Graph characterisation using graphlet-based entropies

Aziz, Furqan; Akbar, Mian Saeed; Muhammad, Jawad; Malik, Abdul Haseeb; Uddin, M. Irfan; Gkoutos, Georgios V.

doi:10.1016/j.patrec.2021.03.031

Cited by 5 publications

(9 citation statements)

References 37 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Entropy 2021, 23, x FOR PEER REVIEW 3 of 18 mation entropy to evaluate the order degree of air cycle systems with different architectures in the cockpit of aircraft. Aziz [48] characterized the complexity of different network graph structures based on information entropy. Existing studies have preliminarily proved that information entropy can be used to evaluate the complexity of system structure.…”

Section: Undirected Structural Entropy Methodsmentioning

confidence: 99%

Complexity Evaluation of an Environmental Control and Life-Support System Based on Directed and Undirected Structural Entropy Methods

Yang

et al. 2021

Entropy

View full text Add to dashboard Cite

During manned space missions, an environmental control and life-support system (ECLSS) is employed to meet the life-supporting requirements of astronauts. The ECLSS is a type of hierarchical system, with subsystem—component—single machines, forming a complex structure. Therefore, system-level conceptual designing and performance evaluation of the ECLSS must be conducted. This study reports the top-level scheme of ECLSS, including the subsystems of atmosphere revitalization, water management, and waste management. We propose two schemes based on the design criteria of improving closure and reducing power consumption. In this study, we use the structural entropy method (SEM) to calculate the system order degree to quantitatively evaluate the ECLSS complexity at the top level. The complexity of the system evaluated by directed SEM and undirected SEM presents different rules. The results show that the change in the system structure caused by the replacement of some single technologies will not have great impact on the overall system complexity. The top-level scheme design and complexity evaluation presented in this study may provide technical support for the development of ECLSS in future manned spaceflights.

show abstract

Section: Undirected Structural Entropy Methodsmentioning

confidence: 99%

Complexity Evaluation of an Environmental Control and Life-Support System Based on Directed and Undirected Structural Entropy Methods

Yang

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…Similarly, designations (numbers) are assigned to new edges that have replaced the «old» vertex. It should be noted separately that seeds are also called graphlets [40][41][42][43]. After that, the ends of the edges 𝑟 = (𝑣 , 𝑢) ∈ 𝑅 of the environment 𝑣 are replaced by the vertex 𝑣 = 𝜑(𝑢) ∈ 𝑊 defined by mapping (1) (see Figure 1c,d).…”

Section: Operation Of Replacing Vertex By Seedmentioning

confidence: 99%

“…Similarly, designations (numbers) are assigned to new edges that have replaced the «old» vertex. It should be noted separately that seeds are also called graphlets [40][41][42][43].…”

Section: Operation Of Replacing Vertex By Seedmentioning

confidence: 99%

Introduction to the Class of Prefractal Graphs

Kochkarov

2022

Mathematics

View full text Add to dashboard Cite

Fractals are already firmly rooted in modern science. Research continues on the fractal properties of objects in physics, chemistry, biology and many other scientific fields. Fractal graphs as a discrete representation are used to model and describe the structure of various objects and processes, both natural and artificial. The paper proposes an introduction to prefractal graphs. The main definitions and notation are proposed—the concept of a seed, the operations of processing a seed, the procedure for generating a prefractal graph. Canonical (typical) and non-canonical (special) types of prefractal graphs are considered separately. Important characteristics are proposed and described—the preservation of adjacency of edges for different ranks in the trajectory. The definition of subgraph-seeds of different ranks is given separately. Rules for weighting a prefractal graph by natural numbers and intervals are proposed. Separately, the definition of a fractal graph as infinite is given, and the differences between the concepts of fractal and prefractal graphs are described. At the end of the work, already published works of the authors are proposed, indicating the main backlogs, as well as a list of directions for new research. This work is the beginning of a cycle of works on the study of the properties and characteristics of fractal and prefractal graphs.

show abstract

“…Historically, the entropy measure originates from information theory and is used to describe the chaos of a system. Built upon the Shannon entropy, the graph entropy is usually associated with features defined on a finite graph such as the probability distribution of vertices [13], [14], edge automorphism group [15], and degree sequence of the subgraph [16], etc. However, the entropy of a graph defined by those elementary properties may encounter severe difficulties in distinguishing the non-isomorphic graphs with similar structural roles and functions.…”

Section: Introductionmentioning

confidence: 99%