`Degree`

takes one or more graphs (`dat`

) and returns the degree centralities of positions (selected by `nodes`

) within the graphs indicated by `g`

. 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).

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`dat` |
one or more input graphs. |

`g` |
integer indicating the index of the graph for which centralities are to be calculated (or a vector thereof). By default, |

`nodes` |
vector 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. |

`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. |

`tmaxdev` |
boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, |

`cmode` |
string indicating the type of degree centrality being computed. |

`rescale` |
if true, centrality scores are rescaled such that they sum to 1. |

`ignore.eval` |
logical; should edge values be ignored when computing degree scores? |

Degree centrality is the social networker's term for various permutations of the graph theoretic notion of vertex degree: for unvalued graphs, 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 *|N^+(v)|+|N^-(v)|*. (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.

When `ignore.eval==FALSE`

, `degree`

weights edges by their values where supplied. `ignore.eval==TRUE`

ensures an unweighted degree score (independent of input). Setting `gmode=="graph"`

forces behavior equivalent to `cmode=="indegree"`

(i.e., each edge is counted only once); to obtain a total degree score for an undirected graph in which both in- and out-neighborhoods are counted separately, simply use `gmode=="digraph"`

.

A vector, matrix, or list containing the degree scores (depending on the number and size of the input graphs).

Carter T. Butts buttsc@uci.edu

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

`centralization`

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