Tiphaine Viard

Computing maximal cliques in link streams

We introduce delta-cliques, that generalize graph cliques to link streams/time-varying graphs.We provide a greedy algorithm to compute all delta-cliques of a link stream.Implementation available on http://www.github.com/JordanV/delta-cliques. A link stream is a collection of triplets ( t , u , v ) indicating that an interaction occurred between u and v at time t. We generalize the classical notion of cliques in graphs to such link streams: for a given Δ, a Δ-clique is a set of nodes and a time interval such that all pairs of nodes in this set interact at least once during each sub-interval of duration Δ. We propose an algorithm to enumerate all maximal (in terms of nodes or time interval) cliques of a link stream, and illustrate its practical relevance to a real-world contact trace.

Identifying roles in an IP network with temporal and structural density

Captures of IP traffic contain much information on very different kinds of activities like file transfers, users interacting with remote systems, automatic backups, or distributed computations. Identifying such activities is crucial for an appropriate analysis, modeling and monitoring of the traffic. We propose here a notion of density that captures both temporal and structural features of interactions, and generalizes the classical notion of clustering coefficient. We use it to point out important differences between distinct parts of the traffic, and to identify interesting nodes and groups of nodes in terms of roles in the network.

Stream Graphs and Link Streams for the Modeling of Interactions over Time

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the intrinsically temporal and structural nature of interactions, which calls for a dedicated formalism. In this paper, we generalize graph concepts to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher level objects such as quotient graphs, line graphs, k-cores, and centralities. This paper also considers discrete versus continuous time assumptions, instantaneous links, and extensions to more complex cases.

Analysis of the Temporal and Structural Features of Threads in a Mailing-List

A link stream is a collection of triplets (t, u, v) indicating that an interaction occurred between u and v at time t. Link streams model many real-world situations like email exchanges between individuals, connections between devices, and others. Much work is currently devoted to the generalization of classical graph and network concepts to link streams. In this paper, we generalize the existing notions of intra-community density and inter-community density. We focus on emails exchanges in the Debian mailing-list and show that threads of emails, like communities in graphs, are dense subsets loosely connected from a link stream perspective.

Complex Networks and Link Streams for the Empirical Analysis of Large Software

Large software may be modeled as graphs in several ways. For instance, nodes may represent modules, objects or functions, and links may encode dependencies between them, calls, heritage, etc. One may then study a large software through such graphs, called complex networks because they have no strong mathematical properties. Studying them sheds much light on the structure of the considered software. If one turns to the analysis of the dynamics of large software, like execution traces, then the considered graphs evolve over time. This raises challenging issues, as there is currently no clear way to study such objects. We develop a new approach consisting in modeling traces as link streams, i.e. series of triplets (t,a,b) meaning that a and b interacted at time t. For instance, such a triplet may model a call between two modules at run time. Analyzing such streams directly turns out to be much easier and powerful than transforming them into dynamic graphs that poorly capture their dynamics. We present our work on this topic, with directions for applications in software analysis.