1. Network
Pajek

2. 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.

3. 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:

4. 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.

5. six data structures in pajek
network – main object (vertices and lines - arcs, edges):
graph, valued network, 2-mode or temporal network
partition
Nominal property of vertices. Default extension: .clu
vector
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: .hie

6. 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”
*Arcslist
1 2 4
2 3
3 1 4
4 5
*Edgeslist
1 5

8. 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.

9. Network – .net 2. Pairs of lines (Arcs / Edges) (see test 2.net)
*Vertices 5
1 ”a”
2 ”b”
3 ”c”
4 ”d”
5 ”e”
*Arcs
1 2 1
1 4 1
2 3 2
3 1 1
3 4 2
4 5 1
*Edges
1 5 1

10. 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.

11. Network – .net 3.Matrix (see test 3.net) *Vertices 5 1 ”a” 2 ”b” 3 ”c”
4 ”d”
5 ”e”
*Matrix

12. 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”

13. 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” box
2 “b” ellipse
3 “c” diamond
4 “d” triangle
5 “e” empty
...

14. Draw Layout of networks
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
Eigen Values: Selecting 2 or 3 eigenvectors to become the coordinates of vertices. Can obtain nice pictures

15. Partition – .clu
Partitions are used to describe nominal properties of vertices.
e.g., 1-men, 2-women
Definition in input file (see test.clu)
*Vertices 5 1 2

16. 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
0.08

17. 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”

18. 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 . . .

19. Global and local views on network

20. 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.

21. 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.
Operations>Extract from Network>Partition
Operations>Shrink Network>Partition

22. Extracting Subnetwork
Operations>Extract from Network>Partition

23. Extracting Subnetwork
Operations>Shrink Network>Partition

24. Removing lines with low values
Network>Info>Line Values

25. Removing lines with low values
Network>Create New Network>Transform>Remove>Lines with value>lower than (340000)

26. Resources Download Text file into Pajek WoS to Pajek Tutorial
The latest version of Pajek is freely available, for non-commercial use, at its home page:
Text file into Pajek
WoS to Pajek
Tutorial
Exploratory Social Network Analysis with Pajek
visit Pajek wiki for more information

27.
WOS to pajek

28. Web of Science
S519

29. Output
S519

30. Output
S519

31. wos2pajek The download link: The new tutorial slides:
The new tutorial slides: 

32. 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\MontyLingua-2.1\Python

33. wos2pajek Download the latest version of WoS2Pajek.
Unpack it, and double click on WoS2Pajek.py to show the main interface of program:

35. You can also put all wos files in a folder

36. WoS2Pajek Program
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.

37. Wos-pajek.txt

40. Cite.net Network/Info/General
Network/Create New Network/Transform/Remove/Loops
Network/Create New Network/Transform/Remove/Multiple lines/Single line

41. CiteNew.net Paper citation network Questions
What are highly cited articles?
The diameter of the network?
What are the major clusters?
More questions?

42. Strong component of cite network
Network/Create Partition/Components/Strong [2]
Operations/Network+Partition/Extract SubNetwork [1-*]
Operations/Network+Partition/Transform/Remove Lines/Between Cluster
Save citestrong.clu

43. Co-author network 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
WANew.net (which is a co-author network)
Questions:
The author with highest co-authors?

44. Bibliographic coupling network
[Read Cite.net]
Network/Create New Network/Transform/1-mode to 2-mode
Network/2-mode Network/2-mode to 1-mode/Rows
Network/Create Partition/Components/Weak [2]
Operations/Network + Partition/Extract SubNetwork [1-*]

45. Co-citation network [Read Cite.net]
Network/Create Partitions/Degree/Output
Operations/Network+Partition/Extract subNetwork [1-*]
Network/Create New Network/Transform/1-mode to 2-mode
Network/2-mode network/2-mode to 1-mode/Columns
Network/Create Partition/Components/Weak [2]
Operations/Network+Partition/Extract SubNetwork [1-*]

46. Network analysis

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

48. Example Suppose we have data as below: P1: 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
3 14
6 13
Suppose we have data as below:
P1: Au1, Au2, Au5
P2: Au2, Au4, Au5
P3: Au4
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
See two_mode.net

49. 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”.

50. 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”.

51. 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 get
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:
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.

52. Metformin Network
Load metformin network to Pajek

53. 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.

54. EntityMetrics

55. 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.

56. Component Strongly connected components Weakly connected components
Network>Create Partition>Components>Strong
Weakly connected components
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.
Example
component.net

57. Component.net

58. Weak Component Go to partition weak component,
Partition>make network>random network>Input
Visualize the new random network

59. Weak Component

60. Strong Component

61. Strong Component

62. 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.

63. Bicomponent example

64. Bicomponent
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

65. Bicomponent
The largest component is 244 airports

66. Bicomponents
Hierarchy>Extract Cluster (13), then result is stored in cluster
Draw the cluster

67. Bicomponents
Operations>Network+Cluster>Extract SubNetwork

68. Bicomponents Operations>Network+Cluster>Extract SubNetwork
The info about the largest cluster (244)

69. Bicomponents Network>Create Partition>Degree>Input
Busy airports

70. 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.
Example
See k_core.net

71. K_core.net

72. Clustering Coefficients
How three nodes are connected
Calculation of local Clustering Coefficients:
Network>Create Vector>Clustering Coefficients>CC1
K_core.net

73. Degree Centrality Degree centrality
Network>Create Partition>Degree, or
Network/Create Vector/Centrality/Degree;
Example: Metformin network

74. Betweenness Centrality
How nodes are connecting different clusters
Betweenness centrality
Network>Create vector>Centrality>Betweenness

75. Betweenness Centrality
The betweenness centrality value for each node

76. Closeness Centrality Closeness centrality
Network>Create Vector>Centrality>Closeness
Showing how one node is close to all other nodes in the network

77. Shortest Path
Network/Create New Network/SubNetwork with Paths/.. ...One Shortest Path between Two Vertices
Enter two vertices
Forget values on lines
Yes, if searching for the shortest path is based on lengths
No, if searching for the shortest path is based o vlaue of lines
Identify vertices in source network No
Result will be a new subnetwork containing the two selected vertices
Layout>Energy>Kamada Kawai>Fix first and last

78. Shortest path
Network/Create New Network/SubNetwork with Paths/.. ...One Shortest Path between Two Vertices ( )