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International audienceDifferent graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to represent time-varying networks. We introduce the concept of MultiAspect Graph (MAG) as a graph generalization that we prove to be isomorphic to a directed graph, and also capable of representing all previous generalizations. In our proposal, the set of vertices, layers, time instants, or any other independent features are considered as an aspect of the MAG. For instance, a MAG is able to represent multilayer or time-varying networks, while both concepts can also be combined to represent a multilayer time-varying network and even other higher-order networks. Since the MAG structure admits an arbitrary (finite) number of aspects, it hence introduces a powerful modeling abstraction for networked complex systems. This paper formalizes the concept of MAG and derives theoretical results useful in the analysis of complex networked systems modeled using the proposed MAG abstraction. We also present an overview of the MAG applicability

International audienceGeolocation of Internet hosts enables a new class of location-aware applications. Previous measurement-based approaches use reference hosts, called landmarks, with a well-known geographic location to provide the location estimation of a target host. This leads to a discrete space of answers, limiting the number of possible location estimates to the number of adopted landmarks. In contrast, we propose Constraint-Based Geolocation (CBG), which infers the geographic location of Internet hosts using multilateration with distance constraints to establish a continuous space of answers instead of a discrete one. However, to use multilateration in the Internet, the geographic distances from the landmarks to the target host have to be estimated based on delay measurements between these hosts. This is a challenging problem because the relationship between network delay and geographic distance in the Internet is perturbed by many factors, including queueing delays and the absence of great-circle paths between hosts. CBG accurately transforms delay measurements to geographic distance constraints, and then uses multilateration to infer the geolocation of the target host. Our experimental results show that CBG outperforms previous geolocation techniques. Moreover, in contrast to previous approaches, our method is able to assign a confidence region to each given location estimate. This allows a location-aware application to assess whether the location estimate is sufficiently accurate for its needs

Graph-based models form a fundamental aspect of data representation in Data Sciences and play a key role in modeling complex networked systems. In particular, recently there is an ever-increasing interest in modeling dynamic complex networks, i.e. networks in which the topological structure (nodes and edges) may vary over time. In this context, we propose a novel model for representing finite discrete Time-Varying Graphs (TVGs), which are typically used to model dynamic complex networked systems. We analyze the data structures built from our proposed model and demonstrate that, for most practical cases, the asymptotic memory complexity of our model is in the order of the cardinality of the set of edges. Further, we show that our proposal is an unifying model that can represent several previous (classes of) models for dynamic networks found in the recent literature, which in general are unable to represent each other. In contrast to previous models, our proposal is also able to intrinsically model cyclic (i.e. periodic) behavior in dynamic networks. These representation capabilities attest the expressive power of our proposed unifying model for TVGs. We thus believe our unifying model for TVGs is a step forward in the theoretical foundations for data analysis of complex networked systems.

Abstract:We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper.

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