Core Decomposition and Densest Subgraph in Multilayer Networks

Galimberti, Edoardo; Bonchi, Francesco; Gullo, Francesco

doi:10.1145/3132847.3132993

Cited by 58 publications

(47 citation statements)

References 35 publications

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“…Algorithm h-LB+UB would partition the computation as follows: ⟨ [30,21], [11,20], [3,10]⟩. Instead for S = 1 it would be ⟨ [30,26], [21,25], [16,20], [11,15], [6,10], [3,5]⟩.…”

Section: Algorithm 4 H-lb+ubmentioning

confidence: 99%

Distance-generalized Core Decomposition

Bonchi

Khan

Severini

2019

Proceedings of the 2019 International Conference on Management of Data

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The k-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least k other vertices within that subgraph. In this work we introduce a distancebased generalization of the notion of k-core, which we refer to as the (k, h)-core, i.e., the maximal subgraph in which every vertex has at least k other vertices at distance ≤ h within that subgraph. We study the properties of the (k, h)core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number) and it preserves its usefulness to speed-up or approximate distancegeneralized notions of dense structures, such as h-club.Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm.

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“…Algorithm h-LB+UB would partition the computation as follows: ⟨ [30,21], [11,20], [3,10]⟩. Instead for S = 1 it would be ⟨ [30,26], [21,25], [16,20], [11,15], [6,10], [3,5]⟩.…”

Section: Algorithm 4 H-lb+ubmentioning

confidence: 99%

Distance-generalized Core Decomposition

Bonchi

Khan

Severini

2019

Proceedings of the 2019 International Conference on Management of Data

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“…For each aforementioned context, experiments are provided within the corresponding section. A preliminary version of this work, covering Sections 3 and 5 only, was presented in [39].…”

Section: Challenges Contributions and Roadmapmentioning

confidence: 99%

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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“…In its simplest form, a multilayer graph (a.k.a. multidimensional graph) G(V, E) is composed of a set of nodes V and a set of edge subsets E = E 1 ∪ E 2 ∪ ... ∪ E , where is the total number of layers and E j contains the set of edges present in the j-th layer of G. The first algorithm for computing the core decomposition of a multilayer graph is reported in [53].…”

Section: Multilayer Graphsmentioning

confidence: 99%

The core decomposition of networks: theory, algorithms and applications

et al. 2019

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The core decomposition of networks has attracted significant attention due to its numerous applications in real-life problems. Simply stated, the core decomposition of a network (graph) assigns to each graph node v, an integer number c(v) (the core number), capturing how well v is connected with respect to its neighbors. This concept is strongly related to the concept of graph degeneracy, which has a long history in Graph Theory. Although the core decomposition concept is extremely simple, there is an enormous interest in the topic from diverse application domains, mainly because it can be used to analyze a network in a simple and concise manner by quantifying the significance of graph nodes. Therefore, there exists a respectable number of research works that either propose efficient algorithmic techniques under different settings and graph types or apply the concept to another problem or scientific area. Based on this large interest in the topic, in this survey, we perform an in-depth discussion of core decomposition, focusing mainly on: i) the basic theory and fundamental concepts, ii) the algorithmic techniques proposed for computing it efficiently under different settings, and iii) the applications that can benefit significantly from it.

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Core Decomposition and Densest Subgraph in Multilayer Networks

Cited by 58 publications

References 35 publications

Distance-generalized Core Decomposition

Distance-generalized Core Decomposition

Core Decomposition in Multilayer Networks

The core decomposition of networks: theory, algorithms and applications

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