function?[bcE]?=?betweenness_centrality（Avarargin）
%?BETWEENNESS_CENTRALITY?Compute?the?betweenness?centrality?for?vertices.
%
%?bc?=?betweenness_centrality（A）?returns?the?betweenness?centrality?for
%?all?vertices?in?A.??
%
%?[bcE]?=?betweenness_centrality（A）?returns?the?betweenness?centrality?for
%?all?vertices?in?A?along?with?a?sparse?matrix?with?the?centrality?for?each
%?edge.??
%
%?This?method?works?on?weighted?or?weighted?directed?graphs.
%?For?unweighted?graphs?（options.unweighted=1）?the?runtime?is?O（VE）.
%?For?weighted?graphs?the?runtime?is?O（VE?+?V（V+E）log（V））.
%
%?...?=?betweenness_centrality（A...）?takes?a?set?of
%?key-value?pairs?or?an?options?structure.??See?set_matlab_bgl_options
%?for?the?standard?options.?
%???options.unweighted:?use?the?slightly?more?efficient?unweighted
%?????algorithm?in?the?case?where?all?edge-weights?are?equal?[{0}?|?1]??
%???options.ec_list:?do?not?form?the?sparse?matrix?with?edge?[{0}?|?1]
%???options.edge_weight:?a?double?array?over?the?edges?with?an?edge
%???????weight?for?each?node?see?EDGE_INDEX?and?EXAMPLES/REWEIGHTED_GRAPHS
%???????for?information?on?how?to?use?this?option?correctly
%???????[{‘matrix‘}?|?length（nnz（A））?double?vector]
%
%?Note:?the?edge?centrality?can?also?be?returned?as?an?edge?list?using?the
%?options.ec_list?options.??This?option?can?eliminate?some?ambiguity?in?the
%?output?matrix?E?when?the?edge?centrality?of?an?edge?is?0?and?Matlab?drops
%?the?edge?from?the?sparse?matrix.??
%
%?Note:?if?the?edge?centrality?matrix?E?is?not?requested?then?it?is?not
%?computed?and?not?returned.??This?yields?a?slight?savings?in?computation
%?time.??
%
%?Example:
%????load?graphs/padgett-florentine.mat
%????betweenness_centrality（A）

%?David?Gleich
%?Copyright?Stanford?University?2006-2008

%%?History
%??2006-04-19:?Initial?version
%??2006-05-31:?Added?full2sparse?check
%??2007-03-01:?Added?edge?centrality?output
%??2007-04-20:?Added?edge?weight?option
%??2007-07-09:?Restricted?input?to?positive?edge?weights
%??2007-07-12:?Fixed?edge_weight?documentation.
%??2008-10-07:?Changed?options?parsing
%%

[trans?check?full2sparse]?=?get_matlab_bgl_options（varargin{:}）;
if?full2sparse?&&?~issparse（A）?A?=?sparse（A）;?end

options?=?struct（‘unweighted‘?0?‘ec_list‘?0?‘edge_weight‘?‘matrix‘）;
options?=?merge_options（optionsvarargin{:}）;

%?edge_weights?is?an?indicator?that?is?1?if?we?are?using?edge_weights
%?passed?on?the?command?line?or?0?if?we?are?using?the?matrix.
edge_weights?=?0;
edge_weight_opt?=?‘matrix‘;

if?strcmp（options.edge_weight?‘matrix‘）
????%?do?nothing?if?we?are?using?the?matrix?weights
else
????edge_weights?=?1;
????edge_weight_opt?=?options.edge_weight;
end

if?check
????%?check?the?values
????if?options.unweighted?~=?1?&&?edge_weights?~=?1
????????check_matlab_bgl（Astruct（‘values‘1‘noneg‘1））;
????else
????????check_matlab_bgl（Astruct（））;
????end
????if?edge_weights?&&?any（edge_weights?????????error（‘matlab_bgl:invalidParameter‘?...
????????????????‘the?edge_weight?array

?屬性????????????大小?????日期????時間???名稱
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?????文件????????3525??2020-11-11?17:17??betweenness_centrality.m