:- lib(mtx).
:- lib(real).
:- lib(options). % /2, _append/4.
:- lib(debug_call).
:- lib(stoics_lib:en_list/2).
:- lib(stoics_lib:kv_decompose/3).
% :- lib(wgraph).
% :- lib(wgraph_adjacency).
% :- lib(wgraph_vertices/2 ).
wgraph_plot_defaults( All, Defs ) :-
All = [graph(WgraphIn)|Args],
wgraph( WgraphIn, WgraphPrv ),
( memberchk(orphan_edge_weight(OrphanW),Args) ->
debug( wgraph_plot, 'Provisional: ~w', [WgraphPrv] ),
wgraph_add_edges_for_orphans( WgraphPrv, OrphanW, Wgraph ),
debug( wgraph_plot, 'Augmented: ~w', [Wgraph] ),
debug_call( wgraph_plot, length, augm_graph/Wgraph )
;
WgraphPrv = Wgraph
),
Tail = [width(7),height(7),format(x11),post_call(true)],
( memberchk(layout_call(LayG),Args) ->
layout_plot_qgraph_layout(LayG,Lay)
;
wgraph_adjacency( Wgraph, lp_adj ),
% wgraph_weights( ... )
findall( W, member(_-_:W,Wgraph), Ws ),
( memberchk(layout_mtx(LayF),Args) ->
mtx( LayF, Lay, convert(true) ),
mtx_column_name_options( Lay, x, layout, Xs, Args ),
mtx_column_name_options( Lay, y, layout, Ys, Args )
;
Lay = [row(x)],
gnet <- 'graph.adjacency'(lp_adj, weighted='T', mode ="undirected"),
( memberchk(layout_fun(LayFun),Args) -> true;
% LayFun = layout.fruchterman.reingold.grid ),
LayFun = 'layout.fruchterman.reingold' ),
( memberchk(layout_args(LayArgS),Args) -> en_list(LayArgS,LayArgs);
LayArgs = [] ),
FunCall =.. [LayFun,gnet|LayArgs], % fixme: parameters
layout1 <- FunCall,
Lay1 <- layout1,
findall( X-Y, member([X,Y],Lay1), XYs ),
kv_decompose( XYs, Xs, Ys )
)
),
mtx_column_name_options( Lay, color, Clrs="steelblue1", Clrs, Args ),
mtx_column_name_options( Lay, label_distance, Ldist=0.5, Ldist, Args ),
% Ldegre = -pi/4, although doc says -pi/2
mtx_column_name_options( Lay, label_degree, Ldegree= -0.7853982, Ldegree, Args ),
wgraph_vertices( Wgraph, Nodes ),
( memberchk(labels(Lbls),Args) ->
true
;
% fixme: was labels() instead or label, which is correct?
mtx_column_name_options( Lay, label, Lbls=Nodes, Lbls, Args )
),
( memberchk(stem(Stem),Args) ->
Save = true
;
Save = false,
Stem = wgraph
),
( memberchk(w_threshold(Thres),Args) -> true; Thres=1 ),
append( Args, [ max_width(3), max_weight(max), min_width(1),
min_weight(min), w_threshold(Thres) ], ArgsLim ),
wgraph_plot_weights_widths( Ws, Wis, Hus, ArgsLim ),
maplist( en_list, [Ws,Wis,Hus], [WsL,WisL,HusL] ),
debug_call( wgraph_plot, length, [ws,wis,hus]/[WsL,WisL,HusL] ),
Defs = [useDingbats('TRUE'),orphan_edge_weight(0),label_distance(Ldist),label_degree(Ldegree),save(Save),stem(Stem),colours(Clrs),labels(Lbls),x(Xs),y(Ys),plotter(qgraph),w(Wis),edge_colours(Hus),node_size(8)|Tail].
wgraph_plot_test( Args ) :-
Wg = [a-b:1,a-c:2,b-c:1,a-d:3,e],
Clrs = c("khaki"), Lbls = ["A","B","C","D","E"],
wgraph_plot( Wg, [colours(Clrs),labels(Lbls),width(3)|Args] ).
/** wgraph_plot( +Wgraph, +Opts ).
Display weighted graph Wgraph possibly from an existing layout that may include positions,
colours and labels. Wgraph should be in a form accepted by wgraph/3.
Layout (see below) should be an mtx/1 matrix with at least two columns: x, y defining
the positions of the nodes. In addition if columns: labels and colours are present but
not given in Opts they will be used.
Graph can be an mtx/1 matrix with at least 2 columns: from and to.
In addition column `weight` is also processed. When missing and no weights option
is given, all weights are set to 1.
Opts
* Ropt=Rval
= paired options are passed to the plotter call, see r_call/2
* cnm_colour(Clrs=colour)
= (layout) colours column name
* cnm_label(Lbs=label)
(layout) labels column name
* cnm_x(Xc=x)
(layout) column name for X position coordinate
* cnm_y(Yc=y)
(layout) column name for Y position coordinate
* cnm_from(From=from)
(graph) column name for From column
* cnm_to(To=to)
(graph) column name for To column
* cnm_weight(Wc=weight)
(graph) column name for edge weight
* colours(Clrs="white")
colours for the nodes - should be known to R
* format(Frm=x11)
output format: _pdf_, _x11_ or _none_ (as x11 without explicit <- x11() call).
when Plotter is ggnet2 then Frm can x11 or any file extension recognised by
your installation of ggsave().
* labels(Lbs=`nodes`)
labels for the nodes, _[]_ for none, _false_ for leaving it unset
* layout_call(LayG)
layout R/qgraph function to use for getting x,y coordinates.
defaults to... which is only used if layout_mtx(LayM) is also missing
* layout_mtx(LayM)
used if layout_call(LayG) is not present
* orphan_edge_weight(OEW)
if present an edge is added for every orphan from a medianed node with this weight
* plotter(Plotter=qgraph)
also known: _igraph_ and _ggnet2_
* save(Save=true)
to save the layout and graph, defaults to false if no stem is given
* stem(Stem)
stem of the output file (def. replaces .csv to .pdf if LayM is a file- else wgraph_plot)
* height(H=7)
height of the plot device
* width(W=7)
width of the plot device
* label_distance(LbD=0.5)
distance for vertex labels
* node_size(Vz)
size of nodes, can be prop(Min,Mult)- size being proportional to label length
* wgraph(Wgraph)
the weighted graph (wgraph/1)
* wgraph_mtx(WgMtx)
the matrix from which to extract the graph if one is not given by Wgraph
* w_threshold(Thres=1)
values below that are not ajusted for width
* useDingbats(DingB='TRUE')
when format is pdf, setting this to FALSE, turns the homonym R option for pdf() function
Also see wgraph/2 options for saving the graph (save/1 and stem/1).
==
?- G = [1-2:50,2-3:100], assert( wg(G) ),
?- wg(M), wgraph_plot(M,[]).
?- M = [row(from,to,weight),row(1,2,50),row(2,3,100)], assert(wg0(M) ).
?- wg0(M), wgraph_plot(M,[]).
?- G = [row(from,to,weight),row(1,2,50),row(2,3,100),row(4,'','')], assert(wg1(G) ).
?- wg1(G1), wgraph_plot(G1,true).
?- G = [1-2:200,2-3:400,4], assert(wg1(G) ).
?- wg1(G1), wgraph_plot(G1,true).
?- wg1(G1), wgraph_plot(G1,orphan_edge_weight(0.1) ).
?- wg1(G1), wgraph_plot(G1,plotter(ggnet2) ).
==
==
?- G1=[1-2:200,2-3:400,4], wgraph_plot(G1, [format(svg),stem(g1),save(false),plotter(ggnet2)] ).
==
Produces file: g1.svg
[[../doc/images/g1.svg]]
@author nicos angelopoulos
@version 0.1 2014/11/21
@version 0.2 2016/01/23
@version 0.3 2019/04/21, added ggnet2
*/
wgraph_plot( ArgS ) :-
en_list( ArgS, Args ),
Args = [Wgraph|Rest],
wgraph_plot( Wgraph, Rest ).
wgraph_plot( WgraphIn, ArgS ) :-
en_list( ArgS, Args ),
wgraph( WgraphIn, Wgraph ),
Self = wgraph_plot,
options_append( Self, [graph(Wgraph)|Args], Opts, process(debug) ),
debug( wgraph_plot, 'Options: ~w', [Opts] ),
options( [x(Xs),y(Ys)], Opts ),
length( Xs, Len ),
lp_coords <- matrix( nrow=Len, ncol=2, 0 ),
lp_coords[*,1] <- Xs,
lp_coords[*,2] <- Ys,
options( labels(Labels), Opts ),
options( colours(Clr), Opts ),
elemental_list_template( Clr, Labels, Clrs ),
options( plotter(Plotter), Opts ),
wgraph( _WgFile, Wgraph, Opts ),
% wgraph_plot_save_layout
options( label_distance(Ldist), Opts ),
options( label_degree(Ldegree), Opts ),
options( w(Ws), Opts ),
options( edge_colours(EClrs), Opts ),
debug( wgraph_plot, 'Node colours: ~w', [Clrs] ),
wgraph_plotter( Plotter, Self, Ws, EClrs, Labels, Clrs, Ldist, Ldegree, Opts ),
options( save(Save), Opts ),
wgraph_layout_save( Save, Labels, Xs, Ys, Clrs, Ldist, Ldegree, Opts ),
wgraph_graph_save( Save, Wgraph, Opts ).
% new 19.4.12
wgraph_plotter( ggnet2, Self, Ws, _Hus, Labels, Clrs, _Ldist, _Ldegr, Opts ) :-
debug( Self, 'Labels: ~w', [Labels] ),
debug( Self, 'Clrs: ~w', [Clrs] ),
debug( Self, 'ggnet2 options: ~w', [Opts] ),
memberchk( node_size(Nsz), Opts ),
findall( Wxh, (member(Wx,Ws),Wxh is Wx / 2), Whs ),
( Whs == [] ->
GGopts = [size=Nsz, label=Labels, color=Clrs, 'edge.color'="#BEAED4"]
;
GGopts = [size=Nsz, label=Labels, color=Clrs, 'edge.size'=Whs, 'edge.color'="#BEAED4"]
),
append( Opts, GGopts, ROpts ),
r_call( ggnet2(lp_adj), [rvar(pltv)|ROpts] ),
options( format(Fmt), Opts ),
( Fmt == none ->
<- print(pltv)
;
( Fmt == x11 ->
<- x11(),
<- print(pltv)
;
( compound(Fmt) -> % eg x11(a,b,c)
<- Fmt
;
options( [width(Wi),height(Hi)], Opts ),
options( stem(Stem), Opts ),
file_name_extension( Stem, Fmt, File ),
<- ggsave(file= +File, plot=pltv, width=Wi, height=Hi )
)
)
).
wgraph_plotter( qgraph, Self, _Ws, _Hus, Labels, Clrs, _Ldist, _Ldegr, Opts ) :-
Qopts = [width(Width),height(Height),format(Form)],
options( Qopts, Opts ),
debug( wgraph_plot, 'Qgraph options: ~w', [Qopts] ),
lp_option_output( Form, Width, Height, Opts, Self, OutputL ),
( memberchk(node_size(VszOpt),Opts) ->
lp_option_labels_vsize( VszOpt, Labels, Vsz ),
QTail = [vsize=Vsz|OutputL]
;
QTail = OutputL
),
QgraphL = [layout=lp_coords,normalize='F',width=Width,colors=Clrs,labels=Labels|QTail],
append( QgraphL, Opts, QgOpts ),
r_call( qgraph(lp_adj), QgOpts ).
% fixme add tkplot & RBL
wgraph_plotter( igraph, Self, Ws, HclS, Labels, Clrs, Ldist, Ldegr, Opts ) :-
% edge.width
ilp <- 'graph.adjacency'(lp_adj, mode="undirected", weighted='TRUE' ),
% findall( Arg=Val, member(Arg=Val,Opts), Pairs ),
en_list( HclS, Hcls ),
wgraph_igraph_hue_luminance_vectors( Hcls, 260, Hus, Lus ),
Qopts = [width(Width),height(Height),format(Form)],
options( Qopts, Opts ),
lp_option_r_call_output( Form, Width, Height, Opts, Self, OutputL ),
% 120 = Green, 260 = Blue
maplist( hcl_colour, Hus, Lus, EClrS ),
% r_call( plot.igraph(ilp), [edge.color=EClrs,edge.width=Ws,layout=lp_coords,vertex.color=Clrs,vertex.label=Labels,vertex.label.dist=Ldist,vertex.label.degree=Ldegr|Opts] ).
% findall( Ropt=Rval, member(Ropt=Rval,Opts), RinOpts ),
append( OutputL, Opts, Aopts ),
en_list( EClrS, EClrs ),
% maplist( en_plus, EnpClrs, EClrs ),
Ropts = ['edge.color'=EClrs,'edge.width'=Ws,layout=lp_coords,'vertex.color'=Clrs,'vertex.label'=Labels,'vertex.label.dist'=Ldist,'vertex.label.degree'=Ldegr,'vertex.size'=Vsize|Aopts],
debug( wgraph_plot, 'igraph R options: ~w', [Ropts] ),
options( node_size(Vsize), Opts ),
r_call( 'plot.igraph'(ilp), Ropts ).
% % r_call( plot.igraph(lp_coords[*,1],lp_coords[*,2]), [layout=lp_coords,vertex.color=Clrs,vertex.label=Labels,vertex.label.dist=Ldist|Opts] ).
% <- Qgraph.
% EClrS <- hcl(Hus,l=Lus,c=100),
hcl_colour( Hu, Lu, Clr ) :-
number( Hu ),
!,
Clr <- hcl( Hu, l=Lu, c=100 ).
hcl_colour( Hu, _Lu, Hu ).
wgraph_igraph_hue_luminance_vectors( [], _DefHue, [], [] ).
wgraph_igraph_hue_luminance_vectors( [H|T], DefHue, [Hu|Hus], [Lu|Lus] ) :-
% ( atomic(H) -> Hu = DefHue, Lu = H ; H=(Hu-Lu) ),
( H=(Hu-Lu) -> true ; Hu=DefHue, Lu=H ),
wgraph_igraph_hue_luminance_vectors( T, DefHue, Hus, Lus ).
wgraph_plot_weights_widths( Wes, Wis, Hus, Opts ) :-
options( max_width(MaxWi), Opts ),
MaxWi == false,
!,
Wis = Wes,
Hus = 50.
wgraph_plot_weights_widths( Wes, Wis, Hus, Opts ) :-
Lims = [max_width(MaxWiM),max_weight(MaxWeM),min_width(MinWiM),min_weight(MinWeM)],
options( w_threshold(Thres), Opts ),
include( =<(Thres), Wes, ThreWes ),
options( Lims, Opts ),
maplist( wgraph_plot_limit_value(ThreWes), [MaxWiM,MaxWeM,MinWiM,MinWeM], [MaxWi,MaxWe,MinWi,MinWe] ),
RangeWe is MaxWe - MinWe,
wgraph_plot_weights_range_widths( RangeWe, MinWe, MaxWi, MinWi, Wes, Thres, Wis, Hus ).
wgraph_plot_weights_range_widths( 0, _MinWe, _MaxWi, _MinWi, Wes, _Thres, Wis, Hus ) :-
!,
Wis = Wes,
Hus = 50.
wgraph_plot_weights_range_widths( RangeWe, MinWe, MaxWi, MinWi, Wes, Thres, Wis, Hus ) :-
Factor is RangeWe / (MaxWi - MinWi),
maplist( wgraph_plot_scale_widths(MinWi,MinWe,Factor,Thres,0.0000001), Wes, Wis ),
MaxHu = 50, MinHu = 90, % higher, means lighter colour, so we are reversing
HuFact is (MaxWi - MinWi) / (MaxHu - MinHu ),
maplist( wgraph_plot_scale_widths(MinHu,MinWi,HuFact,Thres,"white"), Wis, Hus ).
wgraph_plot_scale_widths( _MinWi, _MinWe, _Factor, Thres, Def, We, Wi ) :-
We < Thres,
!,
Wi = Def.
wgraph_plot_scale_widths( MinWi, MinWe, Factor, _Thres, _Def, We, Wi ) :-
Wi is MinWi + ((We - MinWe) / Factor ).
wgraph_plot_limit_value( Wes, Tkn, Val ) :-
atom( Tkn ),
!,
atomic_concat( Tkn, '_list', Pname ),
Goal =.. [Pname,Wes,Val],
( call(Goal) -> true; Val is 1 ).
wgraph_plot_limit_value( _Wes, Val, Val ) :-
number( Val ).
wgraph_plot_lp_adj( [], [], [], _Rvar ).
wgraph_plot_lp_adj( [F|Fs], [T|Ts], [W|Ws], Rvar ) :-
Rvar[F,T] <- W,
wgraph_plot_lp_adj( Fs, Ts, Ws, Rvar ).
lp_option_output( pdf, _W, _H, Opts, Self, Output ) :-
lp_option_stem( Self, Stem, Opts ),
Output = [filetype="pdf", filename=+Stem].
lp_option_output( ps, _W, _H, Opts, Self, Output ) :-
lp_option_stem( Self, Stem, Opts ),
Output = [filetype="postscript", filename=+Stem].
lp_option_output( x11, W, H, _Opts, _Self, [filetype=""] ) :-
<- x11( width = W, height = H ).
lp_option_output( none, _W, _H, _Opts, _Self, [filetype=""] ).
lp_option_stem( Self, Stem, Opts ) :-
( memberchk(stem(Stem),Opts) ->
true
;
( (memberchk(layout_mtx(MtxF),Opts),\+ is_list(MtxF)) ->
( ( file_name_extension(Stem,Ext,MtxF),
memberchk( Ext, [csv,tsv,tab,txt] )
) ->
true
;
Stem = MtxF
)
;
Stem = Self
)
).
lp_option_r_call_output( pdf, W, H, Opts, Self, Output ) :-
lp_option_stem( Self, Stem, Opts ),
/*
( memberchk(stem(Stem),Opts) ->
true
;
( (memberchk(layout_mtx(MtxF),Opts),\+ is_list(MtxF)) ->
( ( file_name_extension(Stem,Ext,MtxF),
memberchk( Ext, [csv,tsv,tab,txt] )
) ->
true
;
Stem = MtxF
)
;
Stem = Self
)
),
*/
options( useDingbats(UseD), Opts ),
Output = [outputs(pdf(width=W,height=H,'useDingbats'=UseD)), stem(Stem) ].
lp_option_r_call_output( ps, W, H, Opts, Self, Output ) :-
lp_option_stem( Self, Stem, Opts ),
Output = [outputs(postscript(fonts=c("serif"),width=W,height=H)), stem(Stem) ].
lp_option_r_call_output( x11, W, H, _Opts, _Self, Output ) :-
Output = [outputs(x11(width=W,height=H))].
lp_option_r_call_output( none, _W, _H, _Opts, _Self, [] ).
lp_option_labels_vsize( prop(Min,Fact), Labels, Vsz ) :-
!,
maplist( label_name_proportional_vsize(Min,Fact), Labels, Vsz ).
lp_option_labels_vsize( Vsz, _Labels, Vsz ).
label_name_proportional_vsize( Min, Fact, Label, Vsz ) :-
( is_list(Label) -> length(Label,Len); functor(Label,_,Len) ),
Vsz is Min + (Len * Fact).
wgraph_layout_save( false, _Labels, _Xs, _Ys, _Clrs, _Ldist, _Ldegr, _Opts ).
wgraph_layout_save( true, Labels, Xs, Ys, Clrs, Ldist, Ldegr, Opts ) :-
options( stem(Stem), Opts ),
atom_concat( Stem, '_layout', LayStem ),
file_name_extension( LayStem, csv, File ),
elemental_list_template( Ldist, Xs, LdistL ),
elemental_list_template( Ldegr, Xs, LdegrL ),
% ( is_list(Ldegr) -> LdegrL = Ldegr; findall(Ldegr,member(_,Xs),LdegrL) ),
mtx_lists( File, [[label|Labels],[x|Xs],[y|Ys],[color|Clrs],[label_distance|LdistL],[label_degree|LdegrL]] ).
wgraph_graph_save( false, _Graph, _Opts ).
wgraph_graph_save( true, Graph, Opts ) :-
options( stem(Stem), Opts ),
atom_concat( Stem, '_graph', GStem ),
file_name_extension( GStem, csv, File ),
wgraph( File, Graph ).
% fixme: add options and put in separate file:
wgraph_add_edges_for_orphans( InW , Ow, Wgraph ) :-
wgraph_undirected_vertex_edge_count( InW, [], Freq ),
debug( wgraph_plot, 'Edge counts: ~w', [Freq] ),
findall( Count, member(_Vertex-Count,Freq), Counts ),
Med <- median( Counts ),
findall( Orphan, member(Orphan-0,Freq), Orphans ),
findall( NonOrphan-Count, (member(NonOrphan-Count,Freq),Count>0), NonOFreq ),
wgraph_add_edges_for_orphans_counts( Orphans, NonOFreq, Med, NonOFreq, InW, Ow, Wgraph ).
wgraph_add_edges_for_orphans_counts( [], _Freq, _Med, _AllFreq, Wgraph, _Ow, Wgraph ).
wgraph_add_edges_for_orphans_counts( [O|Os], ThisFrq, Med, AllFrq, InW, Ow, Wgraph ) :-
kv_v_over( ThisFrq, Med, AllFrq, [], RemFrq, From ),
debug( _, 'InW: ~w', [InW] ),
wgraph_add_edge_for_orphan( InW, O, From, Ow, NxtW ),
debug( _, 'NxtW: ~w', [NxtW] ),
wgraph_add_edges_for_orphans_counts( Os, RemFrq, Med, AllFrq, NxtW, Ow, Wgraph ).
wgraph_add_edge_for_orphan( Wgraph, Orphan, From, OrphanW, Ngraph ) :-
once( select(Orphan,Wgraph,Rgraph) ),
( From @< Orphan -> Edge = From-Orphan:OrphanW; Edge = Orphan-From:OrphanW ),
ord_add_element( Rgraph, Edge, Ngraph ),
!.
wgraph_add_edge_for_orphan( Wgraph, Orphan, From, _OrphanW, _Ngraph ) :-
throw( could_not_fix_orphan(Orphan,From,Wgraph) ).
/*
wgraph_add_edge_for_orphan( [], Orphan, From, _Ow, _NxtW ) :-
throw( fixme(not_orphan_to_connect_to(Orphan,From)) ).
wgraph_add_edge_for_orphan( [Orphan|T], Orphan, From, Ow, Wgraph ) :-
( From @< Orphan -> Edge = From-Orphan:Ow; Edge = Orphan-From:Ow ),
debug( wgraph_plot, 'Adding orphan edge: ~w', Edge ),
Wgraph = [Edge|T],
!.
wgraph_add_edge_for_orphan( [Edge|T], Orphan, From, Ow, [Edge|R] ) :-
wgraph_add_edge_for_orphan( T, Orphan, From, Ow, R ).
*/
kv_v_over( [], _Med, AllFrq, _Acc, RemFrq, From ) :-
random_member( From-_Count, AllFrq ),
RemFrq = AllFrq.
kv_v_over( [K-V|T], Med, _AllFrq, AccFrq, RemFrq, From ) :-
V > Med,
!,
From = K,
reverse( AccFrq, Left ),
append( Left, T, RemFrq ).
kv_v_over( [K-V|T], Med, AllFrq, AccFrq, RemFrq, From ) :-
kv_v_over( T, Med, AllFrq, [K-V|AccFrq], RemFrq, From ).
wgraph_undirected_vertex_edge_count( [], Freq, Freq ).
wgraph_undirected_vertex_edge_count( [Edge|T], Acc, Counts ) :-
wgraph_undirected_edge_count( Edge, Acc, Nxt ),
wgraph_undirected_vertex_edge_count( T, Nxt, Counts ).
wgraph_undirected_edge_count( From-To:_W, Acc, New ) :-
!,
wgraph_increase_edge_count( Acc, From, Nxt ),
wgraph_increase_edge_count( Nxt, To, New ).
wgraph_undirected_edge_count( Orphan, Acc, Nxt ) :-
atomic( Orphan ),
( ord_member_chk(Acc,Orphan-_Count) ->
Nxt = Acc
;
ord_add_element( Acc, Orphan-0, Nxt )
).
wgraph_increase_edge_count( [], Vertex, [Vertex-1] ).
wgraph_increase_edge_count( [Vertex1-Count|T], Vertex2, Nxt ) :-
compare( Op, Vertex1, Vertex2 ),
wgraph_increase_edge_count_op( Op, Vertex1, Count, Vertex2, T, Nxt ).
wgraph_increase_edge_count_op( =, _Vertex1, Count, Vertex2, T, [Vertex2-Inc|T] ) :-
Inc is Count + 1.
wgraph_increase_edge_count_op( <, Vertex1, Count, Vertex2, T, [Vertex1-Count|R] ) :-
wgraph_increase_edge_count( T, Vertex2, R ).
wgraph_increase_edge_count_op( >, Vertex1, Count, Vertex2, T, [Vertex2-1,Vertex1-Count|T] ).
ord_member_chk( [Elem|_], Elem ) :- !.
ord_member_chk( [H|T], Elem ) :-
H @< Elem,
ord_member_chk( T, Elem ).
en_plus( Elem, +(Elem) ).
elemental_list_template( List, _Template, Elemental ) :-
is_list( List ),
!,
Elemental = List.
elemental_list_template( Elem, Template, Elemental ) :-
% \+ var( Elem ), % fixme: if you want to be steadfast
!,
findall( Elem, member(_,Template), Elemental ).