{{pajek:pics:pajek.gif?100}}
====== Pajek format ======

A //network// **N** = (**V**,**L**,**P**,**W**) is determined with four sets:
  * the set of //nodes// **V**,
  * the set of //links// **L**,
  * the set of //node properties// **P**, and
  * the set of //link properties// (weights) **W** .
The set of nodes and the set of links describe its structure and form a
//graph// **G** = (**V**,**L**). 

**A** = ∅ - undirected graph\\
**E** = ∅ - directed graph

{{pajek:pics:graph.png?400}}

===== Basic formats =====


==== Mathematical description ====



**V**  =  { a, b, c, d, e, f, g, h, i, j, k, l } \\
**A**  =  { (a,b), (a,d), (a,f), (b,a), (b,f), (c,b), (c,c), (c,g)<sub>1</sub>, (c,g)<sub>2</sub>, (e,c), (e,f), (e,h), (f,k), (h,d), (h,l), (j,h), (l,e), (l,g), (l,h) } \\
**E**  =  { (b:e), (c:d), (e:g), (f:h) } \\
**G**  =  ( **V**, (**A**, **E**) ) \\
**L**  =  **A** ∪ **E**

==== Sets ====

The nodes are indexed starting with 1. In listing of links (arcs or edges) their end-nodes are replaced by their indices.

A line describing a node (vertex) has the following components: index, label, X, Y, Z. If the label contains a space it should be put in quotes "la bel". Pajek's internal coordinates X, Y, Z are in the range [0,1]. If your coordinates are out of this range (for example geographical longitude and latitude) you can transform them into the Pajek's range in the drawing window using the option
<code>
Options/Transform/Fit Area
</code>
You can even skip the list of nodes - specifying only the line ''*vertex'' //n//. In this case the node labels will be created automatically and the coordinates are put on the circle.

A line describing a link has the following components: 1st-node-index, 2nd-node-index, weight. If the weight is omitted the default value 1 is used.  

A line starting with % is a comment line.
<code>
% Example network
% by Vladimir Batagelj, April 2003
*Vertices  12
  1 "a"     0.1020  0.3226
  2 "b"     0.2860  0.0876
  3 "c"     0.5322  0.2304
  4 "d"     0.3259  0.3917
  5 "e"     0.5543  0.4770
  6 "f"     0.1552  0.6406
  7 "g"     0.8293  0.3249
  8 "h"     0.4479  0.6866
  9 "i"     0.8204  0.8203
 10 "j"     0.4789  0.9055
 11 "k"     0.1175  0.9032
 12 "l"     0.7095  0.6475
*Arcs
  1  2
  2  1
  1  4
  1  6
  2  6
  3  2
  3  3
  3  7
  3  7
  5  3
  5  6
  5  8
  6 11
  8  4
 10  8
 12  5
 12  7
  8 12
 12  8
*Edges
  2  5
  3  4
  5  7
  6  8
</code>

GraphSet: [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/GraphSet.pdf|PDF]] / [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/GraphSet.net|net]]; TinaSet: [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/TinaSet.pdf|PDF]] / [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/TinaSet.net|net]], [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Tina.pdf|PDF picture]].

==== Neighbors ====

N<sub>A</sub>(a) = { b, d, f } \\
N<sub>A</sub>(b) = { a, f } \\
N<sub>A</sub>( c) = { b, c, g, g } \\
N<sub>A</sub>(e) = { c, f, h } \\
N<sub>A</sub>(f) = { k } \\
N<sub>A</sub>(h) = { d, l } \\
N<sub>A</sub>(j) = { h } \\
N<sub>A</sub>(l) = { e, g, h }\\
N<sub>E</sub>(e) = { b, g } \\
N<sub>E</sub>( c) = { d } \\
N<sub>E</sub>(f) = { h } 


N(v) = N<sub>A</sub>(v) ∪ N<sub>E</sub>(v)

The line with node's neighbors description has a form: i<sub>0</sub>, i<sub>1</sub>, i<sub>1</sub>, ..., i<sub>k</sub>
with a meaning: the node i<sub>0</sub> has neighbors  i<sub>1</sub>, i<sub>1</sub>, ..., i<sub>k</sub>.
<code>
*Vertices  12
  1 "a"   0.1020  0.3226
  2 "b"   0.2860  0.0876
  3 "c"   0.5322  0.2304
  4 "d"   0.3259  0.3917
  5 "e"   0.5543  0.4770
  6 "f"   0.1552  0.6406
  7 "g"   0.8293  0.3249
  8 "h"   0.4479  0.6866
  9 "i"   0.8204  0.8203
 10 "j"   0.4789  0.9055
 11 "k"   0.1175  0.9032
 12 "l"   0.7095  0.6475
*Arcslist
  1  2  4  6
  2  1  6
  3  2  3  7  7
  5  3  6  8
  6 11
  8  4 12
 10  8
 12  5  7  8
*Edgeslist
  2  5
  3  4
  5  7
  6  8
</code>


GraphList: [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/GraphList.pdf|PDF]] / [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/GraphList.net|net]];
TinaList: [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/TinaList.pdf|PDF]] /
[[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/TinaList.net|net]].

==== Matrix ====

Our network can be also described using a matrix.
<code>
    a  b  c  d  e  f  g  h  i  j  k  l 
 a  0  1  0  1  0  1  0  0  0  0  0  0 
 b  1  0  0  0  1  1  0  0  0  0  0  0 
 c  0  1  1  1  0  0  2  0  0  0  0  0 
 d  0  0  1  0  0  0  0  0  0  0  0  0 
 e  0  1  1  0  0  1  1  1  0  0  0  0 
 f  0  0  0  0  0  0  0  1  0  0  1  0 
 g  0  0  0  0  1  0  0  0  0  0  0  0 
 h  0  0  0  1  0  1  0  0  0  0  0  1 
 i  0  0  0  0  0  0  0  0  0  0  0  0 
 j  0  0  0  0  0  0  0  1  0  0  0  0 
 k  0  0  0  0  0  0  0  0  0  0  0  0 
 l  0  0  0  0  1  0  1  1  0  0  0  0 
</code>
Graph **G** is simple if in the corresponding matrix all entries are 0 or 1.

In general, a matrix entry can be any real number. Each matrix line should be written in a single line with at least one space between entries as a separator.
<code>
*Vertices  12
  1 "a"    0.1020  0.3226
  2 "b"    0.2860  0.0876
  3 "c"    0.5322  0.2304
  4 "d"    0.3259  0.3917
  5 "e"    0.5543  0.4770
  6 "f"    0.1552  0.6406
  7 "g"    0.8293  0.3249
  8 "h"    0.4479  0.6866
  9 "i"    0.8204  0.8203
 10 "j"    0.4789  0.9055
 11 "k"    0.1175  0.9032
 12 "l"    0.7095  0.6475
*Matrix
 0 1 0 1 0 1 0 0 0 0 0 0
 1 0 0 0 1 1 0 0 0 0 0 0
 0 1 1 1 0 0 2 0 0 0 0 0
 0 0 1 0 0 0 0 0 0 0 0 0
 0 1 1 0 0 1 1 1 0 0 0 0
 0 0 0 0 0 0 0 1 0 0 1 0
 0 0 0 0 1 0 0 0 0 0 0 0
 0 0 0 1 0 1 0 0 0 0 0 1
 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 1 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 1 0 1 1 0 0 0 0
</code>

GraphMat: [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/GraphMat.pdf|PDF]] / [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/GraphMat.net|net]];
TinaMat: [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/TinaMat.pdf|PDF]] / [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/TinaMat.net|net]], [[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Tina.paj|paj]].

===== Special types of networks =====

==== Two mode networks ====

In a **two-mode** network **N**=((**U**,**V**),**L**,**P**,**W**) the set of nodes consists of two disjoint (sub)sets of nodes **U** and **V**, and all the links from **L** have one endnode in  **U** and the other endnode in **V**. Often also a weight w : **L** → ℝ ∈ **W** is given; if not, we assume  w(u,v)=1  for all (u,v) ∈ **L**.

A two-mode network can also be described by a rectangular matrix  **A** = [a<sub>uv</sub>]<sub>**U**☓**V**</sub>.


Examples:\\
((persons, societies), years of membership),\\
((buyers/consumers, goods), quantity),\\
((parlamentarians, problems), positive vote),\\
((persons, journals), reading).

A two-mode network is announced by\\
''*vertices'' n n<sub>U</sub> 

[[http://vlado.fmf.uni-lj.si/pub/networks/data/2mode/sandi/sandi.htm|Authors and works]].\\
The southern women event participation data (Davis)
[[http://vlado.fmf.uni-lj.si/pub/networks/data/GBM/davis.htm|page]].

==== Multirelational networks ====


A **multi-relational network** is denoted by **N** =(**V**, (**L**<sub>1</sub>,**L**<sub>2</sub>,...,**L**<sub>k</sub>),**P**,**W**)
and contains different relations **L**<sub>i</sub> (sets of links) over the same set of nodes. Also the
weights from **W** are defined on different relations or their union.

Examples of such networks are:
Transportation system in a city (stations, lines);
[[http://vlado.fmf.uni-lj.si/pub/networks/data/dic/Wordnet/Wordnet.zip|WordNet]]
(words, semantic relations: synonymy, antonymy, hyponymy, meronymy,...),
[[http://vlado.fmf.uni-lj.si/pub/networks/data/KEDS/|KEDS]]
networks (states, relations between states: Visit, Ask information, Warn, Expel person, ...), ...

The relation can be assigned to a link in two ways:

  * add to a keyword for description of links (''*arcs'', ''*edges'', ''*arcslist'', ''*edgeslist'', ''*matrix'') the number of relation followed by its name:\\ ''*arcslist :3 "sent a letter to"''\\ All links controlled by this keyword belong to the specified relation ([[http://vlado.fmf.uni-lj.si/pub/networks/pajek/data/Sampson.net|Sampson]], [[http://vlado.fmf.uni-lj.si/pub/networks/pajek/data/SampsonL.net|SampsonL]]).
  * Any link controlled by ''*arcs'' or ''*edges'' can be assigned to selected relation by starting its description by the number of this relation\\ ''3: 47 14 5''\\ Link with endnodes ''47'' and ''14'' and weight ''5'' belongs to relation ''3''.


**Multi-relational temporal network -- KEDS/WEIS**

<code>
% Recoded by WEISmonths, Sun Nov 28 21:57:00 2004
% from http://www.ku.edu/~keds/data.dir/balk.html
*vertices 325
1 "AFG" [1-*]
2 "AFR" [1-*]
3 "ALB" [1-*]
4 "ALBMED" [1-*]
5 "ALG" [1-*]
 ...
318 "YUGGOV" [1-*]
319 "YUGMAC" [1-*]
320 "YUGMED" [1-*]
321 "YUGMTN" [1-*]
322 "YUGSER" [1-*]
323 "ZAI" [1-*]
324 "ZAM" [1-*]
325 "ZIM" [1-*]
*arcs :0 "*** ABANDONED"
*arcs :10 "YIELD"
*arcs :11 "SURRENDER"
*arcs :12 "RETREAT"
 ...
*arcs :223 "MIL ENGAGEMENT"
*arcs :224 "RIOT"
*arcs :225 "ASSASSINATE TORTURE"
*arcs
224: 314 153 1 [4]                890402  YUG     KSV     224  (RIOT)  RIOT-TORN
212: 314 83 1 [4]                 890404  YUG     ETHALB  212  (ARREST PERSON) ALB ETHNIC JAILED IN YUG
224: 3 83 1 [4]                   890407  ALB     ETHALB  224  (RIOT)  RIOTS
123: 83 153 1 [4]                 890408  ETHALB  KSV     123  (INVESTIGATE)   PROBING
 ...
42: 105 63 1 [175]                030731  GER     CYP     042  (ENDORSE)       GAVE SUPPORT
212: 295 35 1 [175]               030731  UNWCT   BOSSER  212  (ARREST PERSON) SENTENCED TO PRISON
43: 306 87 1 [175]                030731  VAT     EUR     043  (RALLY) RALLIED
13: 295 35 1 [175]                030731  UNWCT   BOSSER  013  (RETRACT)       CLEARED
121: 295 22 1 [175]               030731  UNWCT   BAL     121  (CRITICIZE)     CHARGES
122: 246 295 1 [175]              030731  SER     UNWCT   122  (DENIGRATE)     TESTIFIED
121: 35 295 1 [175]               030731  BOSSER  UNWCT   121  (CRITICIZE)     ACCUSED
</code>

[[http://www.ukans.edu/~keds/|KEDS - Kansas Event Data System]]

==== Temporal networks ====

A **temporal network** **N**<sub>T</sub> =(**V**,**L**,**P**,**W**, T) is obtained if the //time// T is attached to an ordinary network.
T is a set of  //time points// t ∈ T.

In temporal network nodes v ∈ **V**
and links l ∈ **L** are not
necessarily present or active in all time points.
If a link l(u,v) is active in time point t then
also its endnodes u and v should be active
in time t.


We will denote the network consisting of links and
nodes active in time t ∈ T by **N**(t)
and call it a //time slice// in time point t.
To get time slices in Pajek use

''Network/Temporal Network/Generate in time''


**Temporal networks - presence**

<code>
*Vertices 3
1 "a" [5-10,12-14]
2 "b" [1-3,7]
3 "e" [4-*]
*Edges
1 2 1 [7]
1 3 1 [6-8]
</code>

Node a is present in time points 5, 6, 7, 8, 9, 10 and 12, 13, 14.

Edge (1:3) is present in time points 6, 7, 8.

''*'' means 'infinity'.

A link is present, if both its endnodes are present.


[[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Time.net|Time.net]];
[[https://github.com/bavla/netsJSON|netsJSON]]


**Temporal networks - events**

^   Event        ^  Explanation   ^  
| ''TI'' t        | initial events -- following events happen when   | 
|                 | time point  t  starts                   | 
| ''TE'' t        | end events -- following events happen when   | 
|                 | time point  t  is finished                  | 
| ''AV'' v n s    | add vertex  v  with label  n  and properties  s                               | 
| ''HV'' v        | hide node  v                                                                        | 
| ''SV'' v        | show node  v                                                                        | 
| ''DV'' v        | delete node  v                                                                      | 
| ''AA'' u v s    | add arc  (u,v)  with properties  s                                                | 
| ''HA'' u v      | hide arc  (u,v)                                                                       | 
| ''SA'' u v      | show arc  (u,v)                                                                       | 
| ''DA'' u v      | delete arc  (u,v)                                                                     | 
| ''AE'' u v s    | add edge  (u:v)  with properties  s                                               | 
| ''HE'' u v      | hide edge  (u:v)                                                                      | 
| ''SE'' u v      | show edge  (u:v)                                                                      | 
| ''DE'' u v      | delete edge  (u:v)                                                                    | 
| ''CV'' v s      | change property of node  v  to  s                      | 
| ''CA'' u v s    | change property of arc  (u,v)  to  s                        | 
| ''CE'' u v s    | change property of edge  (u:v)  to  s                  | 
| ''CT'' u v      | change (un)directedness of link  (u,v)                                  | 
| ''CD'' u v      | change direction of arc  (u,v)                                                        | 
| ''PE'' u v s    | replace pair of arcs  (u,v)  and  (v,u)  by single edge  (u:v)    | 
|                 | with properties  s    | 
| ''AP'' u v s    | add pair of arcs  (u,v)  and  (v,u)    | 
|                 | with properties  s                                   | 
| ''DP'' u v      | delete pair of arcs  (u,v)  and  (v,u)                             | 
| ''EP'' u v s    | replace edge  (u:v)  by pair of arcs  (u,v)  and  (v,u)    | 
|                 | with properties  s           | 



 s can be empty.

In case of parallel links :k denotes the k-th link - ''HE:3 14 37''  hides the third edge linking nodes ''14'' and ''37''.

<code>
*Vertices 3
*Events
TI 1
AV 2 "b"
TE 3
HV 2
TI 4
AV 3 "e"
TI 5
AV 1 "a"
TI 6
AE 1 3 1
TI 7
SV 2
AE 1 2 1
TE 7
DE 1 2
DV 2
TE 8
DE 1 3
TE 10
HV 1
TI 12
SV 1
TE 14
DV 1
</code>

[[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Time.tim|Time.tim]];
[[http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Friends.tim|Friends.tim]].

''File/Network/Read Time Events''

Pictures in SVG:
[[http://vlado.fmf.uni-lj.si/pub/networks/doc/Terror/deg50/deg50001.htm|Terror news - 66 days]].

<html>
<!--

% Podatke o obdobjih prisotnosti/dejavnosti posamezne to"cke/povezave
% na koncu pripadajo"ce vrstice v oglatih oklepajih
% \texttt{[} in \texttt{]}. Obdobja so o"stevil"cena od 1 naprej.
% Pri na"stevanju jih lo"cimo z vejico \texttt{,}. Zaporedna obdobja
% od za"cetka $z$ do konca $k$ lahko kraj"se zapi"semo
% $z$\texttt{-}$k$.



%******************************************************************************
\begin{frame}[fragile]
\frametitle{Temporal networks / September 11}

\small

\parbox{52mm}{\includegraphics[width=52mm]{d50t05z.png}} \quad
\parbox{43mm}{
Steve Corman with collaborators from Arizona State University
transformed, using his
Centering Resonance Analysis
(\href{http://locks.asu.edu/terror/}{\textbf{\textit{CRA}}}),
daily Reuters news (66 days) about September 11th into a
temporal network of words coappearance.
}


% \href{http://vlado.fmf.uni-lj.si/pub/networks/doc/seminar/SolomonURLs.htm}%
% {\textbf{\textit{Spletni naslovi}}}.





%******************************************************************************
\begin{frame}[fragile]
\frametitle{Computer-assisted text analysis}

\small

An often used way to obtain networks is the \keyw{computer-assisted text analysis}
(CaTA).\medskip

\keyw{Terms} considered in TA are collected in a \keyw{dictionary} (it can be
fixed in advance, or built dynamically). The main two problems with terms are
\keyw{equivalence} (different words representing the same term) and
\keyw{ambiguity} (same word representing different terms). Because of
these the \keyw{coding} -- transformation of raw text data into formal
\keyw{description} -- is done often manually or semiautomaticly.
As \keyw{units} of TA we usually consider clauses, statements, paragraphs,
news, messages, \ldots

Till now the thematic and semantic TA mainly used statistical methods for
analysis of the coded data.

In thematic TA the units are coded as rectangular matrix\break
\textit{Text units} $\times$ \textit{Concepts}
which can be considered as a two-mode network.

Examples: M.M. Miller: \href{http://mmmiller.com/vbpro/vbpro.html}{VBPro},
H. Klein: \href{http://www.textanalysis.info/}{Text Analysis}/
\href{http://www.textquest.de/eindex.html}{TextQuest}.
\end{frame}


%******************************************************************************
\begin{frame}[fragile]
\frametitle{\ldots  approaches to CaTA}

\small



In semantic TA the units (often clauses) are encoded according
to the S-V-O (\textit{Subject}-\textit{Verb}-\textit{Object})
model or its improvements.\medskip

 \centerline{\includegraphics[width=55mm,bb=11 7 152 47,clip=]{./SVO.pdf}}

Examples:
\href{http://www.fp.rdg.ac.uk/sociology/people/academic/roberto/publications/socmeth89.pdf}{Roberto Franzosi};
\href{http://web.ku.edu/keds/}{\textit{KEDS}},
\href{http://web.ku.edu/keds/software.dir/tabari.html}{\textit{Tabari}},
\href{http://vlado.fmf.uni-lj.si/pub/networks/pajek/data/KEDS/}%
    {KEDS / Gulf}.


This coding can be directly considered as network with
\textit{Subjects} $\cup$ \textit{Objects} as nodes and links (arcs)
labeled with \textit{Verbs}.\medskip

See also \href{http://en.wikipedia.org/wiki/Resource_Description_Framework}{RDF} triples
in \href{http://www.w3.org/RDF/}{semantic web},
\href{http://en.wikipedia.org/wiki/SPARQL}{SPARQL}.

\end{frame}


%******************************************************************************
\begin{frame}[fragile]


\end{frame}

\section{Two-mode networks}

%******************************************************************************
\begin{frame}[fragile]
\frametitle{Two-mode networks}

\pagecolor{LightYellow}
\small

In a \keyw{two-mode} network
$\network{N}=((\vertices{U},\vertices{V}),\edges{L},\functions{P},\functions{W})$
the set of nodes consists of two disjoint sets of
nodes $\vertices{U}$ and $\vertices{V}$, and all
the links from $\edges{L}$ have one endnode
in  $\vertices{U}$ and the other in $\vertices{V}$.
Often also a \keyw{weight}
$w:\edges{L}\to\RR \in \functions{W}$ is given;
if not, we assume  $w(u,v)=1$
for all $(u,v)\in \edges{L}$.

A two-mode network can also be described by a
rectangular matrix  $\mathbf{A} = [a_{uv}]_{\vertices{U} \times \vertices{V}}$.
\[
a_{uv} =
\begin{cases}
 w_{uv}  \quad & (u,v) \in \edges{L} \\
 0  & \mbox{otherwise}
 \end{cases}
\]

Examples:
(persons, societies, years of membership),
(buyers/consumers, goods, quantity),
(parlamentarians, problems, positive vote),
(persons, journals, reading).

A two-mode network is announced by
\texttt{*vertices} $n$ $n_\vertices{U}$ .

\href{http://vlado.fmf.uni-lj.si/pub/networks/data/2mode/sandi/sandi.htm}%
 {Authors and works}.

\end{frame}


%******************************************************************************
\begin{frame}[fragile]
\frametitle{Deep South}



 \includegraphics[width=40mm]{Davis1.jpg} \quad
 \parbox[b]{56mm}{\small Classical example of two-mode network
  are the Southern women (Davis 1941).\\
  \href{http://vlado.fmf.uni-lj.si/vlado/podstat/AO/net/Davis.paj}{\texttt{Davis.paj}}.
  Freeman's \href{http://books.nap.edu/books/0309089522/html/39.html}{overview}.
 }

 \centerline{\includegraphics[width=80mm]{Davis2.jpg}}


\end{frame}
--></html>

===== Extended format =====


See [[http://mrvar.fdv.uni-lj.si/pajek/pajekman.pdf|Pajek manual]], page 89-95.