# The core decomposition of networks: theory, algorithms and applications

@article{Malliaros2019TheCD, title={The core decomposition of networks: theory, algorithms and applications}, author={Fragkiskos D. Malliaros and Christos Giatsidis and Apostolos N. Papadopoulos and Michalis Vazirgiannis}, journal={The VLDB Journal}, year={2019}, volume={29}, pages={61-92} }

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…

## 65 Citations

Hierarchical Core Maintenance on Large Dynamic Graphs

- Computer ScienceProc. VLDB Endow.
- 2021

In this paper, in-depth analyses on the structural properties of the hierarchy are conducted, and well-designed local update techniques are proposed that significantly outperform the baselines on runtime by up to 3 orders of magnitude.

Truss decomposition using triangle graphs

- Computer ScienceSoft Comput.
- 2022

A new structure, called triangle graph is proposed to speed up the process of finding the k -trusses in a large-scale network and prove the correctness and efficiency of the proposed algorithms.

Random Graphs with Prescribed K-Core Sequences: A New Null Model for Network Analysis

- MathematicsWWW
- 2021

This work establishes a new family of network null models that operate on the k-core decomposition, and provides the first efficient sampling algorithm to solve the following basic combinatorial problem: given a graph G, produce a random graph sampled nearly uniformly from among all graphs with the same sequence of core numbers as G.

Multi-stage graph peeling algorithm for probabilistic core decomposition

- Computer ScienceASONAM
- 2021

A multi-stage graph peeling algorithm (M-PA) that has a two-stage data screening procedure added before the previous PA and is more efficient and with the properly set filtering threshold, can produce very similar if not identical dense subgraphs to the previousPA (in terms of graph density and clustering coefficient).

VEK: a vertex-oriented approach for edge k-core problem

- Computer ScienceWorld Wide Web
- 2022

A novel vertex-oriented heuristic algorithm (named VEK), with a well-designed scoring function to guide the search order, that is faster than the state-of-the-art algorithm EKC by 1-3 orders of magnitude.

Alphacore: Data Depth based Core Decomposition

- Computer ScienceKDD
- 2021

This work proposes a novel unsupervised core decomposition method that can be easily applied to directed and weighted networks and evaluates AlphaCore's performance with a focus on financial, blockchain-based token networks, the social network Reddit and a transportation network of international flight routes.

The Generalized Mean Densest Subgraph Problem

- Computer ScienceKDD
- 2021

This paper introduces a new family of dense subgraph objectives, parameterized by a single parameter p, based on computing generalized means of degree sequences of a subgraph, and proves that the standard peeling algorithm can perform arbitrarily poorly on this generalized objective.

Span-core Decomposition for Temporal Networks: Algorithms and Applications

- Computer ScienceACM Trans. Knowl. Discov. Data
- 2021

This paper introduces a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: such cores span-cores, and devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly extract the maximal ones without computing all spans.

Span-core Decomposition for Temporal Networks

- Computer ScienceACM Transactions on Knowledge Discovery from Data
- 2021

This article introduces a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: it derives a connection between this problem and the problem of finding (maximal) span-cores and shows how temporal community search can be solved in polynomial-time via dynamic programming.

## References

SHOWING 1-10 OF 220 REFERENCES

Efficient core decomposition in massive networks

- Computer Science2011 IEEE 27th International Conference on Data Engineering
- 2011

This paper proposes the first external-memory algorithm for core decomposition in massive graphs and demonstrates the efficiency of the algorithm on real networks with up to 52.9 million vertices and 1.65 billion edges.

The k-peak Decomposition: Mapping the Global Structure of Graphs

- Computer ScienceWWW
- 2017

This work presents a novel graph decomposition - the k-peak decomposition- and corresponding algorithm, and performs a theoretical analysis of its properties, and describes a new visualization method, the "Mountain Plot", which can be used to better understand the global structure of a graph.

Density-friendly Graph Decomposition

- Computer ScienceWWW
- 2015

This work defines what it means for a subgraph to be locally-dense, and shows that a nested chain decomposition of the graph, similar to the one given by k-cores, but in this case the components are arranged in order of increasing density, and develops a linear-time algorithm that provides a factor-2 approximation to the optimal locally-Dense decomposition.

Streaming Algorithms for k-core Decomposition

- Computer ScienceProc. VLDB Endow.
- 2013

This paper proposes the first incremental k-core decomposition algorithms for streaming graph data, which locate a small subgraph that is guaranteed to contain the list of vertices whose maximum k-Core values have to be updated, and efficiently process this subgraph to update the k- core decomposition.

Efficient Core Maintenance in Large Dynamic Graphs

- Computer ScienceIEEE Transactions on Knowledge and Data Engineering
- 2014

The main result is that only certain nodes need to update their core numbers when the graph is changed by inserting/deleting an edge, and an efficient algorithm to identify and recompute the core numbers of such nodes is proposed.

Incremental k-core decomposition: algorithms and evaluation

- Computer ScienceThe VLDB Journal
- 2016

This paper proposes a suite of incremental k-core decomposition algorithms for dynamic graph data, and presents incremental algorithms for both insertion and deletion operations, and proposes auxiliary vertex state maintenance techniques that can further accelerate these operations.

K-Core Decomposition of Large Networks on a Single PC

- Computer ScienceProc. VLDB Endow.
- 2015

A thorough analysis of all algorithms concluding that it is viable to compute k-core decomposition for large networks in a consumer-grade PC and an optimized implementation of an external-memory algorithm by Cheng, Ke, Chu, and Ozsu is presented.

Core Discovery in Hidden Graphs

- Computer ScienceArXiv
- 2017

An efficient algorithm is provided to detect the maximal subgraph of $G$ where the induced degree of every node $u \in S_k$ is at least $k$ and results demonstrate that significant performance improvements are achieved in comparison to baseline approaches.

D-cores: measuring collaboration of directed graphs based on degeneracy

- Computer ScienceKnowledge and Information Systems
- 2012

This paper defines a novel D-core framework, extending the classic graph-theoretic notion of $$k$$ -cores for undirected graphs to directed ones, and introduces novel metrics for evaluating the collaborative nature of directed graphs.

Core decomposition of uncertain graphs

- Computer Science, MathematicsKDD
- 2014

It is shown that core decomposition of uncertain graphs can be carried out efficiently as well, and the definitions and methods are evaluated on a number of real-world datasets and applications, such as influence maximization and task-driven team formation.