Finding Dense Subgraphs in Relational Graphs

Jethava, Vinay; Beerenwinkel, Niko

doi:10.1007/978-3-319-23525-7_39

Cited by 28 publications

(40 citation statements)

References 29 publications

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“…We apply multilayer core decomposition to provide provable approximation guarantees for this problem. We also show that our formulation generalizes the minimum-average densestcommon-subgraph problem studied in [25,49,65,70], and our method achieves approximation guarantees for that problem too. Furthermore, in Section 6, we show how to exploit multilayer core decomposition to speed-up the problem of finding frequent cross-graph quasi-cliques [50].Community search.…”

mentioning

confidence: 67%

“…However, this would mean disregarding the different semantics of the layers, incurring in a severe information loss. Within this view, in this work we generalize the problem studied in [25,49,65,70] by introducing a formulation that accounts for a trade-off between high density and number of layers exhibiting the high density. Specifically, given a multilayer graph G = (V , E, L), the average-degree density of a subset of vertices S in a layer ℓ is defined as the number of edges induced by S in ℓ divided by the size of S, i.e., |E ℓ [S ]| |S | .…”

Section: Challenges Contributions and Roadmapmentioning

confidence: 99%

“…Therefore, it is desirable to design algorithms that effectively exploit the maximality property and extract inner-most cores directly, without first computing a complete decomposition. Then, we show how multilayer core decomposition finds application to the problem of densest-subgraph extraction in multilayer networks [25,49]. As a further application, we exploit multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques [50].…”

Section: Introductionmentioning

confidence: 99%

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Core Decomposition in Multilayer Networks

Galimberti

Bonchi

Gullo

et al. 2020

ACM Trans. Knowl. Discov. Data

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Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far.As a first step in this direction, in this work we study the problem of core decomposition of a multilayer network. Unlike the single-layer counterpart in which cores are all nested into one another and can be computed in linear time, the multilayer context is much more challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting we devise three algorithms which differ in the way they visit the core lattice and in their pruning techniques. We assess time and space efficiency of the three algorithms on a large variety of real-world multilayer networks.We then move a step forward and study the problem of extracting the inner-most (also known as maximal) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. Inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. This allows for a consistent speed up over a naïve method that simply filters out non-inner-most ones from all the cores.Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks. We introduce a definition of multilayer densest subgraph that trades-off between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting.Dense structures in multilayer networks. Several recent works have dealt with the problem of extracting dense subgraphs from a set of multiple graphs sharing the same vertex set, which is a setting equivalent to the multilayer one we study in this work. Jethava and Beerenwinkel [49] define the densest common subgraph problem, i.e., find a subgraph maximizing the minimum average degree over all input graphs, and devise a linear-programming formulation and a greedy heuristic for it. Reinthal et al.[65] provide a Lagrangian relaxation of the Jethava and Beerenwinkel's linear program, which can be solved more efficiently. Semertzidis et al. [70] introduce three more variants of the problem, whose goal is to maximize the average average degree, the minimum minimum degree, and the average minimum degree, respectively. They show that the average-average varia...

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confidence: 67%

Section: Challenges Contributions and Roadmapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Core Decomposition in Multilayer Networks

Galimberti

Bonchi

Gullo

et al. 2020

ACM Trans. Knowl. Discov. Data

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“…At first, we prove that the problem is NP-hard. Then, we show that computing the multilayer core decomposition of the input graph and selecting the core maximizing the proposed multilayer density function achieves a 1 2|L | β -approximation for the general multilayer-densest-subgraph problem formulation, and a 1 2 -approximation for the all-layer specific variant studied in [9,19].…”

Section: Methodsmentioning

confidence: 99%

Cores and Other Dense Structures in Complex Networks

Galimberti

2019

Companion Proceedings of the 2019 World Wide Web Conference

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Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better capture real-world phenomena. Despite the keen interest in a variety of problems, algorithms, and analysis methods for these types of network, the problem of extracting cores and dense structures still has unexplored facets.In this work, we present advancements to the state of the art by the introduction of novel definitions and algorithms for the extraction of dense structures from complex networks, mainly cores. At first, we define core decomposition in multilayer networks together with a series of applications built on top of it, i.e., the extraction of maximal multilayer cores only, densest subgraph in multilayer networks, the speed-up of the extraction of frequent cross-graph quasi-cliques, and the generalization of community search to the multilayer setting. Then, we introduce the concept of core decomposition in temporal networks; also in this case, we are interested in the extraction of maximal temporal cores only. Finally, in the context of discovering polarization in large-scale online data, we study the problem of identifying polarized communities in signed networks.The proposed methodologies are evaluated on a large variety of real-world networks against naïve approaches, non-trivial baselines, and competing methods. In all cases, they show effectiveness, efficiency, and scalability. Moreover, we showcase the usefulness of our definitions in concrete applications and case studies, i.e., the temporal analysis of contact networks, and the identification of polarization in debate networks.

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“…Subgraphs, discovered in the network of Twitter hashtags Twitter# by KGAPPROX algorithm with k = 4, DS = DP = 0.1.interval partitioning and consider only graphs that are span continuous intervals. Other close works are by Jethava and Beerenwinkel[50] and Semertzidis et al[16]. However, these works consider a set of snapshots and search for a single heavy subgraph induced by one or several intervals.…”

mentioning

confidence: 99%

Finding Events in Temporal Networks: Segmentation Meets Densest-Subgraph Discovery

Rozenshtein

Bonchi²,

Gionis

et al. 2018

2018 IEEE International Conference on Data Mining (ICDM)

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In this paper we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event-discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime.A naïve solution to our optimization problem has polynomial but prohibitively high running time complexity. We adapt existing recent work on dynamic densest-subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard even for static graphs. However, on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extended this greedy approach for the case of temporal networks. However, the approximation guarantee does not hold. Nevertheless, according to the experiments, the algorithm finds good quality solutions.

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Finding Dense Subgraphs in Relational Graphs

Cited by 28 publications

References 29 publications

Core Decomposition in Multilayer Networks

Core Decomposition in Multilayer Networks

Cores and Other Dense Structures in Complex Networks

Finding Events in Temporal Networks: Segmentation Meets Densest-Subgraph Discovery

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