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Teaching Assistants: V. Nicosia, R. Sinatra
This is an introductory course on the basic methods of network theory to characterize the structural properties of a network and to study the processes taking place over the network. The course is for undergraduates in physics, enginnering, mathematics, biology and computer science of Scuola Superiore di Catania who want to learn the major ideas and the new results achieved in one of the newest and hottest interdisciplinary research fields. The course is organized in 10 lectures of 3 hours each. In each lecture, the theory is supplemented with examples and applications, databases of real world networks, and numerical algorithms. Some of the lectures are organized in 2 hours theory, plus 1 hour recitation consisting in the discussion (and reproduction of the results) of one significant research article from the literature.
- LECTURE 1: Social networks. Centrality and centralization
- The importance of being central.
P. Crucitti and V. Latora, Proc. 31st Workshop Erice, World Scientific (2005). - Centrality measures in spatial networks of urban streets.
P. Crucitti, V. Latora and S. Porta, Phys. Rev. E 73, 036125 (2005). - Interaction ruling animal collective behavior depends on topological rather than metric distance.
M. Ballerini et al, PNAS 105, 1232 (2008). - LECTURE 2: Graph Theory: definitions and measures
- Complex networks: Structure and dynamics.
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Physics Reports 424, 175 (2006). - Physarum solver: A biologically inspired method of road-network navigation.
A. Teroa, R. Kobayashia, T. Nakagaki, Physica A363, 115 (2006). - LECTURE 3: ER random graphs
- LECTURE 4: Small-world networks and random graphs with given Pk
- Collective dynamics of 'small-world' networks
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998). - Efficient Behavior of Small-World Networks
V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001). - Random graphs as models of networks M.E.J. Newman, arXiv:cond-mat/0202208 (2002).
- LECTURE 5: Models of network growth
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Citation Statistics from 110 Years of Physical Review
S. Redner, Physics Today 58, 49 (2005). - Emergence of scaling in random networks
A.-L. Barabasi, R. Albert, Science 286, 509â512 (1999) -
Topology of Evolving Networks: Local Events and Universality
R. Albert, A.L. Barabasi, Phys. Rev. Lett. 85, 5234 (2000). -
Scale-free Nets from Varying Vertex Intrinsic Fitness
G. Caldarelli, A. Capocci, P. De Los Rios, M. A. Munoz, Phys. Rev. Lett. 89, 258702 (2002). -
Mean-field theory for scale-free random networks
A.L. Barabasi, R. Albert, H. Jeong, Physica A 272, 173 (1999). -
Connectivity of Growing Random Networks
P.L. Krapivsky, S. Redner, F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000). - LECTURE 6: Degree-degree correlations
- Dynamical and Correlation Properties of the Internet. R. Pastor-Satorras, A. Vazquez and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).
- Assortative Mixing in Networks M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2001).
- LECTURE 7: Motifs. Community structures
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Network motifs in the transcriptional regulation network of Escherichia coli
S Shen-Orr, R Milo, S Mangan & U Alon, Nature Genetics, 31:64-68 (2002). - Network Motifs: Simple Building Blocks of Complex Networks
R Milo, S Shen-Orr, S Itzkovitz, N Kashtan, D Chklovskii & U Alon, Science 298:824-827 (2002). - Finding and evaluating community structure in networks
M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004). - Community detection in graphs
S. Fortunato, Phys. Rep. 486, 75â174 (2010). - Comparing community structure identification
Leon Danon, Albert Dıaz-Guilera, Jordi Duch and Alex Arenas, JStat. P09008 (2005). - LECTURE 8: Percolation
- Attack and error tolerance of complex networks,
R. Albert, H. Jeong, and A.L. Barabasi, Nature 406, 378 (2000). - Resilience of the internet to random breakdowns,
R. Cohen, K. Erez, D. ben Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000). -
Breakdown of the internet under intentional attack,
R. Cohen, K. Erez, D. ben Avraham, and S. Havlin, Phys. Rev. Lett. 86, 3682 (2001). - Percolation critical exponents in scale-free networks,
R. Cohen, D. ben Avraham, and S. Havlin, Phys. Rev. E66, 36113 (2002). - Percolation in directed scale-free networks,
N. Schwartz, R. Cohen, D. ben Avraham, A.-L. Barabasi and S. Havlin, Phys. Rev. E66, 015104(R) (2002). - Vulnerability and protection of critical infrastructures,
V. Latora and M. Marchiori, Phys. Rev. E71, 015103(R) (2005). - LECTURE 9: Random Walks
- Random Walks on Complex Networks,
J.D. Noh and H. Rieger, Phys. Rev. Lett. 92, 118701 (2004). - Entropy rate of diffusion processes on complex networks,
Jesus Gomez-Gardenes and Vito Latora, Phys. Rev. E 78, 065102(R) (2008). - Maximal-entropy random walks in complex networks with limited information,
Roberta Sinatra, Jesus Gomez-Gardenes, Renaud Lambiotte, Vincenzo Nicosia, and Vito Latora, Phys. Rev. E 83, 030103(R) (2011). - LECTURE 10: Models of disease spreading
- The web of human sexual contacts,
F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y, Aberg, Nature 411, 907 (2001). - Epidemic spreading in scale-free nets,
R. Pastor-Satorras and A. Vespignani. Phys. Rev. Lett. 86, 3200 (2001). - Epidemic dynamics and endemic states in complex nets,
R. Pastor-Satorras and A. Vespignani. Phys. Rev. E63, 066117 (2001) - Epidemic dynamics in finite size scale-free networks,
R. Pastor-Satorras and A. Vespignani, Phys. Rev. E65, 035108(R) (2002) - Spreading of sexually transmitted diseases in heterosexual populations,
J. Gomez-Gardenes, V. Latora, Y. Moreno, E.V. Profumo, PNAS 105, 1399 (2008) - RECITATION 1: Scale-free degree distributions
- Slides and datasets
- Diameter of the World-Wide Web
R. Albert, H. Jeong, A.L. Barabasi, Nature 401, 130 (2001). - Classes of small-world networks
L.A.N. Amaral, A. Scala, M. Barthelemy, H.E. Stanley, PNAS 97:21, 11149 (2000) - RECITATION 2: Bonacich eigenvector centrality
- Slides and datasets
- Eigenvector-like measures of centrality for asymmetric relations
P. Bonacich, P. Lloyd, Social Network 23, 191 (2001). - RECITATION 3: Sampling of ER graphs
- Slides and datasets
ER graphs: < k >=0.9, < k >=1.1, < k >=1.5 - Scientific collaboration networks - I. Network construction and fundamental results
M.E.J. Newman, Phys. Rev. E, 64, 016131 (2001). - Scientific collaboration networks - II. Shortest paths, weighted networks, and centrality
M.E.J. Newman, Phys. Rev. E, 64, 016132. - RECITATION 4: Characteristic path length and clustering coefficient
- Material (slides)
- Collective dynamics of 'small-world' networks
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998). - RECITATION 5: Sampling random graphs with given Pk
- Material (slides and datasets)
- Dynamical and Correlation Properties of the Internet.
R. Pastor-Satorras, A. Vazquez and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001). - RECITATION 6: Networks of motifs from sequences of symbols
- Material (slides)
- Networks of motifs from sequences of symbols.
R. Sinatra, D. Condorelli and V. Latora, Phys. Rev. Lett. 105, 178702 (2010). - PROJECTS
- Background: Scaling Breakdown in Flow Fluctuations on Complex Networks,
Sandro Meloni, Jesus Gomez-Gardenes, Vito Latora, and Yamir Moreno, Phys. Rev. Lett. 100, 208701 (2008). - Main paper: Extreme Events on Complex Networks,
Vimal Kishore, M. S. Santhanam, and R. E. Amritkar, Phys. Rev. Lett. 106, 188701 (2011). - Main paper: Networks of motifs from sequences of symbols,
R. Sinatra, D. Condorelli and V. Latora, Phys. Rev. Lett. 105, 178702 (2010), and supplementary material. - Databases for proteomes: RefSeq and ConsesusCoDingSequence
- Background Evolutionary dynamics of social dilemmas in structured heterogeneous populations,
F.C. Santos, J.M. Pacheco, and T. Lenaerts, PNAS 103, 3490-3494 (2006). - Main paper A: Evolution of cooperation without reciprocity
R.L. Riolo, M.D. Cohen, and R. Axelrod, Nature 414, 441-443 (2001) and notes for extending the model. - Main paper B: Emergent Hierarchical Structures in Multiadaptive Games,
Sungmin Lee, Petter Holme, and Zhi-Xi Wu, Phys. Rev. Lett. 106, 028702 (2011). - Main paper:
Time walkers and spatial dynamics of aging information,
L. Liziana, M. Rosvall and K. Sneppen,Phys. Rev. Lett. 104, 040603 (2010). - Main paper:
Patterns of cooperation: fairness and coordination in networks of interacting agents ,
A.-L. Do, L. Rudolf and T. Gross, New J. of Phys. 12 063023 (2010). - Main paper:
Identifying communities by influence dynamics in social networks,
A. Stanoev, D. Smilkov and L. Kocarev, arxiv:1104.5247 (2011) - Main paper:
Entropic Origin of Disassortativity in Complex Networks,
S. Johnson, J. J. Torres, J. Marro, M. A. Munoz, Phys.Rev.Lett 104, 108702 (2010)
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Extreme Events using Random Walks
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