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Complex networks in nature

Outline. Lectures 1-3: Graph theoretical basics, examples of real networks, basic models (Erdos-R?nyi, small world, scale free graphs) and their properties, examples. Lecture 4: Dynamics on networks: error and attack tolerance, disease spreading, metabolic networks. Lecture 5: Network motifs and communities..

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Complex networks in nature

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    1. Complex networks in nature

    2. Outline

    3. Graph theory basics

    8. Extensions

    9. Random graphs

    10. The Erdos-Rnyi model 02:40

    11. The Erdos-Rnyi model

    14. Are complex networks really random?

    15. Watts-Strogatz model

    16. Watts-Strogatz model

    17. WWW

    18. WWW-power

    19. Internet

    22. Coauthorship

    23. Coauthorship

    27. Origins SF

    28. BA model

    29. MFT

    30. Growth without preferential attachment

    33. More models

    34. Presence of a giant (percolating) component

    35. Prot Interaction map

    42. Robustness

    43. Robust-SF

    44. Absence of a critical percolation threshold for ? = 3

    45. Achilles Heel

    46. Prot- robustness

    47. Disease spreading in the susceptible-infected-susceptible (SIS) epidemic model

    48. SIS in complex networks

    49. SIS in complex networks

    50. Non-uniform immunization of complex networks

    51. Motifs

    52. Three-node connected subgraphs

    53. Network motifs

    54. Why do we have motifs?

    55. Communities: densely connected subgraphs

    56. Traditional method: hierarchical clustering (agglomerative method)

    57. Girvan-Newman method (divisive method)

    58. Modularity

    59. Potts model

    60. Clique percolation method (CPM)

    61.

    62.

    63.

    64. Web of communities for the protein interaction network of yeast

    65. Community statistics

    66. Clique percolation in an ER graph

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