Living Reference Work Entry

Encyclopedia of Social Network Analysis and Mining

pp 1-11

Date: Latest Version

Core Decomposition of Massive, Information-Rich Graphs

  • Francesco BonchiAffiliated withISI Foundation Email author 
  • , Francesco GulloAffiliated withUniCredit, R&D Dept
  • , Andreas KaltenbrunnerAffiliated withEurecat


Core graph decomposition; k-Core decomposition; k-Coreness; k-Cores; k-Shell decomposition


Core decomposition

The set of all k-cores of a graph, for all k.

Core number (or core index)

For each vertex of a graph, the highest order of a core containing that vertex.


The highest order of a core of a graph. It corresponds to the maximum core number over all vertices of the graph.

Distributed graph

Graph that is stored across multiple machines.

Graph (or network)

A set of objects (called vertices or nodes) connected to each other by links (also known as edges or arcs). Links can be represented as unordered or ordered pairs of vertices. In the former case, the graph is said to be undirected, otherwise it is directed. Links may be assigned weights. In this case, the graph is said weighted.

k-core (or core of order k)

Maximal subgraph where each vertex is connected to at least k other vertices within the subgraph.


Subgraph induced by all vertices belonging to the k-core but ...

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