Complex Networks: My view & research

Transcription

1 CSC / Computational Biology September 14, 2007, ACCESS board meeting pholme/

2 what is a network? a system where things interact, or are coupled, pairwise

3 nodes, vertices, links, edges vertex, node, site, actor, agent edge, link, tie, bond, arc number of neighbors = degree

4 examples: internet

5 examples: metabolism

6 examples: scientific collaborations

7 examples: friendship

8 examples: dating Patsy Kensit Salma Hayek Tom Green Kurt Cobain Liam Gallagher David Schwimmer Drew Barrymore Edward Norton Daniel Johns Rod Stewart Nicole Appleton Noah Wyle Cortney Love Eric Erlandsson Rachel Hunter Mel C Luke Wilson Keri Russell Jennifer Aniston Natalie Prince Imbruglia Felipe of Spain Scott Speedman P Diddy Geri Halliwell Prince Nicholas of Greece Jude Law Robbie Williams Chris Martin Jennifer Lopez Gwyneth Paltrow Sadie Frost Ben Affleck Nicole Kidman Lenny Kravitz Brad Gisele Pitt Bundchen Bridget Hall Tom Cruise Liv Leonardo Tyler Alicia DiCaprio Silverstone Jared Janet Leto Jackson Penelope Vanessa Cruz Paradis Juliette Tobey Lewis Maguire Demi Naomi Moore Campbell Claire Cameron Danes Justin Diaz Timberlake Johnny Depp Virgine Ledoyen Alyssa Milano Eric Clapton Neve Campbell Matt Damon Colin Farrell Winona Ryder Kristen Dunst Bruce Willis Britney Spears Matt Dillon Sheryl Crow Ashton Kutcher Pamela Anderson Kid Rock Minnie Driver John Cusack Sherilyn Fenn Kate Moss Fred Dust Jennifer Grey Owen Wils Meg Ryan Beck Brittany Murphy Heather Locklear Marcus Schenkenberg Russell Crowe Tommy Lee Dave Grohl Dennis Quaid Eminem Mariah Carey Richie Sambora

9 what systems can be modeled as networks? items are coupled pairwise the network is relatively sparse (the average degree is constant) there is a dynamic system on the network the time scale of this dynamics is faster than the dynamics of network evolution

10 what systems can be modeled as networks? items are coupled pairwise the network is relatively sparse (the average degree is constant) there is a dynamic system on the network the time scale of this dynamics is faster than the dynamics of network evolution

11 what systems can be modeled as networks? items are coupled pairwise the network is relatively sparse (the average degree is constant) there is a dynamic system on the network the time scale of this dynamics is faster than the dynamics of network evolution

12 what systems can be modeled as networks? items are coupled pairwise the network is relatively sparse (the average degree is constant) there is a dynamic system on the network the time scale of this dynamics is faster than the dynamics of network evolution

13 what systems can be modeled as networks? items are coupled pairwise the network is relatively sparse (the average degree is constant) there is a dynamic system on the network the time scale of this dynamics is faster than the dynamics of network evolution

14 what is? how the network differs a random network to be more precise: how the network differs from a null model

15 what is? how the network differs a random network to be more precise: how the network differs from a null model

16 what is? how the network differs a random network to be more precise: how the network differs from a null model

17 the dogmas of network science real networks have both structure and randomness the relates to the function of the network

18 the dogmas of network science real networks have both structure and randomness the relates to the function of the network

19 the dogmas of network science real networks have both structure and randomness the relates to the function of the network

20 what is network science? Constructing relevant measures of. Measuring structure of real networks, and elucidating correlations between the quantities. Why do real networks have the structure they have? Modeling the evolution of networks. How does the topology affect dynamic systems on the network. How can we control network topology to get some desirable dynamic property.

21 what is network science? Constructing relevant measures of. Measuring structure of real networks, and elucidating correlations between the quantities. Why do real networks have the structure they have? Modeling the evolution of networks. How does the topology affect dynamic systems on the network. How can we control network topology to get some desirable dynamic property.

22 what is network science? Constructing relevant measures of. Measuring structure of real networks, and elucidating correlations between the quantities. Why do real networks have the structure they have? Modeling the evolution of networks. How does the topology affect dynamic systems on the network. How can we control network topology to get some desirable dynamic property.

23 what is network science? Constructing relevant measures of. Measuring structure of real networks, and elucidating correlations between the quantities. Why do real networks have the structure they have? Modeling the evolution of networks. How does the topology affect dynamic systems on the network. How can we control network topology to get some desirable dynamic property.

24 what is network science? Constructing relevant measures of. Measuring structure of real networks, and elucidating correlations between the quantities. Why do real networks have the structure they have? Modeling the evolution of networks. How does the topology affect dynamic systems on the network. How can we control network topology to get some desirable dynamic property.

25 what is network science? Constructing relevant measures of. Measuring structure of real networks, and elucidating correlations between the quantities. Why do real networks have the structure they have? Modeling the evolution of networks. How does the topology affect dynamic systems on the network. How can we control network topology to get some desirable dynamic property.

26 degree distribution

27 clustering coefficient

28 clustering coefficient How many triangles are there in the network? The clustering coefficient: C = the number of triangles 3 the number of connected triples of vertices

29 clustering coefficient How many triangles are there in the network? The clustering coefficient: C = the number of triangles 3 the number of connected triples of vertices

30 clustering coefficient triangle

31 clustering coefficient connected triple

32 assortativity Are high-degree vertices connected to other high-degree vertices? Or are they vertices primarily connected to low-degree vertices. The assortative mixing coefficient: r = 4 k 1 k 2 k 1 + k k k 2 2 k 1 + k 2 2 where k i is the degree of the i th argument of the edges as they appear in an enumeration of the edges.

33 assortativity Are high-degree vertices connected to other high-degree vertices? Or are they vertices primarily connected to low-degree vertices. The assortative mixing coefficient: r = 4 k 1 k 2 k 1 + k k k 2 2 k 1 + k 2 2 where k i is the degree of the i th argument of the edges as they appear in an enumeration of the edges.

34 network null- Network structures are always relative one has to be clear about what to compare with... a null model Null model 1: random graphs (Poisson random graphs, Erdős-Rényi graphs) Null model 2: random graphs constrained to the set of degrees of the original graph

35 network null- Network structures are always relative one has to be clear about what to compare with... a null model Null model 1: random graphs (Poisson random graphs, Erdős-Rényi graphs) Null model 2: random graphs constrained to the set of degrees of the original graph

36 network null- Network structures are always relative one has to be clear about what to compare with... a null model Null model 1: random graphs (Poisson random graphs, Erdős-Rényi graphs) Null model 2: random graphs constrained to the set of degrees of the original graph

37 network null- Network structures are always relative one has to be clear about what to compare with... a null model Null model 1: random graphs (Poisson random graphs, Erdős-Rényi graphs) Null model 2: random graphs constrained to the set of degrees of the original graph

38 random graphs for each pair of vertices, with probability p, add an edge

39 random graphs for each pair of vertices, with probability p, add an edge

40 random graphs for each pair of vertices, with probability p, add an edge

41 random graphs for each pair of vertices, with probability p, add an edge

42 random graphs for each pair of vertices, with probability p, add an edge

43 random graphs for each pair of vertices, with probability p, add an edge

44 random graphs for each pair of vertices, with probability p, add an edge

45 random graphs for each pair of vertices, with probability p, add an edge

46 random graphs for each pair of vertices, with probability p, add an edge

47 random graphs for each pair of vertices, with probability p, add an edge

48 random graphs for each pair of vertices, with probability p, add an edge

49 random graphs for each pair of vertices, with probability p, add an edge

50 random rewiring start from the original graph choose edge pairs, and swap them

51 random rewiring start from the original graph choose edge pairs, and swap them

52 random rewiring start from the original graph choose edge pairs, and swap them

53 random rewiring start from the original graph choose edge pairs, and swap them

54 random rewiring start from the original graph choose edge pairs, and swap them

55 random rewiring start from the original graph edge triples can be swapped too

56 random rewiring start from the original graph edge triples can be swapped too

57 random rewiring start from the original graph edge triples can be swapped too

58 random rewiring start from the original graph edge triples can be swapped too

59 why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics

60 why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics

61 why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics

62 why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics

63 model what? observed network structural quantities possible structure altering events (attacks, overload breakdowns) dynamic processes on the network interaction between such processes and network evolution

64 model what? observed network structural quantities possible structure altering events (attacks, overload breakdowns) dynamic processes on the network interaction between such processes and network evolution

65 model what? observed network structural quantities possible structure altering events (attacks, overload breakdowns) dynamic processes on the network interaction between such processes and network evolution

66 model what? observed network structural quantities possible structure altering events (attacks, overload breakdowns) dynamic processes on the network interaction between such processes and network evolution

67 model what? observed network structural quantities possible structure altering events (attacks, overload breakdowns) dynamic processes on the network interaction between such processes and network evolution

68 Barabási Albert model probability of attachment: k i

69 Barabási Albert model probability of attachment: k i

70 Barabási Albert model probability of attachment: k i

71 Barabási Albert model probability of attachment: k i

72 Barabási Albert model probability of attachment: k i

73 dynamics on networks traffic dynamics (Internet, vehicular traffic, etc.) specific signalling in biology disease spreading spreading of rumours, fads; and other threshold phenomena local search

74 dynamics on networks traffic dynamics (Internet, vehicular traffic, etc.) specific signalling in biology disease spreading spreading of rumours, fads; and other threshold phenomena local search

75 dynamics on networks traffic dynamics (Internet, vehicular traffic, etc.) specific signalling in biology disease spreading spreading of rumours, fads; and other threshold phenomena local search

76 dynamics on networks traffic dynamics (Internet, vehicular traffic, etc.) specific signalling in biology disease spreading spreading of rumours, fads; and other threshold phenomena local search

77 dynamics on networks traffic dynamics (Internet, vehicular traffic, etc.) specific signalling in biology disease spreading spreading of rumours, fads; and other threshold phenomena local search

78 dynamics on networks traffic dynamics (Internet, vehicular traffic, etc.) specific signalling in biology disease spreading spreading of rumours, fads; and other threshold phenomena local search

79 degree distribution a broad degree distribution makes a network sensitive to attacks but robust to vertex failures and robust to overload breakdowns (depends a little on dynamics) information spreads faster but there is a danger of congestion

80 degree distribution a broad degree distribution makes a network sensitive to attacks but robust to vertex failures and robust to overload breakdowns (depends a little on dynamics) information spreads faster but there is a danger of congestion

81 degree distribution a broad degree distribution makes a network sensitive to attacks but robust to vertex failures and robust to overload breakdowns (depends a little on dynamics) information spreads faster but there is a danger of congestion

82 degree distribution a broad degree distribution makes a network sensitive to attacks but robust to vertex failures and robust to overload breakdowns (depends a little on dynamics) information spreads faster but there is a danger of congestion

83 degree distribution a broad degree distribution makes a network sensitive to attacks but robust to vertex failures and robust to overload breakdowns (depends a little on dynamics) information spreads faster but there is a danger of congestion

84 degree distribution a broad degree distribution makes a network sensitive to attacks but robust to vertex failures and robust to overload breakdowns (depends a little on dynamics) information spreads faster but there is a danger of congestion

85 clustering slows down disease spreading makes memory worse in neural networks

86 clustering slows down disease spreading makes memory worse in neural networks

87 clustering slows down disease spreading makes memory worse in neural networks

88 assortativity high assortativity facilitates small disease outbreaks in disassortative networks outbreaks don t form easily, but if they do they can cover a larger fraction of the population

89 assortativity high assortativity facilitates small disease outbreaks in disassortative networks outbreaks don t form easily, but if they do they can cover a larger fraction of the population

90 assortativity high assortativity facilitates small disease outbreaks in disassortative networks outbreaks don t form easily, but if they do they can cover a larger fraction of the population

91 applications navigation system control prediction

92 applications navigation system control prediction

93 applications navigation system control prediction

94 applications navigation system control prediction