Abstract
The size of the orbits or similar vertices of a network provides important information regarding each individual component of the network. In this paper, we investigate the entropy or information content and the symmetry index for several classes of graphs and compare the values of this measure with that of the symmetry index of certain graphs.
Highlights
Graph entropy measures were first introduced in the study of biological and chemical systems, with Rashevsky [1] and Mowshowitz [2,3,4,5] making the main contributions
We prove that there are several classes of graphs whose symmetry index is greater or equal than the orbit-entropy measure, while many other classes have a greater orbit entropy
Partitions of the vertices of a graph are related to symmetry structure if they are based on vertex orbit cardinalities
Summary
Graph entropy measures were first introduced in the study of biological and chemical systems, with Rashevsky [1] and Mowshowitz [2,3,4,5] making the main contributions. Various graph entropy measures have been defined to investigate the structural properties of graphs [6,7,8] as well as [9,10,11,12,13]. Adaptive networks are suitable to model the complex treatment represented by various real-world systems as well as to carry out decentralized information processing tasks such as drifting conditions and learning from online streaming data, see [16]. In this way, some practical graph automorphism group decompositions are created that constitute the whole structure of graph automorphism groups. We prove that there are several classes of graphs whose symmetry index is greater or equal than the orbit-entropy measure, while many other classes have a greater orbit entropy
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