Abstract
Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. The starting point has been always based on assigning a probability distribution to a network when using Shannon’s entropy. In particular, Cao et al. (2014 and 2015) defined special graph entropy measures which are based on degrees powers. In this paper, we obtain some lower and upper bounds for these measures and characterize extremal graphs. Moreover we resolve one part of a conjecture stated by Cao et al.
Highlights
Graph entropy measures have played an important role in a variety of fields, including information theory, biology, chemistry, and sociology
In this paper we study novel properties of graph entropies which are based on an information functional by using degree powers of graphs
We studied a special graph entropy measure which is based on vertex degrees
Summary
Graph entropy measures have played an important role in a variety of fields, including information theory, biology, chemistry, and sociology. Afterwards, Dehmer and Mowshowitz [3] interpreted the entropy of a graph based on vertex orbits as its structural information content. Dehmer [4] presents some novel information functionals that capture, in some sense, the structural information of the underlying graph G Several graph invariants, such as the number of vertices, edges, distances, the vertex degree sequences, extended degree sequences (i.e., the second neighbor, third neighbor, etc.), degree powers and connections, have been used for developing entropy-based measures [3,4,5,6]. In this paper we study novel properties of graph entropies which are based on an information functional by using degree powers of graphs. We obtain some bounds on graph entropy in terms of the maximum degree and minimum degree of graphs
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