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pajek:faq:format [2017/05/20 21:26]
vlado [Matrix] 		pajek:faq:format [2020/09/21 00:24] (current)
vlado [Two mode networks]
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 ==== Two mode 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 ==== ==== 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 ==== ==== 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 ===== ===== Extended format =====
  
 +
 +See [[http://mrvar.fdv.uni-lj.si/pajek/pajekman.pdf|Pajek manual]], page 89-95.
pajek/faq/format.txt · Last modified: 2020/09/21 00:24 by vlado
 
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