A 
-core of a graph 
is a maximal induced subgraph
of 
in which every vertex has vertex
degree at least 
within that subgraph (Seidman 1983). Equivalently, the 
-core is obtained by repeatedly deleting vertices of degree
less than 
until no such vertices remain. A 
-core may be disconnected, in which case
each connected component is itself sometimes
called a 
-core of the original graph.
The largest value 
such that a graph 
has a 
-core is called the graph
degeneracy of 
.
The nested family of all 
-cores
is called the core decomposition of 
and can be computed in linear time in the number of edges
(Batagelj and Zaveršnik 2003).
Algorithm for Cores Decomposition of Networks." 25
Oct 2003.