Identifying Key Nodes in Complex Networks Based on Local Structural Entropy and Clustering Coefficient

Table 1

Notations and definitions.

Notation	Definition
DC	Degree centrality
KS	K-Shell
LE	Local structure entropy
DCL	The method in reference [15]
Cen	The method in reference [19]
EC	The method proposed in this paper
	The graph describing a network
	The node set of graph
E	The edge set of graph
pij	The ratio of the degree of node j to the degree of all nodes in the local network corresponding to node i
Ei	The number of triangles between node i and its neighbors
ki	The degree of node i
	A matching factor for integrating clustering coefficient with local structural entropy of the node i
gnormi	Min-max normalization of
u(x)	The squared and normalized formulas, in this paper do homotopy functions
ξ	The ratio of the number of subgraphs to the number of nodes after deleting the edges related to the node
τ	The ratio of the maximum subgraph size to the number of nodes
Ms	The maximum size of the set {Si}
S	The subgraph set of the network
|S|	The size of the set {Si}
|V|	The total number of nodes in network
|E|	The total number of edges in network
dmax	Maximum degree of nodes
davg	Average degree of nodes
Kavg	Average local clustering coefficient
K	Global clustering coefficient
|T|	The number of triangles