CSC / Computational Biology September 14, 2007, ACCESS board meeting http://www.csc.kth.se/ pholme/
what is a network? a system where things interact, or are coupled, pairwise
nodes, vertices, links, edges vertex, node, site, actor, agent edge, link, tie, bond, arc number of neighbors = degree
examples: internet
examples: metabolism
examples: scientific collaborations
examples: friendship
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
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
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
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
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
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
what is? how the network differs a random network to be more precise: how the network differs from a null model
what is? how the network differs a random network to be more precise: how the network differs from a null model
what is? how the network differs a random network to be more precise: how the network differs from a null model
the dogmas of network science real networks have both structure and randomness the relates to the function of the network
the dogmas of network science real networks have both structure and randomness the relates to the function of the network
the dogmas of network science real networks have both structure and randomness the relates to the function of the network
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.
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.
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.
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.
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.
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.
degree distribution
clustering coefficient
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
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
clustering coefficient triangle
clustering coefficient connected triple
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 2 2 2 k 2 1 + 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.
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 2 2 2 k 2 1 + 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.
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
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
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
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
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random graphs for each pair of vertices, with probability p, add an edge
random rewiring start from the original graph choose edge pairs, and swap them
random rewiring start from the original graph choose edge pairs, and swap them
random rewiring start from the original graph choose edge pairs, and swap them
random rewiring start from the original graph choose edge pairs, and swap them
random rewiring start from the original graph choose edge pairs, and swap them
random rewiring start from the original graph edge triples can be swapped too
random rewiring start from the original graph edge triples can be swapped too
random rewiring start from the original graph edge triples can be swapped too
random rewiring start from the original graph edge triples can be swapped too
why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics
why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics
why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics
why (mechanistic)? to understand the mechanisms behind network evolution to predict the future to generate test networks for studies about dynamics
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
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
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
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
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
Barabási Albert model probability of attachment: k i
Barabási Albert model probability of attachment: k i
Barabási Albert model probability of attachment: k i
Barabási Albert model probability of attachment: k i
Barabási Albert model probability of attachment: k i
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
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
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
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
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
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
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
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
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
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
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
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
clustering slows down disease spreading makes memory worse in neural networks
clustering slows down disease spreading makes memory worse in neural networks
clustering slows down disease spreading makes memory worse in neural networks
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
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
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
applications navigation system control prediction
applications navigation system control prediction
applications navigation system control prediction
applications navigation system control prediction