Vertex-degree sequences in complex networks: New characteristics and applications

• The vertex-degree sequence in a general scale-free network is important for both theory and applications, which is characterized in this article.
• New findings on the major characteristics of vertex-degree sequence in a general scale-free network are reported.
• New findings have great potential applications in complex network modeling, identification and analysis.

Many complex networks exhibit a scale-free vertex-degree distribution in a power-law form ck−γck−γ, where kk is the vertex-degree variable and cc and γγ are constants. To better understand the mechanism of power-law formation in real-world networks, it is effective to explore and analyze their vertex-degree sequences. We had shown before that, for a scale-free network of size NN, if its vertex-degree sequence is k11γ>1, then the length ll of the vertex-degree sequence is of order logNlogN. In the present paper, we further study complex networks with an exponential vertex-degree distribution and prove that the same conclusion also holds. In addition, we verify our claim by showing many real-world examples. We finally discuss some applications of the new finding in various fields of science and technology.