Seixas, "A dynamical characterization of the small world phase," cond-mat/0204573
M. Argollo de Menezes and A.-L. Barabási, "Separating internal and external dynamics of complex systems", cond-mat/0406421
K. B. Athreya, A. P. Ghosh, S. Sethuraman, "Growth of preferential attachment random graphs via continuous-time branching processes", math.PR/0701649
J. P. Bagrow, E. M. Bollt, J. D. Skufca, D. ben-Avraham, "Portraits of Complex Networks", cond-mat/0703470
Duygu Balcan and Ayse Erzan, "Content-based networks: A pedagogical overview", Chaos 17 (2007): 026108
Pierre Baldi et al., Modeling the Internet and the Web: Probabilistic Methods and Algorithms
Dina Barak-Pelleg, Daniel Berend, J.C. Saunders, "A Model of Random Industrial SAT", arxiv:1908.00089
L. Barnett, C. L. Buckley, S. Bullock, "A Graph Theoretic Interpretation of Neural Complexity", arxiv:1011.5334
F. Barra and P. Gaspard, "Classical Dynamics on Graphs," nlin.CD/0011045
Alain Barrat, Marc Barthelemy and Alessandro Vespignani
- "Weighted evolving networks: coupling topology and weights dynamics", cond-mat/0401057 = PRL 92 (2004): 228701
- "Modeling the evolution of weighted networks", cond-mat/0406238
- "The effects of spatial constraints on the evolution of weighted complex networks", physics/0504029
Yaneer Bar-Yam and Irving R. Epstein, "Response of complex networks to stimuli", Proceedings of the National Academy of Sciences 10.1073/pnas.0400673101
E. Ben-Naim and P.L. Krapivsky, "Addition-Deletion Networks", cond-mat/0703636
Eli Ben-Naim and Zoltan Toroczkai (eds.), Complex Networks
N. Berger, C. Borgs, J. T. Chayes, R. M. D'Souza and R. D. Kleinberg
- "Competition-Induced Preferential Attachment", cond-mat/0402268 [Short version]
- "Degree Distribution of Competition-Induced Preferential Attachment Graphs", cond-mat/0502205 [Version with proofs]
Cristoly Biely and Stefan Thurner, "Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?", cond-mat/0507670
Ginestra Bianconi, "A statistical mechanics approach for scale-free networks and finite-scale networks", cond-mat/0703191
Ginestra Bianconi and Matteo Marsili, "Clogging and self-organized criticality in complex networks", Physical Review E 70 (2004): 035105(R), cond-mat/0312537
Sven Bilke and C. Peterson, "Topological Properties of Citation and Metabolic Networks", cond-mat/0103361
Sven Bilke and F. Sjunnesson, "Stability of the Kauffman Model," cond-mat/0107035
Golnoosh Bizhani, Peter Grassberger, and Maya Paczuski, "Random sequential renormalization and agglomerative percolation in networks: Application to Erdos-Renyi and scale-free graphs", Physical Review E 84 (2011): 066111
Philippe Blanchard and T. Krueger, "The `Cameo Principle' and the Origin of Scale-Free Graphs in Social Networks," cond-mat/0302611
Christian Borgs, Jennifer Chayes, Constantinos Daskalakis, Sebastien Roch, "First to Market is not Everything: an Analysis of Preferential Attachment with Fitness", arxiv:0710.4982 ["rigorous analysis of preferential attachment with fitness ... Depending on the shape of the fitness distribution, we observe three distinct phases: a first-mover-advantage phase, a fit-get-richer phase and an innovation-pays-off phase."]
Stefan Bornholdt and H. G. Schuster (eds.), Handbook of Graphs and Networks: From the Genome to the Internet
Romulus Breban, Raffaele Vardavas and Sally Blower, "Linking population-level models with growing networks: A class of epidemic models", Physical Review E 72 (2005): 046110
Markus Brede and Sitabhra Sinha, "Assortative mixing by degree makes a network more unstable", cond-mat/0507710
Tom Britton and Mathias Lindholm, "Dynamic Random Networks in Dynamic Populations", Journal of Statistical Physics 139 (2010): 518--535
Dirk Brockmann and Dirk Helbing, "The Hidden Geometry of Complex, Network-Driven Contagion Phenomena", Science 342 (2013): 1337--1342
Z. Burda, J. D. Correia and Andre Krzywicki, "Statistical ensemble of scale-free random graphs," cond-mat/0104155
Guido Caldarelli, Scale-Free Networks: Complex Webs in Nature and Technology [Publisher's version ]
Guido Caldarelli and Alessandro Vespignani (eds.), Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science Callaway, Hopcroft, Kleinberg, Newman and Strogatz, "Are Randomly Grown Graphs Really Random?" cond-mat/0104546
J. Camacho, R. Guimera and L. A. N. Amaral, "Robust Patterns in Food Web Structure," cond-mat/0103114
Andrea Capocci, G. Caldarelli and P. De Los Rios, "Quantitative description and modeling of real networks," cond-mat/0206336
Damon Centola, "Failure in Complex Social Networks", Journal of Mathematical Sociology 33 (2009): 654--68
Sourav Chatterjee and Partha S. Dey, "Applications of Stein's method for concentration inequalities", Annals of Probability 38 (2010): 2443--2485, arxiv:0906.1034
Mario Chavez, Miguel Valencia, Vito Latora, Jacques Martinerie, "Complex networks: new trends for the analysis of brain connectivity", arxiv:1002.0697
Hanshuang Chen, Feng Huang, Guofeng Li, Haifeng Zhang, "Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks", arxiv:1907.13330
Jihyeok Choi and Sunder Sethuraman, "Large deviations for the degree structure in preferential attachment schemes", Annals of Applied Probability 23 (2013): 722--763
Giulio Cimini, Tiziano Squartini, Fabio Saracco, Diego Garlaschelli, Andrea Gabrielli, Guido Caldarelli, "The Statistical Physics of Real-World Networks", arxiv:1810.05095
L. Cisneros, J. Jimenez, M. G. Cosenza, and A. Parravano, "Information transfer and nontrivial collective behavior in chaotic coupled map networks," nlin.CD/0202010
Jens Christian Claussen, "Offdiagonal Complexity: A computationally quick complexity measure for graphs and networks", q-bio.MN/0410024
Mauro Copelli, Paulo R. A. Campos, "Excitable Scale Free Networks", q-bio.NC/0703004
M. Copelli, R. M. Zorzenon dos Santos and J. S. Sa Martins, "Emergence of Hierarchy on a Network of Complementary Agents," cond-mat/0110350
Francois Coppex, Michel Droz and Adam Lipowski, "Extinction dynamics of Lotka-Volterra ecosystems on evolving networks", q-bio.PE/0312030
Luciano da F. Costa, Francisco A. Rodrigues, Gonzalo Travieso and P. R. Villas Boas, "Characterization of complex networks: A survey of measurements", cond-mat/0505185
Luciano da F. Costa and Olaf Sporns, "Hierarchical Features of Large-Scale Cortical Connectivity", q-bio.NC/0508007
R. W. R. Darling and J. R. Norris, "Structure of large random hypergraphs", Annals of Applied Probability 15 (2005): 125--152, math.PR/0503460
M. A. M. de Aguiar and Y. Bar-Yam, "Spectral Analysis and the Dynamic Response of Complex Networks", nlin.AO/0306043
Charo I. Del Genio, Thilo Gross, and Kevin E. Bassler, "All Scale-Free Networks Are Sparse", Physical Review Letters 107 (2011): 178701
Peter Dodds and Duncan Watts, "Universal behavior in a generalized model of contagion", cond-mat/0403699
S. N. Dorogovtsev
- "Renormalization group for evolving networks," cond-mat/0301008
- Lectures on Complex Networks [2010]
S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes
- "Correlations in interacting systems with a network topology", cond-mat/0506002 [Claims to have an argument establishing "dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions", such that in the large size limit "only the pair correlations between the nearest neighbors are observable". I'm skeptical that they could have an adequately general argument to really establish this, but I'll read it before coming to any conclusion.]
- "Ising Model on Networks with an Arbitrary Distribution of Connections," cond-mat/0203227
- "Pseudofractal Scale-free Web," cond-mat/0112143
S. N. Dorogovtsev and J. F. F. Mendes
- "Comment on `Breakdown of the Internet under Intentional Attack'," cond-mat/0109083
- "Evolution of random networks," cond-mat/0106144
- Evolution of Networks: From Biological Nets to the Internet and WWW [2003]
- The Nature of Complex Networks [2022]
S. N. Dorogovtsev, J. F. F. Mendes and A. N. Samukhin
- "Anomalous percolating properties of growing networks," cond-mat/0106141
- "Giant strongly connected component of directed networks," cond-mat/0103629
Raissa M. D'Souza, Soumen Roy, "Network Growth with Feedback", arxiv:0805.4020
Holger Ebel, Lutz-Ingo Mielsch and Stefan Bornholdt, "Scale-free topology of e-mail networks," cond-mat/0201476
Jean-Pierre Eckmann and Elisha Moses, "Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web," cond-mat/0110338
Victor M. Eguiluz, Dante R. Chialvo, Guillermo A. Cecchi, Marwan Baliki and A. Vania Apkarian, "Scale-free brain functional networks", Physical Review Letters 94 (2005): 018102, cond-mat/0309092
Ernesto Estrada, The Structure of Complex Networks: Theory and Applications
Ernesto Estrada and Juan A. Rodriguez-Velazquez
- "Complex Networks as Hypergraphs", physics/0505137
- "Subgraph Centrality in Complex Networks", cond-mat/0504730
Ying Fan, Menghui Li, Jiawei Chen, Liang Gao, Zengru Di and Jinshan Wu, "Network of Econophysicists: a weighted network to investigate the development of Econophysics", cond-mat/0401054
Nadia Farid and Kim Christensen, "Evolving networks through deletion and duplication", physics/0609172
Iles Farkas, I. Derenyi, H. Jeong, Z. Neda, Z. N. Oltvai, E. Ravasz, A. Schubert, Albert-László Barabási and Tamas Vicsek, "Networks in life: Scaling properties and eigenvalue spectra," cond-mat/0303106
Iles Farkas, I. Derenyi, G. Palla, and T. Vicsek, "Equilibrium statistical mechanics of network structures", cond-mat/0401640
Iles J. Farkas, H. Jeong, Tamas Vicsek, Albert-László Barabási and Z. N. Oltvai, "The topology of the transcription regulatory network in the yeast, S. cerevisiae," cond-mat/0205181
Trevor Fenner, Mark Levene and George Loizou, "A Model for Collaboration Networks Giving Rise to a Power Law Distribution with an Exponential Cutoff", physics/0503184
Ramon Ferrer i Cancho and Ricard V. Sole
- "The Small-World of Human Language," SFI Working Paper 01-03-016
- "Optimization in complex networks," cond-mat/01 1222
Agata Fronczak, Piotr Fronczak, Janusz A. Holyst, "Fluctuation-dissipation relations for complex networks", cond-mat/0509042, Physical Review E 73 (2006): 016108 [The fluctuations are fluctuations of the network structure within an equilibrium ensemble. This is an interesting idea, though I'd need to not just read it but also think carefully before deciding whether it really applies to actual networks]
Xinchu Fu, Michael Small, Guanrong Chen, Propagation Dynamics on Complex Networks: Models, Methods and Stability Analysis
Diego Garlaschelli, Sebastian E. Ahnert, Thomas M. A. Fink and Guido Caldarelli, "Temperature in complex networks", cond-mat/0606805
Kwang-Il Goh, B. Kahng, and D. Kim, "Spectra and eigenvectors of scale-free networks," cond-mat/0103337
Kwang-Il Goh, E. S. Oh, H. Jeong, B. Kahng, and D. Kim, "Classification of scale free networks," cond-mat/0205232
Michael Golosovsky and Sorin Solomon, "Stochastic Dynamical Model of a Growing Citation Network Based on a Self-Exciting Point Process", Physical Review Letters 109 (2012): 098701
A. V. Goltsev, S. N. Dorogovtsev and J. F. F. Mendes, "Critical Phenomena in Networks," cond-mat/0204596
Jesus Gomez-Gardenes and Vito Latora, "Entropy rate of diffusion processes on complex networks", Physical Review E 78 (2008): 065102
Sean P. Gorman, Rajendra G. Kulkarni, Laurie A. Schintler and Roger R. Stough, "A Predator Prey Approach to Diversity Based Defenses in Heterogeneous Networks", cond-mat/0401017
Andreas Grönlund, "The difference in directed structure of Neural and Transcriptional Regulation Networks", cond-mat/0406268
Andreas Grönlund, Kim Sneppen and Petter Minnhagen, "Correlations in Networks Associated to Preferential Growth", cond-mat/0401537
Thilo Gross and Bernd Blasius, "Adaptive Coevolutionary Networks -- A Review", arxiv:0709.1858
Jean-Loup Guillaume and Matthieu Latap, "A Realistic Model for Complex Networks," cond-mat/0307095
Roger Guimera, A. Arenas and A. Diaz-Guilera, "Communication and optimal hierarchical networks," cond-mat/0103112
Aric Hagberg, Pieter J. Swart and Daniel A. Schult, "Designing threshold networks with given structural and dynamical properties", Physical Review E 74 (2006): 056116
Laurent Hébert-Dufresne, Pierre-André Noël, Vincent Marceau, Antoine Allard, Louis J. Dubé, "Propagation dynamics on networks featuring complex topologies", arxiv:1005.1397
Adriano de Jesus Holanda, Ivan Torres Pisa, Osame Kinouchi, Alexandre Souto Martinez and Evandro Eduardo Seron Ruiz, "Thesaurus as a complex network", cond-mat/0312586
Petter Holme
- "Core-periphery organization of complex networks", physics/0506035
- "Scale-free networks with a large- to small-world transition", cond-mat/0607111
- "Signatures of Currency Vertices", arxiv:0812.3487
Petter Holme, Christofer R. Edling and Frederik Liljeros, "Structure and time evolution of an Internet dating community", Social Networks 26 (2004): 155-174
Petter Holme and Gourab Ghoshal, "Dynamics of Networking Agents Competing for High Centrality and Low Degree", Physical Review Letters 96 (2006): 098701
Petter Holme and Beom Jun Kim
- "Growing Scale-Free Networks with Tunable Clustering," cond-mat/0110452
- "Vertex overload breakdown in evolving networks," cond-mat/0204120
Takashi Icinomiya, "Path-integral approach to the dynamics of a sparse random network", cond-mat/0507285 = Physical Review E 72 (2005): 016109
Mads Ipsen and Alexander S. Mikhailov, "Evolutionary reconstruction of networks," nlin.AO/0111023
Shalev Itzkovitz, Reuven Levitt, Nadav Kashtan, Ron Milo, Michael Itzkovitz and Uri Alon, "Coarse-Graining and Self-Dissimilarity of Complex Networks", q-bio.MN/0405011
Junji Ito and Kunihiko Kaneko, "Spontaneous structure formation in a network of chaotic units with variable connection strengths," cond-mat/0108408
Sarika Jalan and R. E. Amritkar, "Self-organized and driven phase synchronization in coupled map scale free networks," nlin.AO/0201051
Henrik Jeldtot Jensen, "Emergence of Network Structure in Models of Collective Evolution and Evolutionary Dynamics", arxiv:0709.2009
Jürgen Jost and M. P. Joy, "Evolving networks with distance preferences," cond-mat/0202343
Alon Keinan, Ben Sandbank, Claus C. Hilgetag, Isaac Meilijson and Eytan Ruppin, "Fair Attribution of Functional Contribution in Artificial and Biological Networks", Neural Computation 16 (2004): 1887--1915
Susan Khor, "Concurrency and Network Disassortativity", Artificial Life 16 (2010): 225--232
Beom Jun Kim, "Performance of networks of artificial neurons: The role of clustering", q-bio.NC/0402045
Beom Jun Kim, Ala Trusina, Petter Holme, Petter Minnhagen, Jean S. Chung, and M. Y. Choi, "Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks," cond-mat/0206533
Beom Jun Kim, Chang No Yoon, Seung Kee Han, and Hawoong Jeong, "Path finding strategies in scale-free networks," cond-mat/0111232
J. Kim, P. L. Krapivsky, B. Kahng and Sidney Redner, "Evolving Protein Interaction Networks," cond-mat/0203167
Osame Kinouchi, A. S. Martinez, G. F. Lima, G. M. Lourenco, S. Risau-Gusman, "Deterministic walks in random networks: an application to thesaurus graphs," cond-mat/0110217
P. L. Krapivsky and Sidney Redner, "Finiteness and Fluctuations in Growing Networks," cond-mat/0207107
P. L. Krapivsky, Sidney Redner, and F. Leyvraz, "Connectivity of Growing Random Networks," cond-mat/0005139
Andre Krzywicki, "Defining statistical ensembles of random graphs," cond-mat/0110574
Marcelo Kuperman and Damian Zanette, "Stochastic resonance in a model of opinion formation on small-world networks," cond-mat/0111289 [Of course social psychology has to be just like the Ising model; how else could physicists study it?]
Maciej Kurant and Patrick Thiran, "Layered Complex Networks", physics/0510194
D.-S. Lee, K.-I. Goh, B. Kahng and D. Kim, "Sandpile avalanche dynamics on scale-free networks", cond-mat/0401531
E. A. Leicht, Petter Holme, and M. E. J. Newman, "Vertex similarity in networks", physics/0510143
Chunguang Li, Philip K. Maini, "An evolving network model with community structure", physics/0510239, Journal of Physics A: Mathematical and General 38 (2005): 9741--9749
Lun Li, David Alderson, Reiko Tanaka, John C. Doyle and Walter Willinger, "Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications", cond-mat/0501169 ["Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims." Ouch.]
Susanna C. Manrubia, Jordi Delgado, and Bartolo Luque, "Small-world behavior in a system of mobile elements," cond-mat/0102069
Sergei Maslov and Kim Sneppen
- "Pattern Detection in Complex Networks: Correlation Profile of the Internet," cond-mat/0205379 [Physicists rediscover bootstrap testing]
- "Specificity and stability in topology of protein networks," cond-mat/0205380
Vincent Marceau, Pierre-André Noël, Laurent Hébert-Dufresne, Antoine Allard, Louis J. Dubé, "Adaptive networks: coevolution of disease and topology", arxiv:1005.1299
Carsten Marr, Marc-Thorsten Huett, "Outer-totalistic cellular automata on graphs", Physics Letters A 373 (2008): 546--549, arxiv:0812.2408
Raoul-Martin Memmesheimer and Marc Timme, "Designing Complex Networks", q-bio.NC/0606041 [i.e., designing networks of stylized neurons to spike in a given periodic pattern. Well, it's a start...]
Ron Milo, Shalev Itzkovitz, Nadav Kashtan, Reuven Levitt, Shai Shen-Orr, Inbal Ayzenshtat, Michal Sheffer and Uri Alon, "Superfamilies of Evolved and Designed Networks", Science 303 (2004): 1538--1542
Andre A. Moreira, Jose S. Andrade, Hans J. Herrmann, Joseph O. Indekeu, "How to make a fragile network robust and vice versa", Physical Review Letters 102 (2009): 018701, arxiv:0812.3591
Stefano Mossa, Marc Barthelemy, H. Eugene Stanley, and Luis A. Nunes Amaral, "Truncation of power law behavior in `scale-free' network models due to information filtering," cond-mat/0201421
Adilson E. Motter, "Cascade control in complex networks", cond-mat/0401074
Adilson E. Motter, Alessandro P. S. de Moura, Ying-Cheng Lai, and Partha Dasgupta, "Topology of the conceptual network of language," cond-mat/0206530 = Physical Review E 65 (2002): 065102(R)
J. C. Nacher, T. Yamada, S. Goto, M. Kanehisa and T. Akutsu, "Two complementary representations of a scale-free network", physics/0402072
M. E. J. Newman, I. Jensen and R. M. Ziff, "Percolation and epidemics in a two-dimensional small world," cond-mat/0108542
Emi M. Nomura, Caterina Gratton, Renee M. Visser, Andrew Kayser, Fernando Perez and Mark D'Esposito, "Double dissociation of two cognitive control networks in patients with focal brain lesions", Proceedings of the National Academy of Sciences (USA) 107 (2010): 121017--12022 [Supposedly involved "graph-theory properties"]
Jukka-Pekka Onnela, Jari Saramaki, Janos Kertesz, and Kimmo Kaski, "Intensity and coherence of motifs in weighted complex networks", Physical Review E 71 (2005): 065103(R)
R. N. Onody and P. A. de Castro, "Nonlinear Barabási-Albert Network", cond-mat/0402315
Pekka Orponen and Satu Elisa Schaeffer, "Efficient Algorithms for Sampling and Clustering of Large Nonuniform Networks", cond-mat/0406048
Juyong Park and M. E. J. Newman, "The origin of degree correlations in the Internet and other networks," cond-mat/0303327
Victor M. Preciado, Michael Zargham, Chinwendu Enyioha, Ali Jadbabaie, George Pappas, "Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks", arxiv:1303.3984
Natasa Przulj, Derek G. Corneil and Igor Jurisica, "Modeling Interactome: Scale-free or Geometric", q-bio.MN/0404017
Amit Puniyani and Rajan Lukose, "Growing random networks under constraints," cond-mat/0107391
Filippo Radicchi, Alain Barrat, Santo Fortunato, Jose J. Ramasco, "Renormalization flows in complex networks", Physical Review E 79 (2009): 026104, arxiv:0811.2761
Abolfazl Ramzanpour and V. Karimipour, "Simple models of small world networks with directed links," cond-mat/0205244
Charles Rathkopf, "Network representation and complex systems", Synthese 195 (2018): 55--78 [Color me skeptical of at least the first of the two main theses set forth in the abstract...]
Erzsebet Ravasz and Albert-László Barabási, "Hierarchical organization in complex networks," cond-mat/0206130 = Physical Review E 67 (2003): 026112
Hermann Riecke, Alex Roxin, Santiago Madruga and Sara A. Solla, "Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons", Chaos 17 (2007): 026110
Olivier Rivoire and Julien Barré "Exactly solvable models of adaptive networks", cond-mat/0606754 ["A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints." Which means what, for the original logic problem? I should read the paper to see...]
Tim Rogers, "Maximum-entropy moment-closure for stochastic systems on networks", Journal of Statistical Mechanics (2011): P05007, arxiv:1103.4980
Hernan Rozenfeld and Daniel ben-Avraham, "Designer Nets from Local Strategies", cond-mat/0401196
Hernan D. Rozenfeld, Joseph E. Kirk, Erik M. Bollt and Daniel ben-Avraham, "Statistics of Cycles: How Loopy is your Network?", cond-mat/0403536
Manoj Pratim Samanta and Shoudan Liang, "Redundancies in Large-scale Protein Interaction Networks," physics/0303027
Alejandro D. Sanchez, Juan M. Lopez and Miguel A. Rodriguez, "Nonequilibrium Phase Transitions in Directed Small-World Networks," cond-mat/0110500
Leonard M. Sander, C. P. Warren and I. M. Sokolov, "Epidemics disorder, and percolation," cond-mat/0301394
Nima Sarshar and Vwani Roychowdhury, "Scale-Free and Stable Structures in Complex Ad hoc Networks," cond-mat/0303041
N. Schwartz, R. Cohen, D. ben-Avraham, A.-L. Barabási and S. Havlin, "Percolation in Directed Scale-Free Networks," cond-mat/0204523
Philip Seliger, Stephen C. Young, and Lev S. Tsimring, "Plasticity and learning in a network of coupled phase oscillators," nlin.AO/0110044
M. Angeles Serrano and Marian Boguna
- "Topology of the World Trade Web," cond-mat/0301015
- "Clustering in complex networks. I. General formalism", cond-mat/0608336
- "Clustering in complex networks. II. Percolation properties", cond-mat/0608337
M. Angeles Serrano, Dmitri Krioukov and Marian Boguna, "Self-Similarity of Complex Networks and Hidden Metric Spaces", Physical Review Letters 100 (2008): 078701
Dinghua Shi, Qinguha Chen and Liming Liu, "A Markov Chain-Based Numerical Method for Calculating Network Degree Distributions", math-ph/0409080
Julian Sienkiewicz, Piotr Fronczak, and Janusz A. Holyst, "Log-periodic oscillations due to discrete effects in complex networks", cond-mat/0608273
Tiago Simas, Luis M. Rocha, "Stochastic model for scale-free networks with cutoffs", arxiv:0901.0159
Ingve Simonsen, Kasper Astrup Eriksen, Sergei Maslov and Kim Sneppen, "Diffusion on Complex Networks : A way to probe their large scale topological structures", cond-mat/0312476 = Physica A 336 (2004): 163--173
Sitabhra Sinha and Sudeshna Sinha, "Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics", nlin.AO/0402002
Arne Skjeltorp and Alexander Belushkin (eds.), Dynamics of Complex Interconnected Systems: Networks and Bioprocesses
David M. D. Smith, Chiu Fan Lee and Neil F. Johnson, "Realistic network growth using only local information: From random to scale-free and beyond", cond-mat/0608733
Sara Nadiv Soffer and Alexei Vazquez, "Network clustering coefficient without degree-correlation biases", Physical Review E 71 (2005): 057101 ["The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show that this signature of hierarchical structure is a consequence of degree-correlation biases in the clustering coefficient definition. We introduce a definition in which the degree-correlation biases are filtered out, and provide evidence that in real networks the clustering coefficient is constant or decays logarithmically with vertex degree."]
Olaf Sporns, Networks of the Brain
Russell K. Standish, "Complexity of Networks (reprise)", arxiv:0911.3482
Dietrich Stauffer and Amnon Aharony, "Efficient Hopfield pattern recognition on a scale-free neural network," cond-mat/0212601
Hrvoje Stefancic and Vinko Zlatic, "Preferential attachment with information filtering: node degree probability distribution properties", cond-mat/0404495
Clara Stegehuis, Bert Zwart, "Large deviations for triangles in scale-free random graphs", arxiv:2303.09198
Gyorgy Szabo and Gabor Fath, "Evolutionary games on graphs", cond-mat/0607344
Gergely J Szollosi, Imre Derenyi, "Hierarchical meanfield theory of evolutionary games on structured populations", arxiv:0704.0357
Kazuhiro Takemoto and Chikoo Oosawa, "Evolving networks by merging cliques", Physical Review E 72 (2005): 046116
Makoto Uchida and Susumu Shirayama, "Effect of initial conditions on Glauber dynamics in complex networks", cond-mat/0702482
S. Valverde, R. Ferrer i Cancho and R. V. Sole, "Scale-free Networks from Optimal Design," cond-mat/0204344
J. van den Berg, Geoffrey R. Grimmett and Rinaldo B. Schinazi, "Dependent Random Graphs and Spatial Epidemics", Annals of Applied Probability 8 (1998): 317--336
Alexei Vazquez and Albert-László Barabási, "The inhomogeneous evolution of subgraphs and cycles in complex networks", cond-mat/0501399
Alexei Vazquez and Martin Weigt, "Computational complexity arising from degree correlations in networks," cond-mat/0207035
R. Vilela Mendes, "Network Dependence of Strong Reciprocity", Advances in Complex Systems 7 (2004): 357--368
Andreas Wagner, "How the global structure of protein interaction networks evolves," cond-mat/0207043
C. P. Warren, Leonard M. Sander and I. M. Sokolov, "Geography in a Scale-Free Network Model," cond-mat/0207324
Martin Weigt, "Dynamics of heuristic optimization algorithms on random graphs," cond-mat/0203281
Chris Wiggins and Ilya Nemenman, "Process Pathway Inference via Time Series Analysis," physics/0206031
Walter Willinger et al., "Scaling Phenomena in the Internet: Critically Examining Criticality", Proceedings of the National Academy of Sciences 99 (2002): 2673--2580
An-Cai Wu, Xin-Jian Xu, and Ying-Hai Wang, "Excitable Greenberg-Hastings cellular automaton model on scale-free networks", Physical Review E 75 (2007): 032901
Ramon Xulvi-Brunet and I. M. Sokolov, "Evolving networks with disadvantaged long-range connections," cond-mat/0205136
Jie Zhang, Changsong Zhou, Xiaoke Xu and Michael Small, "Mapping from Architeture to Dynamics: A Unified View of Dynamical Processes on Networks", arxiv:0908.2248 [From a quick scan, vastly less general and ambitious than the title or even the abstract promises; but worth looking at more closely.]
Chaopin Zhu, Anthony Kuh, Juan Wang and Philippe De Wilde, "Analysis of an evolving email network", Physical Review E 74 (2006): 046109
Alexander Zumdieck, Marc Timme, Theo Geisel and Fred Wolf, "Long Chaotic Transients in Complex Networks", cond-mat/0401038