ABSTRACT
The analysis, discrimination, and synthesis of complex networks rely on the use of measurements for capturing the most relevant topological features. Many kinds of measurements have been introduced to characterize the structure and properties of complex networks, including distance-based measurements, clustering coefficient, degree correlation, graph entropies, centrality, sub graphs, spectral analysis, community-based measurements, hierarchical measurements, and fractal dimensions. Graph theory can be divided into two major categories: Classical Graph Theory, which is basically of descriptive nature and Quantitative Graph Theory. It deals with quantifying structural information of networks by using measurements, which belongs to a new branch of graph theory and network science. The degree is an important characteristic of a vertex, which is the number of edges incident to the vertex. Based on the degree of the vertices, it is possible to derive many measurements for networks. The degree power is one of the most important graphs invariant and well-studied in graph theory.
