Jean-Loup Guillaume and Matthieu Latapy
Physica A 371, pages 795-813, 2006. Extended abstract published in LNCS, proceedings of the 1-st international workshop on Combinatorial and Algorithmic Aspects of Networking CAAN’04, 2004, Banff, Canada
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here the first model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some real-world observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution.
Indeed, we show that any complex network can be viewed as a bipartite graph with some specific characteristics, and that its main properties can be viewed as consequences of this underlying structure.
We also propose a growing model based on this observation.
Anne-Ruxandra Carvunis, Matthieu Latapy, Annick Lesne, Clémence Magnien and Laurent Pezard
Physica A 367, pages 585-612, 2006
The influence of the network topology on the dynamics of systems of coupled excitable
units is studied numerically and demonstrates a lower dynamical variability for power-law networks than for Poisson ones. This effect which reflects a robust collective excitable behavior is however lower than that observed for diffusion processes or network robustness. Instead, the presence (and number) of triangles and larger loops in the networks appears as a parameter with strong influence on the considered dynamics.
Pascal Pons and Matthieu Latapy
Journal of Graph Algorithms and Applications (JGAA) vol. 10, no. 2, pages 191-218, 2006. Extended abstract published in LNCS, proceedings of the 20-th International Symposium on Computer and Information Sciences ISCIS’05, 2005, Istambul, Turquie
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn) and space O(n) in the worst case, and in time O(n log n) and space O(n) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.
Stevens Le Blond, Jean-Loup Guillaume and Matthieu Latapy
LNCS, proceedings of the 4-th International workshop on Peer-to-Peer Systems IPTPS’05, 2005, Ithaka, New York, USA
We propose here an analysis of a rich dataset which gives an exhaustive and dynamic view of the exchanges processed in a running eDonkey system. We focus on correlation in term of data exchanged by peers having provided or queried at least one data in common. We introduce a method to capture these correlations (namely the
data clustering), and study it in detail. We then use it to propose a very simple and efficient way to group data into clusters and show the impact of this underlying structure
on search in typical P2P systems. Finally, we use these results to evaluate the relevance and limitations of a model proposed in a previous publication. We indicate some realistic
values for the parameters of this model, and discuss some possible improvements.
Pierre Fraigniaud, Philippe Gauron and Matthieu Latapy
LNCS, proceedings of the 11-th international conference Euro-Par, 2005, Lisbonne, Portugal
It appeared recently that user interests in a P2P system possess clustering properties that may be used to reduce significantly the amount of traffic of flooding-based
search strategies. It was also observed that they possess scale-free properties that may be used for the design of efficient routing-based search strategies.
In this paper, we show that the combination of these two properties make it possible to design an efficient and simple fully decentralized search strategy.
Further, simulations processed on real-world traces show that other unidentified properties hidden in actual queries make our protocol even more efficient, performing searches in logarithmic expected number of steps.
Jean-Loup Guillaume and Matthieu Latapy
Complex Systems 16, pages 83-94, 2005
In order to study some complex networks like the Internet, the Web, social networks or biological networks, one first has to explore them. This gives a partial and biased view of the real object, which is generally assumed to be representative of the whole. However, up to now nobody knows how and how much the measure influences the results.
Using the example of the Internet and a rough model of its exploration process, we show that the way a given complex network is explored may strongly influence the observed properties. This leads us to argue for the necessity of developing a science of metrology of complex networks. Its aim would be to study how the partial and biased view of a network relates to the properties of the whole network.
Jean-Loup Guillaume, Matthieu Latapy and Damien Magoni
Computer Networks 50, pages 3197-3224, 2006. Extended abstract published in the proceedings of the 24-th IEEE international conference Infocom’05, 2005, Miami, USA
Internet maps are generally constructed using
the traceroute tool from a few sources to many destinations.
It appeared recently that this exploration process
gives a partial and biased view of the real topology, which
leads to the idea of increasing the number of sources to improve
the quality of the maps. In this paper, we present a set
of experiments we have conducted to evaluate the relevance
of this approach. It appears that the statistical properties
of the underlying network have a strong influence on the
quality of the obtained maps, which can be improved using
massively distributed explorations. Conversely, some statistical
properties are very robust, and so the known values
for the Internet may be considered as reliable. We validate
our analysis using real-world data and experiments, and we
discuss its implications.
Fabien Viger and Matthieu Latapy
Extended abstract published in LNCS, proceedings of the 11-th international conference on Computing and Combinatorics COCOON’05, 2005, Kunming, Yunnan, Chine
We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm suitable for practical use both because of its ability to generate very large graphs (efficiency) and because it is easy to implement (simplicity). We focus on a family of heuristics for which we introduce optimality conditions, and show how this optimality can be reached in practice. We then propose a different approach, specifically designed for real-world degree distributions, which outperforms the first one. Based on a conjecture which we discuss rigorously and study empirically, we finally reduce the best asymptotic complexity bound known so far.
Jean-Loup Guillaume, Matthieu Latapy and Stevens Le-Blond
LNCS, proceedings of the 6-th International Workshop on Distributed Computing IWDC’04, 2004, Kolkata, India
Despite their crucial impact on the performances of P2P systems,
very few is known on peers behaviors in such networks. We propose
here a study of these behaviors in a running environment using a semicentralised
P2P system (eDonkey). To achieve this, we use a trace of the
queries made to a large server managing up to fifty thousands peers simultaneously,
and a few thousands queries per second. We analyse these
data using complex network methods, and focus in particular on the degrees,
their correlations, and their time-evolution. Results show a large
variety of observed phenomena, including the variety of peers behaviors
and heterogeneity of data queries, which should be taken into account
when designing P2P systems.
Jean-Loup Guillaume and Matthieu Latapy
Information Processing Letters (IPL) 90:5, pages 215-221, 2004
The analysis and modelling of various complex networks has received much attention in the last few years. Some such networks display a natural bipartite structure: two kinds of nodes coexist with links only between nodes of different kinds. This bipartite structure has not been deeply studied until now, mainly because it appeared to be specific to only a few complex networks. However, we show here that all complex networks can be viewed as bipartite structures sharing some important statistics, like degree distributions. The basic properties of complex networks can be viewed as consequences of this underlying bipartite structure. This leads us to propose the first simple and intuitive model for complex networks which captures the main properties met in practice.
Jean-Loup Guillaume, Matthieu Latapy and Laurent Viennot
LNCS, proceedings of the 3-rd international conference Web-Age Information Management WAIM’02, 2002, Beijing, Chine. Abstract published in the proceedings of the 11-th international conference World Wide Web WWW’02, 2002, Honolulu, Hawaï
In this paper, we propose a set of simple and efficient methods based on standard, free and widely available tools, to store and manipulate large sets of URLs and large parts of the Web graph. Our aim is both to store efficiently the URLs list and the graph in order to manage all the computations in a computer central memory. We also want to make the conversion between URLs and their identifiers as fast as possible, and to obtain all the successors of an URL in the Web graph efficiently. The methods we propose make it possible to obtain a good compromise between these two challenges, and make it possible to manipulate large parts of the Web graph.