sna (version 0.3)

degree: Compute the Degree Centrality Scores of Network Positions

Description

Degree takes a graph stack (dat) and returns the degree centralities of positions within one graph (indicated by nodes and g, respectively). Depending on the specified mode, indegree, outdegree, or total (Freeman) degree will be returned; this function is compatible with centralization, and will return the theoretical maximum absolute deviation (from maximum) conditional on size (which is used by centralization to normalize the observed centralization score).

Usage

degree(dat, g=1, nodes=c(1:dim(dat)[2]), gmode="digraph", diag=FALSE,
    tmaxdev=FALSE, cmode="freeman", rescale=FALSE)

Arguments

dat

Data array to be analyzed. By assumption, the first dimension of the array indexes the graph, with the next two indexing the actors. Provided that FUN is well-behaved, this can be an n x n matrix if only one graph is involved.

g

Integer indicating the index of the graph for which centralities are to be calculated. By default, g==1.

nodes

List indicating which nodes are to be included in the calculation. By default, all nodes are included.

gmode

String indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. gmode is set to "digraph" by default.

diag

Boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. diag is FALSE by default.

tmaxdev

Boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, tmaxdev==FALSE.

cmode

String indicating the type of degree centrality being computed. "indegree", "outdegree", and "freeman" refer to the indegree, outdegree, and total (Freeman) degree measures, respectively. The default for cmode is "freeman".

rescale

If true, centrality scores are rescaled such that they sum to 1.

Value

• A vector containing the degree centrality scores

Details

Degree centrality is the social networker's term for various permutations of the graph theoretic notion of vertex degree: indegree of a vertex, v, corresponds to the cardinality of the vertex set $N^+(v)={i \in V(G) : (i,v) \in E(G)}$; outdegree corresponds to the cardinality of the vertex set $N^-(v)={i \in V(G) : (v,i) \in E(G)}$; and total (or "Freeman") degree corresponds to $\left|N^+(v)\right| + \left|N^-(v)\right|$. (Note that, for simple graphs, indegree=outdegree=total degree/2.) Obviously, degree centrality can be interpreted in terms of the sizes of actors' neighborhoods within the larger structure. See the references below for more details.

References

Freeman, L.C. (1979). ``Centrality in Social Networks I: Conceptual Clarification.'' Social Networks, 1, 215-239.

See Also

centralization

Examples

#Create a random directed graph
dat<-rgraph(10)
#Find the indegrees, outdegrees, and total degrees
degree(dat,cmode="indegree")
degree(dat,cmode="outdegree")
degree(dat)