Enumerating maximal cliques in temporal graphs

Himmel, Anne-Sophie; Molter, Hendrik; Niedermeier, Rolf; Sorge, Manuel

doi:10.1109/asonam.2016.7752255

Cited by 32 publications

(26 citation statements)

References 22 publications

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“…Similarly, Jethava and Beerenwinkel [25] formulate the densestcommon-subgraph problem on an input that can be interpreted as a special type of temporal network, i.e., a set of graphs sharing the same vertex set. The notion of ∆-clique has been proposed in [23,40], as a set of vertices in which each pair is in contact at least every ∆ timestamps. Complementary approaches study the problem of discovering dense temporal subgraphs whose edges occur in short time intervals considering the exact timestamp of the occurrences [34], and the problem of maintaining the densest subgraph in the dynamic graph model [13].…”

Section: Background and Related Workmentioning

confidence: 99%

Mining (maximal) Span-cores from Temporal Networks

Galimberti

Barrat

Bonchi

et al. 2018

Proceedings of the 27th ACM International Conference on Information and Knowledge Management

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When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). We tackle this task by introducing a notion of temporal core decomposition where each core is associated with its span: we call such cores span-cores.As the total number of time intervals is quadratic in the size of the temporal domain T under analysis, the total number of span-cores is quadratic in |T | as well. Our first contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the maximal span-cores, i.e., span-cores that are not dominated by any other span-core by both the coreness property and the span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly compute the maximal ones without computing all span-cores.Experimentation on several real-world temporal networks confirms the efficiency and scalability of our methods. Applications on temporal networks, gathered by a proximity-sensing infrastructure recording face-to-face interactions in schools, highlight the relevance of the notion of (maximal) span-core in analyzing social dynamics and detecting/correcting anomalies in the data.

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Section: Background and Related Workmentioning

confidence: 99%

Mining (maximal) Span-cores from Temporal Networks

Galimberti

Barrat

Bonchi

et al. 2018

Proceedings of the 27th ACM International Conference on Information and Knowledge Management

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show abstract

“…The link streams model is one of them, aiming at providing tools of wider generality for dynamics structures [16]. The model was used in a network-security study [25], while some graph algorithms are progressively adapted to it [12]. Up to our knowledge, our work is the first attempt at using a time-varying graph model in a recommender system setting.…”

Section: Related Workmentioning

confidence: 99%

Augmenting content-based rating prediction with link stream features

Viard

Fournier-S’niehotta

2019

Computer Networks

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While graph-based collaborative filtering recommender systems have been introduced several years ago, there are still several shortcomings to deal with, the temporal information being one of the most important. The new link stream paradigm is aiming at extending graphs for correctly modelling the graph dynamics, without losing crucial information. We investigate the impact of such link stream features for recommender systems. We design link stream features, that capture the intrinsic structure and dynamics of the data. We show that such features encode a fine-grained and subtle description of the underlying system. We focused on a traditional recommender system context, the rating prediction on the MovieLens20M movie dataset and the Goodreads book dataset. We input link stream features along with some content-based ones into a gradient boosting machine (XGBoost) and show that it outperforms significantly a sole content-based solution. These encouraging results call for further exploration of this original modelling and its integration to complete state-of-the-art recommender systems algorithms. Link streams and graphs, as natural visualizations of recommender systems, may offer more interpretability in a time when algorithm transparency is an increasingly important topic of discussion. We also hope that these results will sparkle interesting discussions in the community about the connections between link streams and traditional methods (matrix factorization, deep learning).

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“…We explore cliques as patterns of interest in IP traffic. It is easy to extend to the bipartite case the (non-bipartite) algorithm presented in [4]. However, we face two issues.…”

Section: Finding Cliques Of Interestmentioning

confidence: 99%

Discovering Patterns of Interest in IP Traffic Using Cliques in Bipartite Link Streams

Viard

Fournier-S’niehotta

Magnien

et al. 2018

Complex Networks IX

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Studying IP traffic is crucial for many applications. We focus here on the detection of (structurally and temporally) dense sequences of interactions, that may indicate botnets or coordinated network scans. More precisely, we model a MAWI capture of IP traffic as a link streams, i.e. a sequence of interactions (t1, t2, u, v) meaning that devices u and v exchanged packets from time t1 to time t2. This traffic is captured on a single router and so has a bipartite structure: links occur only between nodes in two disjoint sets. We design a method for finding interesting bipartite cliques in such link streams, i.e. two sets of nodes and a time interval such that all nodes in the first set are linked to all nodes in the second set throughout the time interval. We then explore the bipartite cliques present in the considered trace. Comparison with the MAWILab classification of anomalous IP addresses shows that the found cliques succeed in detecting anomalous network activity.

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Enumerating maximal cliques in temporal graphs

Cited by 32 publications

References 22 publications

Mining (maximal) Span-cores from Temporal Networks

Mining (maximal) Span-cores from Temporal Networks

Augmenting content-based rating prediction with link stream features

Discovering Patterns of Interest in IP Traffic Using Cliques in Bipartite Link Streams

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