C O M P L E X     N E T W O R K S

Winter School on Complex Networks 2014

Network science (aka the science of Complex Networks) has emerged in the last ten years as an inter-disciplinary and yet distinct research field, seeking to discover common principles, algorithms and tools that govern networks as different as the Internet, the web, human social networks, gene regulatory networks, the brain, ecosystems, social organizations, transport networks. "How Kevin Bacon cured cancer" is a very nice introductory video to this new science, including interviews to many of the pioneers in this field.

This winter school is the opportunity to learn about the fundamentals of network science, but also to get exposed to ongoing research activities. All the professors are researchers actively working in this field, so they will provide their first hand point of view.

The target audience is made by master and PhD students. The participation is guaranteed to the students of the Master 1 International in Computer Science. PhD students from the local PhD schools or from other institutions are welcome to attend. The participation is free of charge, but registration is required (how to register).



 Monday 27/1Tuesday 28/1Wednesday 29/1Thursday 30/1Friday 31/1
Morning Introduction to Complex Networks 2 (8.30-10.30)
G. Neglia
Software tools for Complex Networks analysis (10.30-12.30)
F. Huet

room K1-K2, Kahn building, Inria
Consensus dynamics (9.00-12.30)
F. Fagnani

room K1-K2, Kahn building, Inria
Navigation in Small Worlds (9.00-12.00)
N. Nisse

room K1-K2, Kahn building, Inria
Semantic Web and Linked Data Graphs (9.00-12.30)
F. Gandon

Amph E, Templiers
Lunch break
Afternoon Introduction to Complex Networks 1 (14.00-16.00)
G. Neglia
Random-Walk based algorithms (16:00-18:00)
K. Avrachenkov

room K1-K2, Kahn building, Inria
Practical session on Complex Networks analysis (14.00-17.00)
F. Huet

room K1-K2, Kahn building, Inria
Complex Network Analysis for Mobility Modeling (14.00-17.00)
T. Spyropoulos

Amph E, Templiers
Practical session on mobility and navigation (14.00-17.00)
N. Nisse, T. Spyropoulos

room K1-K2, Kahn building, Inria
Unveiling the structure of social networks: the Twitter case. (14.00-17.00)
A. Legout, M. Gabielkov

Amph E, Templiers



Introduction to Complex Networks

Teacher: Giovanni Neglia

In these two lessons we introduce the different definitions of complex networks and we question if network science is really a new science. We look at different topological properties usually present in complex networks (small diameters, high clustering, heavy-tailed degree distribution) and present some random graph models that can explain how these properties can arise.

Prerequisites: basics of probability, elementary differential equations solving

Slides: Lecture

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Random-walk based algorithms

Teacher: Konstantin Avrachenkov

Typical questions in the analysis of large complex networks are how large is a network in terms of nodes and links? which nodes are most important/central? the degree distribution follows a power law? if yes, what is the exponent of the power law? how to estimate quickly the clustering coefficient? how to detect quickly principal clusters/communities of the network? All these questions can be answered with the help of the theory of random walks on graphs. In particular, using the theory of random walks on graphs, we can design algorithms with linear or even sublinear complexity. Such light complexity is necessary if we need to deal with networks of billions of nodes and links.

Slides: Part 1, Part 2

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Software Tools for Complex Networks Analysis

Teacher: Fabrice Huet

Analyzing complex networks can be done using various software, depending on the type of analysis, the size of the graph and the runtime environment. Choosing the one best adapted to the problem at hand can make a world of difference. The aim of this lecture is to give a broad (but non exhaustive) view of some of the most commonly used frameworks for analyzing complex graph. We will present the various programming models used and focus on three frameworks: Networkx, Giraph, Hadoop. The following topics will be addressed

This lecture will be followed by a practical session. Prerequisites for the lecture Prerequisites for the practical session

Slides: Lecture, Practical session

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Consensus dynamics over networks

Teacher: Fabio Fagnani consensus

Consensus dynamics is one of the most popular multi-agent dynamical system. It shows up in socio-economic contexts as a model for consensus formation in a society of individuals. In the engineering world, it has been considered as a basic algorithm to be employed in sensor or computer networks for solving global inferential problems. In these lectures we will review the following topics:

  1. Linear consensus dynamics driven by a stochastic matrix. The Perron-Frobenius convergence theory. Analysis of convergence speed in grid-like graphs, graphs with a bottleneck, expansive graphs. Distributed inferential algorthms.
  2. Consensus models in presence of stubborn agents. The electrical network interpretation: agents’ opinion as voltages. Analytic solutions obtained through electrical principles and equivalent transformations. Agreement versus polarization phenomena

Material: Notes, Slides

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Complex Network Analysis for Mobility Modeling

Teacher: Thrasyvoulos Spyropoulos consensus

Realistic mobility models are crucial for the simulation of wireless networks, where mobility plays a key role (e.g. device-to-device networking, vehicular networking, etc.). When mobility is driven by social actors (e.g. humans carrying mobile devices, human-driven vehicles, etc.) the underlying social networks of these actors and the locations they are moving between, will significantly affect the observed mobility behaviors. Understanding these (hidden) underlying links can be done by macroscopic analysis of mobility traces using complex/social network analysis, where rather than focusing on micro-time scales and individual interactions, one builds a (complex) graph of node interactions over a larger time scale. Observing the properties of the graph has been shown to lead to better algorithm design, and performance predictions formulas (e.g. of information dissemination) that would otherwise be very difficult to obtain, among other things. This lecture will comprise:

  1. a short background on standard mobility modeling techniques
  2. how mobility data traces can be modeled as complex networks
  3. an analysis of such networks for some real mobility traces collected
  4. applications of the complex network analysis approach on improving mobility models, designing networking protocols, and predicting performance.

Slides: Part 1, Part 2

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Navigation in Small Worlds

Teacher: Nicolas Nisse

The Milgram experiment (1967) has shown that the "human network" has small diameter and that short paths could be found using only local knowledge. Various theoretical models have been proposed in order to understand this behaviour. Augmenting graphs (Kleinberg 2000) provide an interesting approach for this purpose. An augmenting graph consists of an undirected graph (representing the global knowledge) plus some directed links that are only known locally. We survey some recent results based on the seminal work of Kleinberg. In particular, we show how greedy routing schemes may perform well on these networks. To conclude this talk (if time allows), we will present some algorithms that have recently allowed to compute the diameter of large social networks.

Prerequisites: basics of probability, basics of graph theory

Material: Notes

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Practical Session on Mobility and Navigation

Material: Exercise on navigation, Exercise on mobility

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Semantic Web and Linked Data Graphs

lod-cloud Teacher: Fabien Gandon

This course will provide an introduction to the semantic web graph formalisms with both an historical perspective and an explanation based on the web architecture core concepts. We will first introduce RDF as a W3C standard oriented labelled multi-graph model for data linkage on the web. We will then proceed with the SPARQL query and manipulation language for RDF data and RDFS and OWL schema languages to type and reason over RDF data. Applications and practical sessions will use the Corese/KGRAM engine.


Slides: Lecture

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Unveiling the structure of social networks: the Twitter case

image_fol_fri-crop Teachers: Arnaud Legout, Maksym Gabielkov

In this course, we will explore how to practically unveil the inner structure of social networks, and we will discuss its possible applications. We will use as a use case, Twitter, the most popular micro blogging system, with more than 500 millions users. In a first part, we will show how such a large system can be crawled in order to retrieve the full social graph interconnecting Twitter accounts. Then, we will show how to unveil the inner structure of this social graph using. We will discuss both simple theoretical aspects and practical issues. Finally, we will present how to sample a social graphs, discuss the bias of state of the art techniques, and explain how to solve this bias.

Prerequisites: classical computer science background (internet protocols, basic graph theory).

Slides: Lecture

Back to planning


The participation is guaranteed to the students of the Master 1 International in Computer Science. PhD students from the local PhD schools or from other institutions are welcome to attend, but they need to register by sending an email to the school organizer Giovanni Neglia. Participation will be granted to a maximum of 30 students on a first-come, first-served basis. This winter school is recognized by the Ecole Doctorale STIC. Every participant should check the prerequisites and bring his/her own laptop with the required software installed.



The lessons suppose a basic background on probability (some notes are available here), graph theory and internet protocols. The practical sessions require also a knowledge of Python and Java.

Every student should have a laptop with the following software installed: Python (2.x), Java (JDK7 or later), Java Virtual Machine.



The school will be located on the SophiaTech campus. A plan and directions are available here.

Most of the lessons will be given in the rooms K1-K2, at the ground floor of Inria's Kahn building. The lessons on Wednesday afternoon and on Friday will be given in the Amphitheater East of Templiers building.





The students of the Master 1 International in Computer Science have to pass an exam in order to get the corresponding credits. The students will have to answer one open-ended question for each of the module of the winter school.


Last modified: January 30, 2014