Transcript network analysis

Network
Pajek
Introduction
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Pajek is a program, for Windows, for analysis
and visualization of large networks having some
thousands or even millions of vertices. In
Slovenian language the word pajek means
spider.
Application
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Pajek should provide tools for analysis and visualization of
such networks:
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collaboration networks,
organic molecule in chemistry,
protein-receptor interaction networks,
genealogies,
Internet networks,
citation networks,
diffusion (AIDS, news, innovations) networks,
data-mining (2-mode networks), etc.
See also collection of large networks at:
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http://vlado.fmf.uni-lj.si/pub/networks/data/
Main goals
to support abstraction by (recursive)
decomposition of a large network into several
smaller networks that can be treated further
using more sophisticated methods;
 to provide the user with some powerful
visualization tools;
 to implement a selection of efficient
(subquadratic) algorithms for analysis of large
networks.
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six data structures in pajek
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network – main object (vertices and lines - arcs, edges):
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partition
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reordering of vertices. Default extension: .per
cluster
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numerical property of vertices. Default extension: .vec
permutation
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Nominal property of vertices. Default extension: .clu
vector
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graph, valued network, 2-mode or temporal network
subset of vertices (e.g. a class from partition). Default extension: .cls.
hierarchy
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hierarchically ordered clusters and vertices. Default extension: .hie
Network – .net
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Network can be defined in different ways on input file. Look at three of
them:
1. List of neighbours (Arcslist / Edgeslist)(see test 1.net)
*Vertices 5
1 ”a”
2 ”b”
3 ”c”
4 ”d”
5 ”e”
*Arcslist
124
23
314
45
*Edgeslist
15
Explanation
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Data must be prepared in an input (ASCII) file. Program NotePad
can be used for editing. Much better is a shareware editor, TextPad.
Words, starting with *, must always be written in first column of the
line. They indicate the start of a definition of vertices or lines.
Using *Vertices 5 we define a network with 5 vertices. This must
always be the first statement in definition of a network.
Definition of vertices follows after that – to each vertex we give a
label, which is displayed between “ and ”.
Using *Arcslist, a list of directed lines from selected vertices are
declared (1 2 4 means, that there exist two lines from vertex 1, one
to vertex 2 and another to vertex 4).
Similarly *Edgeslist, declares list of undirected lines from selected
vertex.
In the file no empty lines are allowed – empty line means end of
network.
Network – .net
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2. Pairs of lines (Arcs / Edges) (see test 2.net)
*Vertices 5
1 ”a”
2 ”b”
3 ”c”
4 ”d”
5 ”e”
*Arcs
121
141
232
311
342
451
*Edges
151
Explanation
Directed lines are defined using *Arcs, undirected
lines are defined using *Edges. The third number
in rows defining arcs/edges gives the value/weight
of the arc/edge.
 In the previous format (Arcslist / Edgeslist) values
of lines are not defined
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the format is suitable only if all values of lines are 1.
If values of lines are not important the third
number can be omitted (all lines get value 1).
 In the file no empty lines are allowed – empty
line means end of network.
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Network – .net
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3.Matrix (see test 3.net)
*Vertices 5
1 ”a”
2 ”b”
3 ”c”
4 ”d”
5 ”e”
*Matrix
01011
00200
10020
00001
10000
Explanation
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In this format directed lines (arcs) are given in
the matrix form (*Matrix). If we want to
transform bidirected arcs to edges we can use
“Network>create new network>Transform>Arcs
to Edges>Bidirected only”
Additional definition of network
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Additionally, Pajek enables precise definition of
elements used for drawing networks (coordinates of
vertices, shapes and colors of vertices and lines, ...).
Example: (see test 4.net)
*Vertices 5
1 “a” box
2 “b” ellipse
3 “c” diamond
4 “d” triangle
5 “e” empty
...
Draw
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Layout of networks
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Energy: The network is presented like a physical
system, and we are searching for the state with
minimal energy
Kamada-Kawai: using separate components, you can tile
connected components in a plane
 Fruchterman-Reingold: draw in a plane or space and
selecting the repulsion factor
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Eigen Values: Selecting 2 or 3 eigenvectors to
become the coordinates of vertices. Can obtain
nice pictures
Partition – .clu
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Partitions are used to describe nominal
properties of vertices.
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e.g., 1-men, 2-women
Definition in input file (see test.clu)
*Vertices 5
1
2
2
2
1
Vector – .vec
Vectors are used to describe numerical
properties of vertices (e.g., centralities).
 Definition in input file (see test.vec)
*Vertices 5
0.58
0.25
0.25
0.08
0.25
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Pajek project files
It is time consuming to load objects one by
one. Therefore it is convenient to store all
data in one file, called Pajek project file (.paj).
(see test.paj)
 Project files can be produced manually by
using “File>Pajek Project File>Save”
 To load objects stored in Pajek project file
select “File>Pajek Project File>Read”
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Menu structure
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Commands are put to menu according to the
following criterion:
commands that need only a network as input are
available in menu Net,
commands that need as input two networks are
available in menu Networks,
commands that need as input two objects (e. g.,
network and partition) are available in menu
Operations,
commands that need only a partition as input are
available in menu Partition . . .
Global and local views on network
Global and local views on network
Local view is obtained by extracting sub-network
induced by selected cluster of vertices.
 Global view is obtained by shrinking vertices in the
same cluster to new (compound) vertex. In this
way relations among clusters of vertices are
shown.
 Combination of local and global view is contextual
view: Relations among clusters of vertices and
selected vertices are shown.
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Example
Import and export in 1994 among 80
countries are given. They is given in 1000$.
(See Country_Imports.net)
 Partition according to continents (see
Country_Continent.clu)
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1 – Africa, 2 – Asia, 3 – Europe, 4 – N. America, 5 –
Oceania, 6 – S. America.
Operations>Extract from Network>Partition
 Operations>Shrink Network>Partition
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Extracting Subnetwork
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Operations>Extract from Network>Partition
Extracting Subnetwork
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Operations>Shrink Network>Partition
Removing lines with low values
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Network>Info>Line Values
Removing lines with low values
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Network>Create New Network>Transform>Remove>Lines
with value>lower than (340000)
Resources
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Download
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Text file into Pajek
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http://vlado.fmf.uni-lj.si/pub/networks/pajek/WoS2Pajek/default.htm
Tutorial
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http://vlado.fmf.uni-lj.si/pub/networks/pajek/howto/text2pajek.htm
WoS to Pajek
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The latest version of Pajek is freely available, for non-commercial use,
at its home page: http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Exploratory Social Network Analysis with Pajek
visit Pajek wiki for more information
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http://pajek.imfm.si/doku.php
http://pajek.imfm.si/doku.php?id=wos2pajek/
WOS TO PAJEK
Web of Science
S519
Output
S519
Output
S519
wos2pajek
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The download link:
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http://pajek.imfm.si/doku.php?id=wos2pajek
The new tutorial slides:
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http://pajek.imfm.si/lib/exe/fetch.php?media=faq:wo
s:wos2pajek07.pdf
MontyLingua
Download from:
http://web.media.mit.edu/~hugo/montylingua/
 Unpack it and copy ‘montylingua-2.1’ to
C:\Python26\Lib\site-packages
 Set up a new environment variable named
‘MONTYLINGUA’ and set the variable value
as c:\Python26\Lib\site-packages\MontyLingua2.1\Python
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wos2pajek
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Download the latest version of WoS2Pajek.
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http://pajek.imfm.si/doku.php?id=wos2pajek
Unpack it, and double click on WoS2Pajek.py
to show the main interface of program:
You can also put all wos
files in a folder
WoS2Pajek Program
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The current version of WoS2Pajek requires 7 parameters to be given by
the user:
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MontyLingua directory: path to the directory in which the MontyLingua
package is installed;
project directory: where the output files are saved;
WoS file;
maxnum – estimate of the number of all vertices (number of records+number
of cited Works) –30*number of records;
step – prints info about each k*step record as a trace; step= 0– no trace.
use ISI name / short name;
make a clean WoS file without duplicates;
boolean list[DE, ID, TI, AB] specifying which fields are sources of keywords.
Wos-pajek.txt
Cite.net
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Network/Info/General
Network/Create New Network/Transform/Remove/Loops
Network/Create New Network/Transform/Remove/Multiple
lines/Single line
CiteNew.net
Paper citation network
 Questions
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What are highly cited
articles?
 The diameter of the
network?
 What are the major
clusters?
 More questions?
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Strong component of cite network
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Network/Create Partition/Components/Strong [2]
Operations/Network+Partition/Extract SubNetwork [1-*]
Operations/Network+Partition/Transform/Remove
Lines/Between Cluster
Save citestrong.clu
Co-author network
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Read WA.net
Network/2-mode network/2-mode to 1-mode/Columns
Network/Create Partition/Components/Weak [2]
Operations/Network+Partition/Extract SubNetwork[1-*]
Network/Create New Network/Transform/Remove/Loops
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WANew.net (which is a co-author network)
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Questions:
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The author with highest co-authors?
Bibliographic coupling network
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[Read Cite.net]
Network/Create New Network/Transform/1-mode to 2mode
Network/2-mode Network/2-mode to 1-mode/Rows
Network/Create Partition/Components/Weak [2]
Operations/Network + Partition/Extract SubNetwork [1-*]
Co-citation network
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[Read Cite.net]
Network/Create Partitions/Degree/Output
Operations/Network+Partition/Extract subNetwork [1-*]
Network/Create New Network/Transform/1-mode to 2mode
Network/2-mode network/2-mode to 1-mode/Columns
Network/Create Partition/Components/Weak [2]
Operations/Network+Partition/Extract SubNetwork [1-*]
NETWORK ANALYSIS
Two-mode network
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One-mode network
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each vertex can be related to each other vertex.
Two-mode network
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vertices are divided into two sets and vertices can
only be related to vertices in the other set.
Example
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Suppose we have data as below:
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P1: Au1, Au2, Au5
P2: Au2, Au4, Au5
P3: Au4
See two_mode.net
P4: Au1, Au5
P5: Au2, Au3
P6: Au3
P7: Au1, Au5
P8: Au1, Au2, Au4
P9: Au1, Au2, Au3, Au4, Au5
P10: Au1, Au2, Au5
*vertices 15 10
1 "P1"
2 "P2"
3 "P3"
4 "P4"
5 "P5"
6 "P6"
7 "P7"
8 "P8"
9 "P9"
10 "P10"
11 "Au1"
12 "Au2"
13 "Au3"
14 "Au5"
15 "Au5"
*edgeslist
1 11 12 15
2 12 14 15
3 14
4 11 15
5 12 13
6 13
7 11 15
8 11 12 14
9 11 12 13 14 15
10 11 12 15
Transforming to valued networks
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The network is transformed into an ordinary network, where
the vertices are elements from the first subset, using
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“Network>2 mode network>2-Mode to 1-Mode>Rows”.
Transforming to valued networks
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If we want to get a network with elements from the
second subset we use
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“Network>2 mode network>2-Mode to 1-Mode>Columns”.
Basic information about a network
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Basic information can be obtained by “Network>Info>General” which
is available in the main window of the program. We get
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number of vertices
number of arcs, number of directed loops
number of edges, number of undirected loops
density of lines
Additionally we must answer the question:
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Input 1 or 2 numbers: +/highest, -/lowest where we enter the number of
lines with the highest/lowest value or interval of values that we want
to output.
If we enter 10 , 10 lines with the highest value will be displayed. If we
enter -10, 10 lines with the lowest value will be displayed. If we enter 3
10 , lines with the highest values from rank 3 to 10 will be displayed.
Metformin Network
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Load metformin network to Pajek
EntityMetrics
Entitymetrics is defined as using entities (i.e., evaluative entities or
knowledge entities) in the measurement of impact, knowledge usage,
and knowledge transfer, to facilitate knowledge discovery.
Ding, Y., Song, M., Han, J., Yu, Q., Yan, E., Lin, L., & Chambers, T. (2013).
Entitymetrics: Measuring the impact of entities. PLoS One, 8(8): 1-14.
EntityMetrics
Diameter of the network
Network/Create New Network/SubNetwork
with Paths/Info on Diameter
 Pajek returns only the two vertices that are
the furthest away.
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Component
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Strongly connected components
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Weakly connected components
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Network>Create Partition>Components>Weak
Result is represented by a partition
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Network>Create Partition>Components>Strong
vertices that belong to the same component have
the same number in the partition.
Example
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component.net
Component.net
Weak Component
Go to partition weak component,
 Partition>make network>random
network>Input
 Visualize the new random network
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Weak Component
Strong Component
Strong Component
Bicomponent
A cut-vertex is a vertex whose deletion
increases the number of components in the
network.
 A bi-component is a component of minimum
size 3 that does not contain a cut-vertex.
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Bicomponent example
Bicomponent
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Network/Create New Network/......with
Bi-Connected Components stored as
Relation Numbers
Bicommponents are stored in hierarchy
Load USAir97.net
Get bicomponents with (14 of them) with
component size >3
Bicomponent
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The largest component is 244 airports
Bicomponents
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Hierarchy>Extract Cluster (13), then result is stored in cluster
Draw the cluster
Bicomponents
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Operations>Network+Cluster>Extract SubNetwork
Bicomponents
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Operations>Network+Cluster>Extract SubNetwork
The info about the largest cluster (244)
Bicomponents
Network>Create Partition>Degree>Input
 Busy airports
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K-Cores
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A subset of vertices is called a k-core if every vertex from
the subset is connected to at least k vertices from the
same subset.
K-Cores can be computed using “Network>Create
Partitions>K-Core” and selecting Input, Output or All core.
Result is a partition: for every vertex its core number is
given.
In most cases we are interested in the highest core(s) only.
The corresponding subnetwork can be extracted using
“Operations>Extract from Network>Partition” and typing the
lower and upper limit for the core number.
Example
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See k_core.net
K_core.net
Clustering Coefficients
How three nodes are connected
 Calculation of local Clustering Coefficients:
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Network>Create Vector>Clustering
Coefficients>CC1
 K_core.net
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Degree Centrality
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Degree centrality
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Network>Create Partition>Degree, or
 Network/Create Vector/Centrality/Degree;
Example: Metformin network
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Betweenness Centrality
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How nodes are connecting different clusters
Betweenness centrality
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Network>Create vector>Centrality>Betweenness
Betweenness Centrality
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The betweenness centrality value for each
node
Closeness Centrality
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Closeness centrality
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Network>Create Vector>Centrality>Closeness
Showing how one node is close to all other nodes in the network
Shortest Path
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Network/Create New Network/SubNetwork with Paths/..
...One Shortest Path between Two Vertices
Enter two vertices
 Forget values on lines
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Identify vertices in source network
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Yes, if searching for the shortest path is based on lengths
No, if searching for the shortest path is based o vlaue of lines
No
Result will be a new subnetwork containing the two selected
vertices
Layout>Energy>Kamada Kawai>Fix first and last
Shortest path
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Network/Create New Network/SubNetwork with Paths/..
...One Shortest Path between Two Vertices (17-7045)