{smcl}
{* *! version 1.1 05April2020}{...}

{title:Title}

{p2colset 9 18 22 2}{...}
{p2col :nw_projection {hline 2} Projects a bipartite network into one of its two dimensions.}
{p2colreset}{...}


{title:Syntax}

{p 8 17 2}
{cmdab: nw_projection}
[{cmd:,}
{opt X()}
{opt Y()}
{opt sequence()}
{opt nsequence()}
{opt output()}
{opt netname()}
{opt binary}
{opt normalize}
]


{synoptset 25 tabbed}{...}
{synopthdr}
{synoptline}
{synopt:{opt X(varname)}} Indicate the set of nodes into which the projection is generated. Required.

{synopt:{opt Y(varname)}} Indicate the second set of nodes in the initial bipartite network. Required .

{synopt:{opt s:equence(varname)}} For directed projections : Indicate the sequence of linkages.

{synopt:{opt ns:equence()}} Indicate the nomber of previous sequences to be considered. Default is all of them. 

{synopt:{opt out:put()}} Output display, eitheir adjacency {it:matrix} (default) or {it:edgelist} 

{synopt:{opt net:name()}} Name of the resulting network  

{synopt:{opt norm:alize}} Build a normalized network (max weight=1).

{synopt:{opt bin:ary}} Build a binary network (all positive edges' weights set to 1).

{synoptline}
{p2colreset}{...}



{title:Description}

{pstd}
A bipartite network is made of two sets of nodes (X and Y) where only connections between nodes in different sets are allowed.
From an edgelist of a bipartite network, {cmd:nw_projection} returns the resulting projection into one dimension (Zhou et al., 2007, Phys. Rev. E). A projection consists in liking two nodes in the same set X according to the number of neighboring Y nodes.
The projection reduces the network into a unimodular one where remaining X nodes are identified in the {cmd:X(varlist)}. The Y nodes must be identified in {cmd:Y(varlist)}.

{pstd}
{cmd:nw_projection} returns etiher the adjacency matrix of the projected network, or its edgelist, and the former dataset is deleted. The adjacency matrix is also stored as a mata matrix, and as a network.

{pstd}
By default, the resulting matrix is weighted by the frequency of linkages from the bipartite network. Options {cmd:binary} or {cmd:normalize} can modify the weights.

{pstd}
A directed network can be generated by providing a sequence order of linkages in the initial bipartite network in option {cmd:sequence(varlist)}. Then the subsequent option {cmd:nsequence(#)} indicates how many previous linkages' sequence are considered. 

{pstd}
{cmd:nw_projection} Note that nw_projection requires {bf : nwcommands} package developed by Thomas Grund (see below).

{title:Examples}

clear
input float X_nodes str1 Y_nodes 
1 "A" 
1 "B" 
1 "C" 
2 "C" 
3 "A" 
3 "B" 
end

nw_projection , x(X_nodes) y(Y_nodes)  

{pstd} 
clear
input float X_nodes str1 Y_nodes float year
1 "A" 1999
1 "B" 2000
1 "C" 2002
2 "C" 2002
3 "A" 2002
3 "B" 2002
end

nw_projection , x(X_nodes) y(Y_nodes)  sequence(year) nsequence(2) 


{title:Saved results}
{pstd}{cmd:nw_projection} saves the following in {cmd:r()}:

{synoptset 14 tabbed}{...}
{p2col 5 20 30 2: matrices}{p_end}
{synopt:{cmd:r(M_proj)}} Adjacency matrix of projected network {p_end}
{p2colreset}{...}

{pstd}{cmd:nw_projection} also saves the adjacency matrix in a Mata matrix {it:M}:
{cmd:. mata M_proj}

{title:See also}	
{pstd}
{cmd:nw_projection}  requires the {bf : nwcommands} package developed by Thomas Grund.

{pstd}

For do-files and ancillary files, see:

	{cmd:. net describe nwcommands-ado, from(http://www.nwcommands.org)}
	}
For help files, see :

	{cmd:. net describe nwcommands-hlp, from(http://www.nwcommands.org)}
	}


{title:Author}
Charlie Joyez, Université Côte d'Azur
charlie.joyez@univ-cotedazur.fr