function?[DP]?=?all_shortest_paths（Avarargin）
%?all_shortest_paths?Compute?the?weighted?all?pairs?shortest?path?problem.
%
%?D?=?all_shortest_paths（A）?returns?the?distance?matrix?D?for?all?vertices
%?where?D（ij）?indicates?the?shortest?path?distance?between?vertex?i?and
%?vertex?j.??
%
%?For?the?Floyd-Warshall?algorithm?this?function?can?return?the?
%?predecessor?matrix?as?well:
%???[D?P]=all_shortest_paths（Astruct（‘algname‘‘floyd_warshall‘））;
%?returns?P?so?that?the?P（ij）?is?the?node?preceeding?j?on?the?path?from
%?i?to?j.??To?build?the?path?between?（ij）?use?the?commands
%???p=[];?while?j~=0?p（end+1）=j;?j=P（ij）;?end;?p=fliplr（p）;
%?
%?...?=?all_shortest_paths（Au...）?takes?a?set?of
%?key-value?pairs?or?an?options?structure.??See?set_matlab_bgl_options
%?for?the?standard?options.?
%???options.algname:?the?algorithm?to?use?
%???????[{‘auto‘}?|?‘johnson‘?|?‘floyd_warshall‘]
%???options.inf:?the?value?to?use?for?unreachable?vertices?
%???????[double?>?0?|?{Inf}]
%???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:?‘auto‘?cannot?be?used?with?‘nocheck‘?=?1.??The?‘auto‘?algorithms
%?checks?the?number?of?edges?in?A?and?if?the?graph?is?more?than?10%?dense
%?it?uses?the?Floyd-Warshall?algorithm?instead?of?Johnson‘s?algorithm.
%
%?Example:
%????load?graphs/clr-26-1.mat
%????all_shortest_paths（A）
%????all_shortest_paths（Astruct（‘algname‘‘johnson‘））
%
%?See?also?JOHNSON_ALL_SP?FLOYD_WARSHALL_ALL_SP.

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

%%?History
%??2006-04-19:?Initial?version
%??2006-05-31:?Added?full2sparse?check
%??2007-03-01:?Added?option?for?predecessor?matrix?from?floyd_warshall
%??2007-04-20:?Added?edge?weight?option
%??2007-07-08:?Fixed?typos?in?strings?and?documentation
%????Removed?fixes?for?the?Johnson?algorithm
%??2007-07-12:?Fixed?edge_weight?documentation.
%??2007-07-21:?Fixed?divide?by?0?error?in?check?for?algorithm?type
%??2008-04-02:?Added?documenation?for?predecessor?matrix
%??2008-10-07:?Changed?options?parsing
%%

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

options?=?struct（‘algname‘?‘auto‘?‘inf‘?Inf?‘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_weight_opt?=?options.edge_weight;
end

if?check
????%?check?the?values?of?the?matrix
????check_matlab_bgl（Astruct（‘values‘1））;
????
????%?set?the?algname
????if?strcmpi（options.algname?‘auto‘）
????????nz?=?nnz（A）;
????????if?（nz/（numel（A）+1）?>?.1）
????????????opti

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????4560??2011-12-03?11:04??Contents.m

?????文件???????3252??2011-12-03?11:04??core_numbers.m

?????文件???????1226??2011-12-03?11:04??cycle_graph.m

?????文件???????1253??2011-12-03?11:04??dag_sp.m

?????文件???????2942??2011-12-03?11:04??depth_first_search.m

?????文件???????2283??2011-12-03?11:04??dfs.m

?????文件???????1603??2011-12-03?11:04??dijkstra_sp.m

?????文件???????2969??2011-12-03?11:04??edge_weight_index.m

?????文件???????1739??2011-12-03?11:04??edge_weight_vector.m

?????文件???????1360??2011-12-03?11:04??edmonds_maximum_cardinality_matching.m

?????文件????????957??2011-12-03?11:04??edmunds_karp_max_flow.m

?????文件????????611??2011-12-03?11:04??erdos_reyni.m

?????文件???????1220??2011-12-03?11:04??floyd_warshall_all_sp.m

?????文件???????2532??2011-12-03?11:04??fruchterman_reingold_force_directed_layout.m

?????文件???????2553??2011-12-03?11:04??grid_graph.m

?????文件???????3631??2011-12-03?11:04??gursoy_atun_layout.m

?????文件???????2550??2011-12-03?11:04??indexed_sparse.m

?????文件???????1071??2011-12-03?11:04??is_kuratowski_graph.m

?????文件???????2080??2011-12-03?11:04??is_straight_line_drawing.m

?????文件???????1051??2011-12-03?11:04??johnson_all_sp.m

?????文件???????3544??2011-12-03?11:04??kamada_kawai_spring_layout.m

?????文件????????886??2011-12-03?11:04??kolmogorov_max_flow.m

?????文件????????861??2011-12-03?11:04??kruskal_mst.m

?????文件????????586??2011-12-03?11:04??kuratowski_subgraph.m

?????文件???????1535??2011-12-03?11:04??lengauer_tarjan_dominator_tree.m

?????文件???????1426??2011-12-03?11:04??make_biconnected_planar.m

?????文件???????1200??2011-12-03?11:04??make_connected.m

?????文件???????1327??2011-12-03?11:04??make_maximal_planar.m

?????文件???????4110??2011-12-03?11:04??matching.m

?????文件???????2976??2011-12-03?11:04??max_flow.m

............此處省略451個文件信息