2018版Pajek：复杂网络分析与可视化手册

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《2018版Pajek使用手册》是一份详细的指南，专为分析和可视化非常大型网络而设计，尤其适用于电力、金融和医学等领域的研究。该手册由Andrej Mrvar和Vladimir Batagelj两位作者编写，他们在Ljubljana的University of Ljubljana分别来自Faculty of Social Sciences和Department of Mathematics。此版本为5.04a，自1996年起，其源代码免费供非商业用途使用，并提供了一个PdfLaTeX版本，日期为2003年10月1日。手册的核心内容分为四个部分： 1. **Pajek**：首先介绍了Pajek程序本身，作为一款强大的网络分析工具，它为处理和探索复杂网络结构提供了基础。这部分可能包括软件的概述、安装指导和基本操作介绍。 2. **Dataobjects**：这部分详细解释了数据对象在Pajek中的角色，包括文件输入（可能是网络数据文件）、网络数据结构（如节点和边）、以及与之相关的数据类型，如顶点ID、向量、排列和聚类等。用户可以通过这些对象进行网络数据的组织和管理。 3. **MainWindowTools**：这部分着重于主窗口的各种工具，涵盖了文件操作（如打开、保存、导入/导出数据）、网络操作（如连接、断开、复制节点）、数据处理（如ID管理、网络操作、聚类分析）、选项设置和获取网络信息等功能。用户可以通过这些工具对网络进行深入分析和定制。 4. **DrawWindowTools**：这部分主要关注图形绘制工具，如布局算法的选择（如层次、环形等）、图层管理、图形模式切换（仅显示节点或边）、导航（前进、后退、缩放）等，帮助用户创建和优化网络可视化效果。《2018版Pajek使用手册》不仅包含了丰富的命令列表和简短的解释，还为用户提供了解决实际问题的实用指导，使研究人员能够更有效地利用Pajek工具来解析复杂的网络数据，挖掘潜在的关联和结构特征。无论是初学者还是专业用户，这份手册都是深入理解并操作Pajek软件不可或缺的参考资料。

14 Pajek– Manual

3.2 Network

Operations, for which only a network (or nothing in case of random networks) is

needed as input.

• Create Random Network – Generate random network of selected dimen-

sion

– Total No. of Arcs – Generate random directed network of selected

dimension and given number of arcs.

– Vertices Output Degree – Generate random directed network of se-

lected dimension and output degree of each vertex in given range.

– Bernoulli/Poisson – Generate undirected, directed, acyclic, bipartite

or 2-mode random network according to model deﬁned by Bernoulli

/ Poisson: each line is selected with the given probability p. Instead

of p, which is for large and sparse networks (very) small number, in

Pajek a more intuitive average degree d is used. They are connected

with relations d =

v∈V

deg(v) =

and m = pM where n = |V |,

m = |L| and M is the number of lines in maximal possible network –

for example, for undirected graphs M = n(n − 1).

– Scale Free – Generate scale free undirected, directed or acyclic net-

work. The procedure is based on a reﬁnement of the model for gener-

ating scale free networks, proposed in [56]. At each step of the growth

a new vertex and k edges are added to the network N. The endpoints

of the edges are randomly selected among all vertices according to the

probability

Pr(v) = α

indeg(v)

|E|

+ β

outdeg(v)

|E|

+ γ

|V |

where α + β + γ = 1. It is easy to check that

v∈V

Pr(v) = 1.

– Small World – Generate Small world random network. See [12].

– Extended Model – Generate random network according to extended

model deﬁned by Albert and Barabasi [3].

• Create New Network – Create a new network from selected network (or

create empty or complete network).

– Empty Network - Create new network with given number of vertices

and no lines.

A. Mrvar and V. Batagelj Pajek 5.04a / April 21, 2018

Pajek– Manual 15

– Complete Network - Create undirected or directed network with given

number of vertices and all possible lines.

– with Bi-Connected Components stored as Relation Numbers – Bi-

connected Components of selected network. Articulation points be-

long to several classes, so the result cannot be stored in partition –

biconnected components are stored in hierarchy. In newer Pajek ver-

sions they are stored also as multiple relations network. Minimal num-

ber of vertices in components can be selected. Partition containing

vertices belonging to exactly one bicomponent, vertices outside bi-

components and articulation points is also produced: vertices outside

bicomponents get class zero, each bicomponent is numbered consecu-

tively (from 1 to number of bicomponents) and articulation points get

class number 999999998. Additionally vector containing articulation

points is produced: number of biconnected components to which each

vertex belongs is given.

– with Ring Counts stored as Line Values - how many times each line

belongs to predeﬁned rings

∗ 3-Rings – For each line count number of 3-rings to which the line

belongs.

· Undirected – for undirected networks – count undirected 3-

rings.

· Directed – for directed networks – count cyclic, transitive, or

all 3-rings, or count how many times each line is a transitive

shortcut (see Figure 10).

∗ 4-Rings – For each line count number of 4-rings to which the line

belongs.

· Undirected – for undirected networks – count undirected 4-

rings.

· Directed – for directed networks – count cyclic, diamonds,

genealogical, transitive, or all 4-rings, or count how many

times each line is a transitive shortcut (see Figure 11).

– SubNetwork with Paths

∗ One shortest Path between Two Vertices – Find the shortest

path between two vertices. Result is new network. Values on

lines can be taken into account (if they present distances between

vertices) or not (graph theoretical distance). The latter possibility

is faster.

∗ All Shortest Paths between Two Vertices – Find all shortest

paths between two vertices. Result is new network. Values on

A. Mrvar and V. Batagelj Pajek 5.04a / April 21, 2018

16 Pajek– Manual

lines can be taken into account (if they present distances between

vertices) or not (graph theoretical distance). The latter possibility

is faster.

∗ Walks with Limited Length between Two Vertices – Find all

walks between two vertices with limited maximum length.

∗ Geodesics Matrices* – Compute the shortest path length matrix

and the geodesics count matrix (for small networks only!).

∗ Info on Diameter – Find diameter – the length of the longest

shortest path in network and corresponding two vertices. Full

search is performed, so the operation may be slow for very large

networks (number of vertices larger than 2000).

– SubNetwork with Flows

∗ Maximum Flow between Two Vertices – Find maximum ﬂow

between selected two vertices (algorithm looks for paths to be

saturated and among them it always selects the shortest path). Al-

gorithm can be used in the technical area (actual ﬂow, values on

lines mean capacities) or for analysing graphs (if all values are

1). Result is a new network, containing the two vertices and lines

contributing to maximum ﬂow between them.

∗ Maximum Flow between Pairs in Cluster* – Find maximum

ﬂow among vertices determined by cluster. Result is a new net-

work, where a value on line means maximum ﬂow between cor-

responding two vertices. Algorithm is slow: Use it on smaller

networks or clusters with limited number of vertices only!

– Transform

∗ Transpose 1-Mode – Transposed network of selected 1-mode

network – change direction of arcs.

∗ Remove

· Selected Vertices – Remove selected vertices from network.

· all Edges – Remove all edges from selected network.

· all Arcs – Remove all arcs from selected network.

· Multiple Lines – Remove all multiple lines from selected

network.

1. Sum Values – Values of all deleted lines are added to not

deleted line between corresponding two vertices.

2. Number of Lines – Value of line between two vertices in

a new network correspond to the number of lines between

the two vertices in original network.

A. Mrvar and V. Batagelj Pajek 5.04a / April 21, 2018

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