Network Pajek Introduction - PowerPoint Presentation

Slide1

Network

PajekSlide2

Introduction

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.Slide3

Application

Pajek

should provide tools for analysis and visualization of such networks:

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:

http://vlado.fmf.uni-lj.si/pub/networks/data/Slide4

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.Slide5

six data structures in

pajek

network

– main object (vertices and lines - arcs, edges):graph, valued network, 2-mode or temporal networkpartition

To which cluster a vertex belongs,

Nominal

property of vertices. Default extension

:

.

clu

vector

Values of vertices

numerical

property of vertices. Default

extension:

.

vec

permutation

reordering

of vertices. Default extension:

.

per

cluster

subset

of vertices (e.g.

a

class from partition). Default extension:

.

cls

.

hierarchy

hierarchically ordered clusters and vertices

. Default extension

:

.

hieSlide6

Network – .net

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”*Arcslist1 2 42 33 1 44 5*Edgeslist1 5Slide7
Slide8

Explanation

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.Slide9

Network – .net

2.

Pairs of lines (Arcs / Edges

) (see test 2.net)*Vertices 51 ”a”

2

”b”

3

”c”

4

”d”

5

”e”

*Arcs1 2 11 4 12 3 23 1 13 4 24 5 1*Edges1 5 1Slide10

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

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.Slide11

Network – .net

3.Matrix (

see test 3.net

)*Vertices 51 ”a”

2

”b”

3

”c”

4

”d”

5

”e”

*Matrix0 1 0 1 10 0 2 0 01 0 0 2 00 0 0 0 11 0 0 0 0Slide12

Explanation

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

”Slide13

Additional definition of network

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” box2 “b” ellipse3 “c” diamond4 “d” triangle5 “e” empty...Slide14

Layout of networksEnergy: 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 factorEigen Values: Selecting 2 or 3 eigenvectors to become the coordinates of vertices. Can obtain nice picturesDrawSlide15

Partition – .

clu

Partitions are used to describe

nominal properties of vertices.e.g., 1-men, 2-womenDefinition in input file (see test.clu

)

*

Vertices

5

1

2

2

2

1Slide16

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

0.25Slide17

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”Slide18

Menu structure

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 .

. . Slide19

Global and local views on networkSlide20

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

.Slide21

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)

1

– Africa, 2 –

Asia, 3

– Europe, 4 – N. America, 5 – Oceania, 6 – S. America

.Slide22

Operations>

Network+Partition

>Extract Subnetwork

Extracting SubnetworkSlide23

Network>Info>Line Values

Removing lines with low valuesSlide24

Network>Create New Network>Transform>Remove>Lines with value>lower than (340000)

Removing lines with low valuesSlide25

Resources

Download

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/Text file into Pajek

http://

vlado.fmf.uni-lj.si/pub/networks/pajek/howto/text2pajek.htm

WoS

to

Pajek

http://

vlado.fmf.uni-lj.si/pub/networks/pajek/WoS2Pajek/default.htm

Tutorial

Exploratory Social Network Analysis with Pajekvisit Pajek wiki for more information http://pajek.imfm.si/doku.phpSlide26

WOS to pajek

http://pajek.imfm.si/doku.php?id=wos2pajek/Slide27

Web of Science

S519Slide28

Output

S519Slide29

Output

S519Slide30

The download link: http

://pajek.imfm.si/doku.php?id=wos2pajek

The new tutorial slides: 

http://pajek.imfm.si/lib/exe/fetch.php?media=faq:wos:wos2pajek07.pdfwos2pajekSlide31

Download from: http://web.media.mit.edu/~hugo/montylingua/

Unpack

it and copy ‘montylingua-2.1’ to

C:\Program Files (x86)\Python27\Lib\site-packagesSet up a new environment variable named ‘MONTYLINGUA’ and set the variable value as C:\Program Files (x86)\Python27\Lib\site-packages\montylingua-2.1\montylingua-2.1\pythonMontyLinguaSlide32

Download the latest version of WoS2Pajek.

http

://pajek.imfm.si/doku.php?id=wos2pajek

Unpack it, and double click on WoS2Pajek.py to show the main interface of program:wos2pajekSlide33
Slide34

You can also put all

wos

files in a folderSlide35

The current version of WoS2Pajek requires

7 parameters to be given by the user:

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.WoS2Pajek ProgramSlide36

Wos-pajek.txtSlide37
Slide38
Slide39

Network/Info/GeneralNetwork/Create New Network/Transform/Remove/Loops

Network/Create New Network/Transform/Remove/Multiple lines/Single line

Cite.netSlide40

Paper citation networkQuestions

What are highly cited articles?

The diameter of the network?

What are the major clusters?More questions?CiteNew.netSlide41

Network/Create Partition/Components/Strong [2]

Operations/

Network+Partition

/Extract SubNetwork [1-*]Operations/Network+Partition/Transform/Remove Lines/Between ClusterSave citestrong.clu

Strong component of cite networkSlide42

Read WA.netNetwork/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/LoopsWANew.net (which is a co-author network)Questions:The author with highest co-authors?

Co-author networkSlide43

[Read Cite.net]

Network/Create New Network/Transform/1-mode

to 2-mode

Network/2-mode Network/2-mode to 1-mode/RowsNetwork/Create Partition/Components/Weak [2]Operations/Network + Partition/Extract SubNetwork [1-*]Bibliographic coupling networkSlide44

[Read Cite.net]

Network/Create Partitions/Degree/Output

Operations/

Network+Partition/Extract subNetwork [1-*]Network/Create New Network/Transform/1-mode to 2-modeNetwork/2-mode network/2-mode to 1-mode/ColumnsNetwork/Create Partition/Components/Weak [2]Operations/Network+Partition

/Extract

SubNetwork

[1-*]

Co-citation networkSlide45

Network analysisSlide46

Two-mode network

One-mode network

each

vertex can be related to each other vertex.Two-mode networkvertices are divided into two sets and vertices can only be related to vertices in the other set.Slide47

Example

Suppose we have data as below:

P1: Au1, Au2, Au5

P2: Au2, Au4, Au5P3: Au4P4: Au1, Au5P5: Au2, Au3P6: Au3P7: Au1, Au5P8: Au1, Au2, Au4P9: 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

See two_mode.netSlide48

Transforming to valued networks

The network is transformed into an ordinary network, where the vertices are elements from the first

subset, using

“Network>2 mode network>2-Mode to 1-Mode>Rows”. Slide49

Transforming to valued networks

If

we want to get a network with elements from the second subset we

use“Network>2 mode network>2-Mode to 1-Mode>Columns”. Slide50

Basic information about a network

Basic information

can

be obtained by “Network>Info>General” which is available in the main window of the program. We getnumber of verticesnumber of arcs, number of directed loops

number

of edges, number of undirected loops

density

of

lines

Additionally we must answer the

question:

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.Slide51

Load metformin network to Pajek

Metformin NetworkSlide52

EntityMetrics

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

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. Slide53

EntityMetricsSlide54

Network/Create New Network/SubNetwork with Paths/Info on Diameter

Pajek

returns only the two vertices that are the furthest away.

Diameter of the networkSlide55

Component

Strongly

connected components

Every vertex is reachable from every other vertexNetwork>Create Partition>Components>StrongWeakly connected componentsA weakly connected component is a maximal group of nodes that are mutually reachable by violating the edge directions.

Network>Create Partition>Components>Weak

Result is represented

by a

partition

vertices

that belong to the same

component have

the same number

in the partition.Examplecomponent.netSlide56

Component.netSlide57

Go to partition weak component, Partition>make network>random network>Input

Visualize the new random network

Weak ComponentSlide58

Weak ComponentSlide59

Strong ComponentSlide60

Strong ComponentSlide61

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.

BicomponentSlide62

Bicomponent exampleSlide63

Network/Create New Network

/......

with Bi-Connected Components stored as Relation

NumbersBicommponents are stored in hierarchyLoad USAir97.netGet bicomponents with (14 of them) with component size >3BicomponentSlide64

The largest component is 244 airports

BicomponentSlide65

Hierarchy>Extract Cluster (13), then result is stored in clusterDraw the cluster

B

icomponentsSlide66

Operations>Network+Cluster

>Extract

SubNetwork

BicomponentsSlide67

Operations>Network+Cluster>Extract

SubNetwork

The info about the largest cluster (244)

BicomponentsSlide68

Network>Create Partition>Degree>InputBusy airports

BicomponentsSlide69

K-Cores

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.ExampleSee k_core.net Slide70

K_core.netSlide71

Clustering Coefficients

How three nodes are connected

Calculation of local Clustering Coefficients:

Network>Create Vector>Clustering Coefficients>CC1K_core.netSlide72

Degree Centrality

Deg

ree centrality

Network>Create Partition>Degree, or Network/Create Vector/Centrality/Degree;Example: Metformin networkSlide73

How nodes are connecting different clustersBetweenness

centrality

Network>Create vector>Centrality>BetweennessBetweenness CentralitySlide74

The betweenness centrality value for each node

Betweenness

CentralitySlide75

Closeness centrality

Network>Create Vector>Centrality>Closeness

Showing how one node is close to all other nodes in the network

Closeness CentralitySlide76

Network/Create New Network/SubNetwork with Paths/.. ...One Shortest Path between Two

Vertices

Enter two vertices

Forget values on linesYes, if searching for the shortest path is based on lengthsNo, if searching for the shortest path is based on value of linesIdentify vertices in source networkNoResult will be a new subnetwork containing the two selected vertices

Layout>Energy>

Kamada

Kawai>Fix first and last

Shortest PathSlide77

Network/Create New Network/SubNetwork with Paths/.. ...One Shortest Path between Two

Vertices (17-7045

)

Network/Create New Network/SubNetwork with Paths/.. ...All Shortest Paths between Two Vertices (17-7045)17: GENE_otc7045: GENE_ube2v1

Shortest

Path