当前位置:网站首页>Complex network modeling (III)
Complex network modeling (III)
2022-07-07 08:06:00 【Dam head count】
Centrality
Degree centrality is divided into node degree centrality and network degree centrality . The former refers to the centrality of the node among its directly connected neighbor nodes , The latter focuses on the centrality of nodes in the whole network , It represents the concentration of the whole network .
node Vi Degree centrality of CD(Vi) Defined as
C D ( V i ) = k i / ( N − 1 ) C_D(V_i)=k_i/(N-1) CD(Vi)=ki/(N−1)
Betweenness centrality
The intermediate number centrality is node intermediate number centrality and network intermediate number centrality .
node Vi Intermediate centrality of CB(Vi) Defined as
C B ( V i ) = 2 B i / [ ( N − 2 ) ( N − 1 ) ] C_B(V_i)=2B_i/[(N-2)(N-1)] CB(Vi)=2Bi/[(N−2)(N−1)]
Proximity centrality
For connected graphs , node Vi Proximity centrality of Cc(Vi) Defined as
C c ( v i ) = ( N − 1 ) / [ ∑ j = 1 , j ≠ i N d i j ] C_c(v_i)=(N-1)/[\sum_{j=1,j\neq i}^{N}d_{ij}] Cc(vi)=(N−1)/[j=1,j=i∑Ndij]
Centrality of eigenvectors
It is defined according to the adjacency matrix of the network
A x = λ x Ax=\lambda x Ax=λx
Only the eigenvector corresponding to the largest eigenvalue is required by the centrality measure . In the obtained eigenvector , The first i Weight xi It's a node Vi Centrality of eigenvectors CE(Vi).
Static characteristics of directed networks
1. In and out
Because the arc associated with a node of a directed network points to the node , There are also back to the node outward , Therefore, in addition to counting the number of arcs associated with a node ( That is, degrees ), It is necessary to count the number of arcs in both directions separately , Become the in degree and out degree of the node respectively .
Static characteristics of weighted networks
1. Point right
node vi Right to the point of si Defined as
S j = ∑ j ∈ N i w i j S_j=\sum_{j\in N_i}^{}w_{ij} Sj=j∈Ni∑wij
In style ,Ni Representation node Vi Set of adjacent points ,wij Represents the connection node vi And nodes vj The weight of the edge of .
2. Unit rights
node vi The right of the unit Ui Defined as Ui=Si/ki
3. Node based weight - Degree correlation
Node based weight - Degree correlation refers to a single node , The correlation between its point weight and its degree
s ˉ ( k ) = ( ∑ i : k i = k s i ) / [ N ⋅ P ( k ) ] \bar{s}(k)=(\sum_{i:k_i=k}s_i)/[N\cdot P(k)] sˉ(k)=(i:ki=k∑si)/[N⋅P(k)]
4. Differences in weight distribution
node Vi The difference of weight distribution Yi Representations and nodes Vi The degree of dispersion of the connected edge weight distribution , Defined as
Y i = ∑ j ∈ N i ( w i j / s i ) 2 Y_i=\sum_{j\in N_i}(w_{ij}/s_i)^{2} Yi=j∈Ni∑(wij/si)2
The relationship between difference and degree is as follows : If with nodes Vi There is little difference in the weight of the associated edges , be Yi Proportional to 1/ki, If the weight difference is relatively large , be Yi About equal to 1
边栏推荐
- 【数字IC验证快速入门】10、Verilog RTL设计必会的FIFO
- 芯片资料 网站 易特创芯
- CTF daily question day43 rsa5
- [UVM practice] Chapter 2: a simple UVM verification platform (2) only driver verification platform
- Paddlepaddle 29 dynamically modify the network structure without model definition code (relu changes to prelu, conv2d changes to conv3d, 2D semantic segmentation model changes to 3D semantic segmentat
- 王爽 《汇编语言》之寄存器
- game攻防世界逆向
- These five fishing artifacts are too hot! Programmer: I know, delete it quickly!
- paddlepaddle 29 无模型定义代码下动态修改网络结构(relu变prelu,conv2d变conv3d,2d语义分割模型改为3d语义分割模型)
- 有 Docker 谁还在自己本地安装 Mysql ?
猜你喜欢
【数字IC验证快速入门】12、SystemVerilog TestBench(SVTB)入门
Linux server development, detailed explanation of redis related commands and their principles
Linux server development, SQL statements, indexes, views, stored procedures, triggers
game攻防世界逆向
【数字IC验证快速入门】15、SystemVerilog学习之基本语法2(操作符、类型转换、循环、Task/Function...内含实践练习)
Network learning (II) -- Introduction to socket
Qt学习28 主窗口中的工具栏
Dedecms collects content without writing rules
Qt学习26 布局管理综合实例
Cnopendata American Golden Globe Award winning data
随机推荐
Linux server development, redis protocol and asynchronous mode
C language queue
海信电视开启开发者模式
Ansible
Bugku CTF daily one question chessboard with only black chess
让Livelink初始Pose与动捕演员一致
Avatary的LiveDriver试用体验
Linux server development, MySQL process control statement
王爽 《汇编语言》之寄存器
Niu Mei's mathematical problem --- combinatorial number
[UVM basics] summary of important knowledge points of "UVM practice" (continuous update...)
QT learning 26 integrated example of layout management
Relevant data of current limiting
LeetCode简单题之找到一个数字的 K 美丽值
[quickstart to Digital IC Validation] 15. Basic syntax for SystemVerilog Learning 2 (operator, type conversion, loop, Task / Function... Including practical exercises)
LeetCode中等题之我的日程安排表 I
Padavan manually installs PHP
Linux server development, MySQL cache strategy
Linux server development, MySQL index principle and optimization
快解析内网穿透助力外贸管理行业应对多种挑战