Complex network modeling (II)

Betweenness

Intermediate numbers are divided into node intermediate numbers and edge intermediate numbers , It reflects the role and influence of nodes or edges in the whole network .
The number of nodes Bi Defined as
$$B_i=\sum _{j\ne l\ne i}[N_{jl}(i)/N_{j}l]$$
among ,N_jl Representation node V_j And nodes V_l The number of shortest paths between ,N_jl（i） Representation node V_j And nodes V_l The shortest path between nodes V_i The article number .
The intermediate number of edges B_ij Defined as
$$B_{ij}=\sum _{(l,m)\ne (i,j)}[N_{lm}(e_{ij})/N_{l}m]$$
In style ,N_lm Representation node V_l and V_m The number of shortest paths between ,N_lm(e_ij) Representation node V_l and V_m The shortest path between passes through the edge e_ij The article number .

Nuclear degree

A graph of k- Core refers to the value of repeated removal degree less than k Node and its connection , Remaining subgraphs , The number of nodes of the subgraph is the size of the kernel .
The maximum value of the node kernel degree is called the network kernel degree .

Network density

Network density refers to the degree of tightness between nodes in a network . The Internet G Network density d(G) Defined as
$$d(G)=2M/[N(N-1)]$$
M Is the number of connections actually owned in the network ,N Is the number of network nodes , When the network is fully connected , The density is 1.