Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing algorithms use this to accelerate their execution and to bound their time complexity. Yet, only basic orderings have been tested. In this paper, we show that studying the precise cost of algorithms instead of their bounded complexity leads to faster solutions. We introduce cost functions that link ordering properties with the running time of a given algorithm. We prove that their minimization is NP-hard and propose heuristics to obtain new orderings with different trade-offs between cost reduction and ordering time. Using datasets with up to two billion edges, we show that our heuristics accelerate the listing of triangles by an average of 38% when the ordering is already given as an input, and 16% when the ordering time is included.

Community detection is a popular approach to understand the organization of interactions in static networks. For that purpose, the Clique Percolation Method (CPM), which involves the percolation of k-cliques, is a well-studied technique that offers several advantages. Besides, studying interactions that occur over time is useful in various contexts, which can be modeled by the link stream formalism. The Dynamic Clique Percolation Method (DCPM) has been proposed for extending CPM to temporal networks. However, existing implementations are unable to handle massive datasets. We present a novel algorithm that adapts CPM to link streams, which has the advantage that it allows us to speed up the computation time with respect to the existing DCPM method. We evaluate it experimentally on real datasets and show that it scales to massive link streams. For example, it allows to obtain a complete set of communities in under twenty-five minutes for a dataset with thirty million links, what the state of the art fails to achieve even after a week of computation. We further show that our method provides communities similar to DCPM, but slightly more aggregated. We exhibit the relevance of the obtained communities in real world cases, and show that they provide information on the importance of vertices in the link streams.

The Heterogeneous Information Network (HIN) formalism is very flexible and enables complex recommendations models. We evaluate the effect of different parts of a HIN on the accuracy and the diversity of recommendations, then investigate if these effects are only due to the semantic content encoded in the network. We use recently-proposed diversity measures which are based on the network structure and better suited to the HIN formalism. Finally, we randomly shuffle the edges of some parts of the HIN, to empty the network from its semantic content, while leaving its structure relatively unaffected. We show that the semantic content encoded in the network data has a limited importance for the performance of a recommender system and that structure is crucial.

A link stream is a sequence of triplets (t, u, v) meaning that nodes u and v have interacted at time t. Capturing both the structural and temporal aspects of interactions is crucial for many real world datasets like contact between individuals. We tackle the issue of activity prediction in link streams, that is to say predicting the number of links occurring during a given period of time and we present a protocol that takes advantage of the temporal and structural information contained in the link stream. We introduce a way to represent the information captured using different features and combine them in a prediction function which is used to evaluate the future activity of links.

The ability of a node to relay information in a network is often measured using betweenness centrality. In order to take into account the fact that the role of the nodes vary through time, several adaptations of this concept have been proposed to time-evolving networks. However, these definitions are demanding in terms of computational cost, as they call for the computation of time-ordered paths. We propose a definition of centrality in link streams which is node-centric, in the sense that we only take into account the direct neighbors of a node to compute its centrality. This restriction allows to carry out the computation in a shorter time compared to a case where any couple of nodes in the network should be considered. Tests on empirical data show that this measure is relatively highly correlated to the number of times a node would relay information in a flooding process. We suggest that this is a good indication that this measurement can be of use in practical contexts where a node has a limited knowledge of its environment, such as routing protocols in delay tolerant networks.