kcores | R Documentation |
kcores
calculates the k-core structure of the input network, using the centrality measure indicated in cmode
.
kcores(dat, mode = "digraph", diag = FALSE, cmode = "freeman",
ignore.eval = FALSE)
dat |
one or more (possibly valued) graphs. |
mode |
|
diag |
logical; should self-ties be included in the degree calculations? |
cmode |
the |
ignore.eval |
logical; should edge values be ignored when computing degree? |
Let G=(V,E)
be a graph, and let f(v,S,G)
for v \in V, S\subseteq V
be a real-valued vertex property function (in the language of Batagelj and Zaversnik). Then some set H \subseteq V
is a generalized k-core for f
if H
is a maximal set such that f(v,H,G)\ge k
for all v \in H
. Typically, f
is chosen to be a degree measure with respect to S
(e.g., the number of ties to vertices in S
). In this case, the resulting k-cores have the intuitive property of being maximal sets such that every set member is tied (in the appropriate manner) to at least k others within the set.
Degree-based k-cores are a simple tool for identifying well-connected structures within large graphs. Let the core number of vertex v
be the value of the highest-value core containing v
. Then, intuitively, vertices with high core numbers belong to relatively well-connected sets (in the sense of sets with high minimum internal degree). It is important to note that, while a given k-core need not be connected, it is composed of subsets which are themselves well-connected; thus, the k-cores can be thought of as unions of relatively cohesive subgroups. As k-cores are nested, it is also natural to think of each k-core as representing a “slice” through a hypothetical “cohesion surface” on G
. (Indeed, k-cores are often visualized in exactly this manner.)
The kcores
function produces degree-based k-cores, for various degree measures (with or without edge values). The return value is the vector of core numbers for V
, based on the selected degree measure. Missing (i.e., NA
) edge are removed for purposes of the degree calculation.
A vector containing the maximum core membership for each vertex.
Carter T. Butts buttsc@uci.edu
Batagelj, V. and Zaversnik, M. (2002). “An O(m)
Algorithm for Cores Decomposition of Networks.” arXiv:cs/0310049v1
Batagelj, V. and Zaversnik, M. (2002). “Generalized Cores.” arXiv:cs/0202039v1
Wasserman, S. and Faust,K. (1994). Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.
degree
#Generate a graph with core-periphery structure
cv<-runif(30)
g<-rgraph(30,tp=cv%o%cv)
#Compute the k-cores based on total degree
kc<-kcores(g)
kc
#Plot the result
gplot(g,vertex.col=kc)
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