Extracting information from Extracting information from complex networkscomplex networks

From the metabolism to collaboration networksFrom the metabolism to collaboration networks

Roger GuimeràDepartment of Chemical and Biological Engineering

Northwestern University

Bloomington, April 11th, 2005

High-throughput techniques in biology

Protein interactions in fruit flyGiot et al., Science (2003)

Metabolic network

Large databases for critical infrastructures

World-wide airport network

Large databases for social networks

Collaborations in Econometrica Collaborations in the Astronomical Journal

What do “statistical properties” tell us about the network?

What are the important cities in the world-wide airport network?

Most connected cities

Most central

cities

Cartography of complex Cartography of complex (metabolic) networks(metabolic) networks

with L. A. N. Amaral

Cartography of complex (metabolic) networks

Modules One divides the system into “regions”

Roles One highlights important players

Real metabolic networks are extremely complex…

…and “regions” are not so well defined

Metabolic network of E. coli

One can define a quantitative measure of modularity

Low modularity

High modularity

Newman & Girvan, PRE (2003)

One can define a quantitative measure of modularity

Modularity of a partition: M = (ds – Ds)

Newman & Girvan, PRE (2003); Guimera, Sales-Pardo, Amaral, PRE (2004)

ds: fraction of links within module s

Ds: expected fraction of links within module s, for a random partition

of the nodes

We use simulated annealing to obtain the partition with largest modularity

Simulated Annealing

The new algorithm for module detection outperforms previous algorithms

Now we need to identify the role of each node

We define the within-module degree and the participation coefficient

eddistributuevenly links1

module onein links all0P

Within-module relative degree k: number of links of a node to other nodes in the same module

Within-module degree:

Participation coefficient fis: fraction of links of node i in module s

Participation coefficient: Pi = 1 - fis

k

kkz

2

The within-module degree and the participation coefficient define the role of each node

We define seven different roles

Hubs

Non-hubsPeripheral

Non

-hub

co

nnec

tors

Ultra-peripheral

Pro

vinc

ial

hubs

Con

nect

or

hu

bs

Kin

less

no

n-hu

bsK

inle

ss

hubs

The cartographic representation of the metabolic network of E. coli

Guimera & Amaral, Nature (2005)

The loss rate quantifies the importance of a role

Metabolite Role in Species A Role in Species B A Ultra-peripheral Peripheral B Connector hub Connector hub C Ultra-peripheral LOST D LOST Peripheral ...

Loss rate of role R: ploss(R) = p(lost | R)

Non-hub connectors are more conserved across species than provincial hubs

Comparison between 12 organisms: 4 archaea 4 bacteria 4 eukaryotes

Ultra-perip

heral

Peripheral

Non-hub co

nnecto

rs

Provinc

ial hubs

Connecto

r hubs

1 – Ultra-peripheral 2 – Peripheral 3 – Non-hub connectors

5 – Provincial hubs 6 – Connector hubs

Different networks have different role structures

Collaboration networks: Collaboration networks: Team assembly, network Team assembly, network

structure, and performancestructure, and performance

with B. Uzzi, J. Spiro, and L. A. N. Amaral

Different collaboration networks have different properties

Collaborations in Econometrica Collaborations in the Astronomical Journal

How do collaboration networks grow? How are teams assembled?

A model for collaboration network formation must specify what rules determine the participation of an individual in a team

Balancing expertise and diversity

Expertise Diversity

Performance

But:

Need to incorporate new people

But:

It is easier to work with similar people and with former collaborators

Assembling a new team

1

2

3

5

4

1

Incumbents

25

4

Newcomers

3 p1-p

Assembling a new team

1

2

3

5

4

1

Incumbents

25

434

Assembling a new team

1

2

3

5

4

1

Incumbents

25

4

Newcomers

3

p

1-p4

Assembling a new team

1

2

3

5

4

Newcomers4

6

Assembling a new team

1

2

3

5

4

1

Incumbents

25

4

Newcomers

3

p1-p4

6

Assembling a new team

1

2

3

5

4

1

Incumbents

25

434

6

Assembling a new team

1

2

3

5

4

1

Any incumbent

25

434

6

5

3

Repeat collaboration

1-qq

Assembling a new team

1

2

3

5

4

4

6

5

3

Repeat collaboration

3

Assembling a new team

1

2

3

5

4

4

6 3

1

2

3

5

4

6

The structure of the network depends on the fraction of incumbents...

Guimera, Uzzi, Spiro & Amaral, Science (forthcoming 2005)

...and on the tendency to repeat past collaborations

The size of the “invisible college” increases with the fraction of incumbents, p, and decreases with the tendency to repeat collaborations, q.

Most fields have very similar values of p and q

The fraction of incumbents is positively correlated with the impact factor of journals

The tendency to repeat collaborations is negatively correlated with the impact factor of journals

Conclusions

We need to go one step further in the analysis of complex networks, so that we can provide specific answers to specific problems.

Modules and roles give important information about the structure of a network and about the importance of each node.

Networks with different functions have different role structure.

In creative collaboration networks, the emergence of the invisible college and team performance are correlated to expertise and diversity (in a “network sense”), and there may be a universal optimum.

Acknowledgements

Marta Sales-Pardo, André A. Moreira, and Daniel B. Stouffer.

Fulbright Commission and Spanish Ministry of Education, Culture, and Sports.

More information:http://amaral.northwestern.edu/roger/http://amaral.northwestern.edu/