introductionnetwork structure

modelstopology vs. dynamics

Complex Networks: My view & research

Petter Holme

CSC / Computational Biology

September 14, 2007, ACCESS board meeting

http://www.csc.kth.se/∼pholme/

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is a network?

a system where things interact, or are coupled, pairwise

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

nodes, vertices, links, edges

vertex, node, site, actor, agent

number of neighbors = degree

edge, link, tie, bond, arc

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

examples: internet

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

examples: metabolism

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

examples: scientific collaborations

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

examples: friendship

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

examples: dating

Owen WilsonSheryl Crow

Beck

Jennifer LopezJude LawNicole Kidman

Tom Green

Virgine Ledoyen

Keri RussellScott Speedman

Edward Norton

Luke Wilson

Chris Martin

Liv TylerGisele Bundchen

Neve Campbell Winona Ryder

Tobey Maguire

Colin Farrell

Brad Pitt

Tommy LeeDave Grohl

David SchwimmerDaniel Johns

Natalie ImbrugliaPrince Felipe of Spain

Fred Dust

Meg Ryan

Geri Halliwell

Kristen DunstBruce WillisAshton Kutcher

Brittany Murphy

Eminem

Mariah Carey

Britney Spears

Naomi CampbellDemi Moore Justin Timberlake

Matt Dillon

Heather Locklear

Richie Sambora

Janet Jackson

Alyssa Milano

Pamela AndersonKid Rock

Marcus Schenkenberg

Bridget HallJared LetoLeonardo DiCaprio

Claire Danes

Noah Wyle

Jennifer Aniston

Robbie Williams

Mel CNicole Appleton

Rachel HunterRod Stewart

Sadie FrostTom Cruise

Penelope Cruz

Matt Damon

Vanessa Paradis

Lenny Kravitz

Johnny DeppJuliette Lewis

Kate MossJennifer GreySherilyn FennMinnie Driver

John CusackRussell Crowe

Dennis Quaid

Patsy Kensit

Liam Gallagher Drew Barrymore

Eric ErlandssonCortney Love

Kurt Cobain

Ben AffleckGwyneth PaltrowPrince Nicholas of Greece

Alicia Silverstone

Cameron Diaz

P Diddy

Eric Clapton

Salma Hayek

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what systems can be modeled as networks?

items are coupled pairwise

the network is relatively sparse (the average degree isconstant)

there is a dynamic system on the network

the time scale of this dynamics is faster than thedynamics of network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what systems can be modeled as networks?

items are coupled pairwise

the network is relatively sparse (the average degree isconstant)

there is a dynamic system on the network

the time scale of this dynamics is faster than thedynamics of network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what systems can be modeled as networks?

items are coupled pairwise

the network is relatively sparse (the average degree isconstant)

there is a dynamic system on the network

the time scale of this dynamics is faster than thedynamics of network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what systems can be modeled as networks?

items are coupled pairwise

the network is relatively sparse (the average degree isconstant)

there is a dynamic system on the network

the time scale of this dynamics is faster than thedynamics of network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what systems can be modeled as networks?

items are coupled pairwise

the network is relatively sparse (the average degree isconstant)

there is a dynamic system on the network

the time scale of this dynamics is faster than thedynamics of network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network structure?

how the network differs a random network

to be more precise: how the network differs from a nullmodel

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network structure?

how the network differs a random network

to be more precise: how the network differs from a nullmodel

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network structure?

how the network differs a random network

to be more precise: how the network differs from a nullmodel

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

the dogmas of network science

real networks have both structure and randomness

the network structure relates to the function of the network

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

the dogmas of network science

real networks have both structure and randomness

the network structure relates to the function of the network

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

the dogmas of network science

real networks have both structure and randomness

the network structure relates to the function of the network

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network science?

Constructing relevant measures of network structure.

Measuring structure of real networks, and elucidatingcorrelations between the quantities.

Why do real networks have the structure they have? Modelingthe evolution of networks.

How does the topology affect dynamic systems on thenetwork.

How can we control network topology to get somedesirable dynamic property.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network science?

Constructing relevant measures of network structure.

Measuring structure of real networks, and elucidatingcorrelations between the quantities.

Why do real networks have the structure they have? Modelingthe evolution of networks.

How does the topology affect dynamic systems on thenetwork.

How can we control network topology to get somedesirable dynamic property.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network science?

Constructing relevant measures of network structure.

Measuring structure of real networks, and elucidatingcorrelations between the quantities.

Why do real networks have the structure they have? Modelingthe evolution of networks.

How does the topology affect dynamic systems on thenetwork.

How can we control network topology to get somedesirable dynamic property.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network science?

Constructing relevant measures of network structure.

Measuring structure of real networks, and elucidatingcorrelations between the quantities.

Why do real networks have the structure they have? Modelingthe evolution of networks.

How does the topology affect dynamic systems on thenetwork.

How can we control network topology to get somedesirable dynamic property.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network science?

Constructing relevant measures of network structure.

Measuring structure of real networks, and elucidatingcorrelations between the quantities.

Why do real networks have the structure they have? Modelingthe evolution of networks.

How does the topology affect dynamic systems on thenetwork.

How can we control network topology to get somedesirable dynamic property.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

what is network science?

Constructing relevant measures of network structure.

Measuring structure of real networks, and elucidatingcorrelations between the quantities.

Why do real networks have the structure they have? Modelingthe evolution of networks.

How does the topology affect dynamic systems on thenetwork.

How can we control network topology to get somedesirable dynamic property.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

degree distribution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

clustering coefficient

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

clustering coefficient

trianglePetter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

clustering coefficient

connected triplePetter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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〈k1 k2〉 − 〈k1 + k2〉

2

2〈k 21 + k 2

2 〉 − 〈k1 + k2〉2

where ki is the degree of the i’th argument of the edges as theyappear in an enumeration of the edges.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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〈k1 k2〉 − 〈k1 + k2〉

2

2〈k 21 + k 2

2 〉 − 〈k1 + k2〉2

where ki is the degree of the i’th argument of the edges as theyappear in an enumeration of the edges.

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

network null-models

Network structures are always relative . . .

. . . one has to be clear about what to compare with . . . a nullmodel

Null model 1: random graphs (Poisson random graphs,Erdos-Renyi graphs)

Null model 2: random graphs constrained to the set ofdegrees of the original graph

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

network null-models

Network structures are always relative . . .

. . . one has to be clear about what to compare with . . . a nullmodel

Null model 1: random graphs (Poisson random graphs,Erdos-Renyi graphs)

Null model 2: random graphs constrained to the set ofdegrees of the original graph

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

network null-models

Network structures are always relative . . .

. . . one has to be clear about what to compare with . . . a nullmodel

Null model 1: random graphs (Poisson random graphs,Erdos-Renyi graphs)

Null model 2: random graphs constrained to the set ofdegrees of the original graph

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

network null-models

Network structures are always relative . . .

. . . one has to be clear about what to compare with . . . a nullmodel

Null model 1: random graphs (Poisson random graphs,Erdos-Renyi graphs)

Null model 2: random graphs constrained to the set ofdegrees of the original graph

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random graphs

with probability p, add an edgefor each pair of vertices,

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphchoose edge pairs, and swap them

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphchoose edge pairs, and swap them

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphchoose edge pairs, and swap them

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphchoose edge pairs, and swap them

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphchoose edge pairs, and swap them

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphedge triples can be swapped too

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphedge triples can be swapped too

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphedge triples can be swapped too

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

random rewiring

start from the original graphedge triples can be swapped too

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

why (mechanistic) models?

to understand the mechanisms behind network evolution

to predict the future

to generate test networks for studies about dynamics

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

why (mechanistic) models?

to understand the mechanisms behind network evolution

to predict the future

to generate test networks for studies about dynamics

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

why (mechanistic) models?

to understand the mechanisms behind network evolution

to predict the future

to generate test networks for studies about dynamics

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

why (mechanistic) models?

to understand the mechanisms behind network evolution

to predict the future

to generate test networks for studies about dynamics

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

model what?

observed network structural quantities

possible structure altering events (attacks, overloadbreakdowns)

dynamic processes on the network

interaction between such processes and network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

model what?

observed network structural quantities

possible structure altering events (attacks, overloadbreakdowns)

dynamic processes on the network

interaction between such processes and network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

model what?

observed network structural quantities

possible structure altering events (attacks, overloadbreakdowns)

dynamic processes on the network

interaction between such processes and network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

model what?

observed network structural quantities

possible structure altering events (attacks, overloadbreakdowns)

dynamic processes on the network

interaction between such processes and network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

model what?

observed network structural quantities

possible structure altering events (attacks, overloadbreakdowns)

dynamic processes on the network

interaction between such processes and network evolution

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

Barabasi–Albert model

probability of attachment: ∝ ki

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

Barabasi–Albert model

probability of attachment: ∝ ki

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

Barabasi–Albert model

probability of attachment: ∝ ki

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

Barabasi–Albert model

probability of attachment: ∝ ki

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

Barabasi–Albert model

probability of attachment: ∝ ki

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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 ondynamics)

information spreads faster

but there is a danger of congestion

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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 ondynamics)

information spreads faster

but there is a danger of congestion

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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 ondynamics)

information spreads faster

but there is a danger of congestion

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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 ondynamics)

information spreads faster

but there is a danger of congestion

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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 ondynamics)

information spreads faster

but there is a danger of congestion

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

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 ondynamics)

information spreads faster

but there is a danger of congestion

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

clustering

slows down disease spreading

makes memory worse in neural networks

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

clustering

slows down disease spreading

makes memory worse in neural networks

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

clustering

slows down disease spreading

makes memory worse in neural networks

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

assortativity

high assortativity facilitates small disease outbreaks

in disassortative networks outbreaks don’t form easily, but ifthey do they can cover a larger fraction of the population

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

assortativity

high assortativity facilitates small disease outbreaks

in disassortative networks outbreaks don’t form easily, but ifthey do they can cover a larger fraction of the population

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

assortativity

high assortativity facilitates small disease outbreaks

in disassortative networks outbreaks don’t form easily, but ifthey do they can cover a larger fraction of the population

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

applications

navigation

system control

prediction

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

applications

navigation

system control

prediction

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

applications

navigation

system control

prediction

Petter Holme Complex Networks: My view & research

introductionnetwork structure

modelstopology vs. dynamics

applications

navigation

system control

prediction

Petter Holme Complex Networks: My view & research