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Complex network modeling (II)
2022-07-07 08:06:00 【Dam head count】
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 = ∑ j ≠ l ≠ i [ N j l ( i ) / N j l ] B_i=\sum_{j\neq l\neq i}^{}[N_{jl}(i)/N_jl] Bi=j=l=i∑[Njl(i)/Njl]
among ,Njl Representation node Vj And nodes Vl The number of shortest paths between ,Njl(i) Representation node Vj And nodes Vl The shortest path between nodes Vi The article number .
The intermediate number of edges Bij Defined as
B i j = ∑ ( l , m ) ≠ ( i , j ) [ N l m ( e i j ) / N l m ] B_{ij}=\sum_{ {(l,m)}\neq (i,j)}^{}[N_{lm}(e_{ij})/N_lm] Bij=(l,m)=(i,j)∑[Nlm(eij)/Nlm]
In style ,Nlm Representation node Vl and Vm The number of shortest paths between ,Nlm(eij) Representation node Vl and Vm The shortest path between passes through the edge eij 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 ) = 2 M / [ N ( N − 1 ) ] d(G)=2M/[N(N-1)] 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.
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