Complex Networks team

Complex Networks team

http://complexnetworks.fr

LIP6 laboratory (CNRS, Sorbonne Universit´e)

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Networks/graphs from different contexts

computer science: internet, P2P, web, usages, etc.

social sciences: friendships, communications, collaborations, exchanges, economics, etc.

biology: brain, genes, proteins, ecosystems, etc.

linguistics: synonymy, co-occurrences, etc.

transportation: roads, air, electrical networks, etc etc

Various contexts, but common properties

common problems to solve

Some common questions

Measurement and metrology

How to acquire data about these networks? Reliability?

Algorithmic questions

Efficient computations on very large networks

Modeling

Generate artificial networks resembling a given network

⇒Goals: understanding, simulations, . . .

Analysis

How to describe the structure of very large networks?

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Computational tools for observing and analysing opinion dynamics in the media

(R. Lamarche-Perrin)

Opinion dynamics in social media (Twitter, Facebook, Instagram) Analysis of interaction patterns:

polarisation effects, echo chambers, filter bubbles, information leadership

Conflicting world views inmass media(printed press)

Study the co-occurrences of countries in articles from different newspapers

field: data analysis, interdisciplinarity

Robustness of Web of Trust Mechanisms (N. Gensollen and M. Latapy)

Motivations:

CryptocurrencyG1: a cryptocurrency in which each member receives the same share of the monetary growth

For this to work, each account should match exactly one person⇒based on a web of trust

Objectives of the internship:

Model and describeG1 web of trust as a dynamical network Study the robustnessof generated and existing webs of trust against malicious attacks

Propose sets of rulesthat guarantee the integrity of the system

field: data analysis, modeling

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Node Ordering for Efficiency and Compression (M.Danisch)

Handling very large graphs (billion of nodes, links)

Ordering nodes is a key problem to solve a variety of problems:

listing cliques, counting motifs, compressing graphs . . . Project: design efficient orderings to make compression algorithms more efficient

field: algorithmics

Studying a random graph model conserving maximal bicliques in bipartite networks

(F.Tarissan, L.Tabourier)

Random generation :

Erdös Rényi

Con g.

Model size and

density

+ degree

distribution +

Random Bipartite local density +

Real graph redundancy ?

+

A B C D

α β

3 2

1 4 5 6 t

A B C D

α β

3 2

1 4 5 6

A B C D

3 2

1 4 5 6 t

Rand Bip

?

Several research questions:

Algorithmics: How to (efficiently)enumeratebicliques? Tripartite encoding: Which tripartite encodingstrategy? Generation: Whichrandomizationprocess ?

−→Empirical approach:Starting fromreal bipartite data.

field: modeling

http://complexnetworks.fr 7/9

Studying a random graph model conserving maximal bicliques in bipartite networks

(F.Tarissan, L.Tabourier)

Random generation :

Erdös Rényi

Con g.

Model size and

density

+ degree

distribution +

Random Bipartite local density +

Real graph redundancy ?

+

A B C D

α β

3 2

1 4 5 6 t

A B C D

α β

3 2

1 4 5 6

A B C D

3 2

1 4 5 6 t

Rand Bip ^{A B C D}

3 2

1 4 5 6

Several research questions:

Algorithmics: How to (efficiently)enumeratebicliques? Tripartite encoding: Which tripartite encodingstrategy? Generation: Whichrandomizationprocess ?

−→Empirical approach:Starting fromreal bipartite data.

field: modeling

Studying a random graph model conserving maximal bicliques in bipartite networks

(F.Tarissan, L.Tabourier)

Random generation :

Erdös Rényi

Con g.

Model size and

density

+ degree

distribution +

Random Bipartite local density +

Real graph redundancy ?

+

A B C D

α β

3 2

1 4 5 6 t

A B C D

α β

3 2

1 4 5 6

A B C D

3 2

1 4 5 6

≡

A B C D

5 2

1 3 4 6

Several research questions:

Algorithmics: How to (efficiently)enumeratebicliques?

Tripartite encoding: Which tripartite encodingstrategy?

Generation: Whichrandomizationprocess ?

−→Empirical approach:Starting fromreal bipartite data.

field: modeling

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Random graph models with fixed constraints:

proving the validity of a generation method (L. Tabourier)

General purpose:

Proposing more realistic graph models Problem:

Limitations of the current methods Internship goal:

Proving the validity of the k-edge switching method What does it mean?

To be discussed. . .

field: graph theory

Conclusion

Topics require

some data manipulation some formal approaches

some taste in interdisciplinary matters To be discussed with the applicant

More details: http://www.complexnetworks.fr/projects/

Contact: [email protected]

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