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In this paper, we compute the first Zagreb temperature entropy, the second Zagreb temperature entropy, the sum-connectivity temperature entropy, and the product-connectivity temperature entropy of the silicate network. We find the relationship between the temperature entropies of the silicate network. We also analyze and compare the different regressions of these entropies and try to find the best one for each case. [ABSTRACT FROM AUTHOR]

Porphyrazine is a macrocyclic molecule that has potential uses in biology and materials research. In this work, we investigate the topological characteristics of porphyrazine via topological indices. These indices are important in QSPR and QSAR modeling because they aid in the analysis and prediction of physical, biological, and chemical properties associated with a specific chemical structure. In this paper, we investigate neighborhood M-polynomial and graph index-entropy of porphyrazine graph, deriving several topological indices based on neighborhood degree sum from it, and numerical computation and graphical interpretation are used to explain the results further. This research advances our understanding of the basic principles of physics and chemistry by shedding light on the intricate connections between biological processes, chemical reactivity, and molecular structure. [ABSTRACT FROM AUTHOR]

The porphyrazine structure, known for its high chemical and thermal stability, has become a significant focus in materials science, chemical reactivity, functionalization, and drug design. By utilizing the new Zagreb-type indices to analyze the chemical structure of porphyrazine, we can gather more information about their bonding and connecting patterns. This enables us to construct an entropy measure that helps evaluate the stability of the material and predict its behavior in different scenarios. Furthermore, establishing correlations between these indices and entropy using logarithmic regression models allows for a deeper understanding of complex properties of porphyrazine. This, in turn, opens up new possibilities for the compound’s potential applications across various scientific and technical fields. In our work, we have used the M-polynomial to derive molecular descriptors for degree-based topological indices and determine the entropy of the porphyrazine structure based on these descriptors. [ABSTRACT FROM AUTHOR]

The analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras induced by significant classes of Brauer configurations) is generally a tricky problem. Ringel previously proposed an analysis of this type in the case of Dynkin algebras, for which so-called Dynkin functions were used to study the numerical behavior of invariants associated with such algebras. This paper introduces two additional tools (the entropy and the covering graph of a Brauer configuration) for Brauer analysis, which is applied to Dynkin and Euclidean diagrams to define Dynkin functions associated with Brauer configuration algebras. Properties of graph entropies defined by the corresponding covering graphs are given to establish relationships between the theory of Dynkin functions, the Brauer configuration algebras theory, and the topological content information theory.

The analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras induced by significant classes of Brauer configurations) is generally a tricky problem. Ringel previously proposed an analysis of this type in the case of Dynkin algebras, for which so-called Dynkin functions were used to study the numerical behavior of invariants associated with such algebras. This paper introduces two additional tools (the entropy and the covering graph of a Brauer configuration) for Brauer analysis, which is applied to Dynkin and Euclidean diagrams to define Dynkin functions associated with Brauer configuration algebras. Properties of graph entropies defined by the corresponding covering graphs are given to establish relationships between the theory of Dynkin functions, the Brauer configuration algebras theory, and the topological content information theory. [ABSTRACT FROM AUTHOR]

A numerical parameter, referred to as a topological index, is used for representing the molecular structure of a compound by analyzing its graph-theoretical characteristics. In the context of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies, topological indices serve as predictive tools for the physicochemical properties of chemical compounds. Graph entropies have evolved into information-theoretic instruments for exploring the structural information of molecular graphs. In this research, we compute the Nirmala index, as well as the first and second inverse Nirmala index, for the silicon carbide network S i 2 C 3 - I I I [ α , β ] , using its M-polynomial. The comparison of the Nirmala indices and corresponding entropy measures are presented through numerical computation and 2D line plots. A regression model is built to investigate the relationship between the Nirmala indices and corresponding entropy measures. [ABSTRACT FROM AUTHOR]

A nanotube is a nanometer–scale tube-like structure, it is a kind of nanoparticle, and may be large enough to serve as a pipe through which other nanoparticles can be channeled, or, depending on the material, may be used as an electrical conductor or an electrical insulator. For computing the structural information of nanotubes, the graph entropies have become the information theoretic quantities. The graph entropy measure has attracted the research community due to its potential application in discrete mathematics, biology, and chemistry. In this paper, our contribution is to explore graph entropies for structures of some nanotubes based on novel information function, which is the number of different degree vertices along with the number of edges between various degree vertices. More precisely, we computed entropies of some classes of nanotubes such as titania nanotube TNT 3 [ m , n ] , TNT 6 [ m , n ] and carbon nanotubes HAC 5 C 6 C 7 [ m , n ] by making a relation of degree-based topological indices with the help of information function. [ABSTRACT FROM AUTHOR]

Online disinformation has become one of the most severe concerns in today's world. Recognizing disinformation timely and effectively is very hard, because the propagation process of disinformation is dynamic and complicated. The existing newest research leverage uniform time intervals to study the multi-stage propagation features of disinformation. However, uniform time intervals are unrealistic in the real world, cause the process of information propagation is not regular. In light of these facts, we propose a novel and effective framework Multi-stageDynamicDisinformationDetection with Graph Entropy Guidance(MsDD) to better analyze multi-stage propagation patterns. Instead of traditional snapshots, we analyze the dynamic propagation network via graph entropy, which can work effectively in finding the dynamic and variable-length stages. In this way, we can explicitly learn the changing pattern of propagation stages and support timely detection even at the early stages. Based on this effective multi-stage analysis framework, we further propose a novel dynamic analysis model to model both the structural and sequential evolving features. Extensive experiments on two real-world datasets prove the superiority of our model. We open the datasets and source code at https://github.com/researchxr/MsDD. [ABSTRACT FROM AUTHOR]

Anomaly detection is critical in the internet of things (IoT) environment. To this issue, this study provides a novel approach for detecting anomalies in multivariate IoT time series. The proposed approach identified relationships between IoT time series to establish a dynamic graph and estimated the graph entropy to detect anomalies. The presented approach was applied to industrial IoT datasets. The results have shown that the presented method outperformed other models by 0.21 with respect to F1‐score. In addition, we used three distinct algorithms to detect the anomalies from the multivariate IoT time series. According to the results, the local outlier factor approach outperformed the others by 0.18 with respect to F1‐score. [ABSTRACT FROM AUTHOR]

Macromolecules are gaining much attention in various fields today. Dendrimers are artificially synthesized macromolecules by convergent or divergent approach. They are compact regular structures with spherical dimension and has a vast number of application in disparate fields such as drug delivery, material science, and biology, magnetic resonance imaging, an organic light-emitting device, etc. Determining the pharmacological, chemical, and biological characteristics of a substance necessitates a significant amount of effort. From the chemical graph of the dendrimer structure, we can infer those characteristics with the help of numerical descriptors known as the topological index. The Wiener and Szeged indices are two important distance-based topological indices applicable in nanoscience. The degree-based topological indices also have great importance and huge applications in structural chemistry. These indices together with graph entropy are found to be more effective and have found application in different sciences. In this work, the Wiener index, Szeged indices, Mostar indices, and Padmakar Ivan index for cyclen cored dendrimers are evaluated by converting the original graph into quotient graphs using Θ * - classes. This technique is applied since the regular cut method is a lengthy process while moving on to higher generations and also due to the presence of odd cycles in the structure. The degree-based indices and the degree-based graph entropies for the cyclen cored dendrimers are further studied. The comparison graphs with respect to the topological indices as well as graph entropies are also presented. [ABSTRACT FROM AUTHOR]

Let GG be a simple graph with degree sequence D(G)=(d1,d2,…,dn)D\left(G)=\left({d}_{1},{d}_{2},\ldots ,{d}_{n}). The first degree-based entropy of GG is defined as I1(G)=ln∑i=1ndi−1∑i=1ndi∑i=1n(dilndi){I}_{1}\left(G)=\mathrm{ln}{\sum }_{i=1}^{n}{d}_{i}-\frac{1}{{\sum }_{i=1}^{n}{d}_{i}}{\sum }_{i=1}^{n}\left({d}_{i}\mathrm{ln}{d}_{i}). In this article, we give sharp upper and lower bounds for the first degree-based entropy of graphs in C(n,k){\mathcal{C}}\left(n,k) and characterize the corresponding extremal graphs when each bound is attained, where C(n,k){\mathcal{C}}\left(n,k) is the set of all cacti with nn vertices and kk cycles.

Graph invariants are extensively being used in different fields for analysing the structural properties of different compounds. Several topological indices, their properties and relations between different indices have been explored. Ivan Gutman recently introduced a new topological index, based on the vertex degree, termed as Sombor indices in the field of Chemical Graph theory. It is based on the Eulerian (distance) metric. Sombor indices and its properties have been explored on a wide range of graphs. However, the existing literature of graph theory bears fewer exploration in the analysis of topological indices of product graphs, a significant operation on graphs. Studying the topological features of molecular paths and cycles is vital for understanding chemical compounds, offering key insights into their structures and behaviours, benefiting diverse sectors such as drug discovery, material science, and chemical engineering. With this motivation, the Sombor indices of tensor product and 2-tensor product of certain families of graphs are established in this paper. Some of these product graphs are analysed by means of SO based graphical entropy.

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces directly is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. However, many problems of interest, such as active SLAM, exhibit structure that can be harnessed to expedite planning. Also, in order to choose an optimal action, an exact value of the objective function is not required as long as the actions can be sorted in the same way. In this paper we leverage these two key aspects and present the topological belief space planning (t-bsp) concept that uses topological signatures to perform this ranking for information-theoretic cost functions, considering only topologies of factor graphs that correspond to future posterior beliefs. In particular, we propose a highly efficient topological signature based on the von Neumann graph entropy that is a function of graph node degrees and supports an incremental update. We analyze it in the context of active pose SLAM and derive error bounds between the proposed topological signature and the original information-theoretic cost function. These bounds are then used to provide performance guarantees for t-bsp with respect to a given solver of the original information-theoretic BSP problem. Realistic and synthetic simulations demonstrate drastic speed-up of the proposed method with respect to the state-of-the-art methods while retaining the ability to select a near-optimal solution. A proof of concept of t-bsp is given in a small-scale real-world active SLAM experiment. [ABSTRACT FROM AUTHOR]

Carbon nanotubes are one of the most extensively studied nanomaterials because of their remarkable mechanical and electrical properties. The Y-junction structures within carbon nanotubes have received significant attention in the field of nanotechnology, primarily due to their immense potential for powering the next generation of multi-terminal nanodevices. Topological indices play a crucial role in exploring the physicochemical properties and structural attributes of chemical compounds, as they are numerical values intricately linked to the molecular structure of these compounds. Moreover, graph-based entropies serve as essential thermophysical parameters used to quantify the heterogeneity and relative stabilities of molecular structures. In this article, we have utilized the NM-polynomial technique to calculate various neighborhood degree sum-based topological indices and graph-based entropies for carbon nanotube Y-junction graphs. [ABSTRACT FROM AUTHOR]

In 1997, Sierpinski graphs, S (n , k) , were obtained by Klavzar and Milutinovic. The graph S (1 , k) represents the complete graph K k and S (n , 3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by S i e (Λ , t) , already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph S i e (Λ , t) . In the second step, we extract some degree-based indices of a generalized Sierpinski graph S i e (Λ , t) using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph S i e (Λ , t) by using the Randić index. [ABSTRACT FROM AUTHOR]

Quantifying similarities/dissimilarities among different graph models and studying the irregularity (heterogeneity) of graphs in graphs and complex networks are one of the fundamental issues as well as a challenge of scientific and practical importance in many fields of science and engineering. This paper has been motivated by the necessity to establish novel and efficient entropy-based methods to quantify the structural irregularity properties of graphs, measure structural complexity, classify, and compare complex graphs and networks. In particular, we explore how criteria such as Shannon entropy, Von Newman, and generalized graph entropies, already defined for graphs, can be used to evaluate and measure irregularities in complex graphs and networks. To do so, we use some results obtained from graph spectral theory related to the construction of matrices obtained from graphs. We show how to use these irregularity indices based on graph entropies and demonstrate the usefulness and efficiency of each of these complexity measures on both synthetic networks and real-world data sets. [ABSTRACT FROM AUTHOR]

Bearing faults are one kind of primary failure in rotatory machines. To avoid economic loss and casualties, it is important to diagnose bearing faults accurately. Vibration-based monitoring technology is widely used to detect bearing faults. Graph signal processing methods promising for the extraction of the fault features of bearings. In this work, graph multi-scale permutation entropy (MPEG) is proposed for bearing fault diagnosis. In the proposed method, the vibration signal is first transformed into a visibility graph. Secondly, a graph coarsening method is used to generate coarse graphs with different reduced sizes. Thirdly, the graph’s permutation entropy is calculated to obtain bearing fault features. Finally, a support vector machine (SVM) is applied for fault feature classification. To verify the effectiveness of the proposed method, open-source and laboratory data are used to compare conventional entropies and other graph entropies. Experimental results show that the proposed method has higher accuracy and better robustness and de-noising ability.

In this study, we analyzed structural changes in financial markets under COVID-19 to support investors' investment decisions. Because an explanation of these changes is necessary to respond appropriately to said changes and prepare for similar major changes in the future, we visualized the financial market as a graph. The hypothesis was based on expertise in the financial market, and the graph was analyzed from a detailed perspective by dividing the graph into domains. We also designed an original change-detection indicator based on the structure of the graph. The results showed that the original indicator was more effective than the comparison method in terms of both the speed of response and accuracy. Explanatory change detection of this method using graphs and domains allowed investors to consider specific strategies. [ABSTRACT FROM AUTHOR]

Objective: This paper applies graph methods to distinguish major depression disorder (MDD) and healthy (H) subjects using the graph features of single-channel electroencephalogram (EEG) signals. Methods: Four network features—graph entropy, mean degree, degree two, and degree three—were extracted from the 19-channel EEG signals of 64 subjects (26 females and 38 males), and then these features were forwarded to a support vector machine to conduct depression classification based on the eyes-open and eyes-closed statuses, respectively. Results: Statistical analysis showed that graph features with degree of two and three, the graph entropy of MDD was significantly lower than that for H (p < 0.0001). Additionally, the accuracy of detecting MDD using single-channel T4 EEG with leave-one-out cross-validation from H was 89.2% and 92.0% for the eyes-open and eyes-closed statuses, respectively. Conclusion: This study shows that the graph features of a short-term EEG can help assess and evaluate MDD. Thus, single-channel EEG signals can be used to detect depression in subjects. Significance: Graph feature analysis discovered that MDD is more related to the temporal lobe than the frontal lobe. [ABSTRACT FROM AUTHOR]

The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. Graph entropies defined for various graph invariants have shown applications in different fields of physics, chemistry, statistics, biology, and social sciences. In this paper, we define graph entropies in terms of fifth geometric-arithmetic index, fourth atom-bond connectivity index and Sanskruti index. We computed the bounds of these graph entropies for arbitrary graphs and for molecular graphs of single-walled armchair carbon nanotube Y-junctions and constructed the regression equations between the computed entropies and topological invariants. [ABSTRACT FROM AUTHOR]

One of the fundamental challenges in reticular chemistry is the characterization of the complexity of the underlying molecular network, in which high complexity signifies low symmetry and high diversity. The entropy of a network is one such topological descriptor that serves to characterize the order/disorder structural complexity. In this paper, we obtain the entropy measures by computing systematic expressions of the self-powered degree-based topological indices for three isoreticular metal organic frameworks with a zinc based central unit and stringed binding linkers with varying benzene molecule counts. We have also enumerated the self-returning and nonreturning walks for these isoreticular structures in order to provide potential pathways for charge and ion transport. We have considered other properties such as eccentricities, radius, diameter, vertex and edge equivalence classes that facilitate rapid computations of thermochemistry and hence relative stabilities of isoreticular networks. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this note we resolve three conjectures from Dehmer et al. (2019) on the comparison of distance measures based on the graph spectra, by constructing families of counterexamples and using computer search. In addition, we prove other results and conditions under which the conjectures hold true. [ABSTRACT FROM AUTHOR]

Learning treatment methods and disease progression is significant part of medicine. Graph representation of data provides wide area for visualization and optimization of structure. Present work is dedicated to suggest method of data processing for increasing information interpretability. Graph compression algorithm based on maximum clique search is applied to data set with acute coronary syndrome treatment trajectories. Results of compression are studied using graph entropy measures. [ABSTRACT FROM AUTHOR]

Scientific research has been facing the problem of increase in size and complexity. Hence, the utilization of scientometric methodology for management of science has been expected because of needs for strategic and organizational management of basic and academic scientific research. Present study focuses on collaboration and knowledge structures in an interdisciplinary research project and proposes an evaluation framework to assist data-driven decision-making in scientific research by measuring the complexity of these structures. Co-author and co-word networks were constructed from the bibliographic information of publications generated in an interdisciplinary research project, and cross-sectional and longitudinal analyses of complexity were conducted by calculating the graph entropy. Observations of these networks demonstrated the different structural features and modes of time evolution. The results of the cross-sectional analysis indicated that the correlations between the amount of change in these complexities suggested the possibility of induction in the knowledge structure by the collaboration structure. The results of the longitudinal analysis informed that the decrease in the increment of complexity over time reflected the transition of observed case's strategy from promoting interdisciplinary research to the integration of research outcomes to realize the vision. The proposed framework will allow to implement real-time and evidence-based management practices in scientific research. [ABSTRACT FROM AUTHOR]

• We define the entropy of a graph using induced connected subgraphs (called graphlets) of different size. • We embed a graph in a feature space using entropies estimated from graphlets of different sizes. • We also include the higher-order graphlets in the feature vector to provide a more richer representation of a graph. • The higher-order graphlets can be computed in polynomial times and their inclusion can increase the classification accuracy. In this paper, we present a general framework to estimate the network entropy that is represented by means of an undirected graph and subsequently employ this framework for graph classification tasks. The proposed framework is based on local information functionals which are defined using induced connected subgraphs of different sizes. These induced subgraphs are termed graphlets. Specifically, we extract the set of all graphlets of a specific sizes and compute the graph entropy using our proposed framework. To classify the network into different categories, we construct a feature vector whose components are obtained by computing entropies of different graphlet sizes. We apply the proposed framework to two different tasks, namely view-based object recognition and biomedical datasets with binary outcomes classification. Finally, we report and compare the classification accuracies of the proposed method and compare against some of the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer Engineering & Applications is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Marginal entropy is one of the distances based on the graph entropy. Then, this entropy is computed by the Wiener index of graphs. In this paper, we obtain the marginal entropy of paths, stars, double stars, cycles and vertex-transitive graphs. [ABSTRACT FROM AUTHOR]

Under the fierce competition and budget constraints, most mobile apps are launched without sufficient tests. Thus, there exists a great demand for automated app testing. Recent developments in various machine learning techniques have made automated app testing a promising alternative to manual testing. This work proposes novel approaches for one of the core functionalities of automated app testing: the detection of changes in usage-phases of a mobile app. Because of the flexibility of app development languages and the lack of standards, each mobile app is very different from other apps. Furthermore, the graphical user interfaces for similar functionalities are rarely consistent or similar. Thus, we propose methods detecting usage-phase changes through object recognition and metrics utilizing graphs and generative models. Contrary to the existing change detection methods requiring learning models, the proposed methods eliminate the burden of training models. This elimination of training is suitable for mobile app testing whose typical usage-phase is composed of less than 10 screenshots. Our experimental results on commercial mobile apps show promising improvement over the state-of-the-practice method based on SIFT (scale-invariant feature transform). [ABSTRACT FROM AUTHOR]

The classical graph entropy based on the vertex coloring proposed by Mowshowitz depends on a graph. In fact, a hypergraph, as a generalization of a graph, can express complex and high-order relations such that it is often used to model complex systems. Being different from the classical graph entropy, we extend this concept to a hypergraph. Then, we define the graph entropy based on the vertex strong coloring of a hypergraph. Moreover, some tightly upper and lower bounds of such graph entropies as well as the corresponding extremal hypergraphs are obtained.

With the fast development of many event-based social networks (EBSNs), event recommendation, which is to recommend a list of upcoming events to a user according to his preference, has attracted a lot of attentions in both academia and industry. In this paper, we propose a successive event recommendation based on graph entropy (SERGE) to deal with the new event cold start problem by exploiting diverse relations as well as asynchronous feedbacks in EBSNs. The SERGE creates recommendation lists at discrete times during each publication period. At the beginning, it constructs a primary graph (PG) based on the entities and their relations in an EBSN and computes the user-event similarity scores by applying a random walk with restart (RWR) algorithm on PG. At each recommendation time, it then constructs a feedback graph (FG) based on the up-to-date user feedbacks on event reservations and applies the RWR again on FG to compute new user-event similarity scores. We then propose to weight the two sets of similarity scores with the graph entropies of both PG and FG and create the final recommendation lists accordingly. We have crawled two datasets from a real EBSN for two cities, Beijing and Shanghai in China. Experimental results validate the effectiveness and superiority of the proposed SERGE scheme over the peer schemes.

Functional modules can be predicted using genome-wide protein–protein interactions (PPIs) from a systematic perspective. Various graph clustering algorithms have been applied to PPI networks for this task. In particular, the detection of overlapping clusters is necessary because a protein is involved in multiple functions under different conditions. graph entropy (GE) is a novel metric to assess the quality of clusters in a large, complex network. In this study, the unweighted and weighted GE algorithm is evaluated to prove the validity of predicting function modules. To measure clustering accuracy, the clustering results are compared to protein complexes and Gene Ontology (GO) annotations as references. We demonstrate that the GE algorithm is more accurate in overlapping clusters than the other competitive methods. Moreover, we confirm the biological feasibility of the proteins that occur most frequently in the set of identified clusters. Finally, novel proteins for the additional annotation of GO terms are revealed.

Abstract Entropy-based methods are useful tools for investigating various problems in mathematical chemistry, computational physics and pattern recognition. In this paper we introduce a general framework for applying Shannon entropy to fullerene graphs, and used it to investigate their properties. We show that important physical properties of these molecules can be determined by applying Hosoya entropy to their corresponding graphs. [ABSTRACT FROM AUTHOR]

Let H be a hypergraph with n vertices. Suppose that d1,d2,...,dn are degrees of the vertices of H . The t-th graph entropy based on degrees of H is defined as I d t (H) = − ∑ i = 1 n ( d i t ∑ j = 1 n d j t log d i t ∑ j = 1 n d j t ) = log ( ∑ i = 1 n d i t ) − ∑ i = 1 n ( d i t ∑ j = 1 n d j t log d i t) , where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of I d t (H) for t = 1, when H is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively. [ABSTRACT FROM AUTHOR]

Abstract Matrix-based centrality measures have enjoyed significant popularity in network analysis, in no small part due to our ability to rigorously analyze their behavior as parameters vary. Recent work has considered the relationship between subgraph centrality, which is defined using the matrix exponential f (x) = exp ⁡ (x) , and the walk structure of a network. In a walk-regular graph, the number of closed walks of each length must be the same for all nodes, implying uniform f -subgraph centralities for any f (or maximum f - walk entropy). We consider when non-walk-regular graphs can achieve maximum entropy, calling such graphs entropic. For parameterized measures, we are also interested in which values of the parameter witness this uniformity. To date, only one entropic graph has been identified, with only two witnessing parameter values, raising the question of how many such graphs and parameters exist. We resolve these questions by constructing infinite families of entropic graphs, as well as a family of witnessing parameters with a limit point at zero. [ABSTRACT FROM AUTHOR]

In order to measure the amount of different information in a system, entropy concept can be used. Graph entropy measures nodes' contribution to the entropy of the graph. By this way, the influential actors can be identified. Due to this case, a new entropy-based method was proposed to identify the influential actors. Karcı entropy was applied to the social networks first time. The alpha parameter allowed us to combine many different conditions together when measuring in the network. The other important contribution of this paper is to predict the value of alpha parameter of Karcı entropy by using fuzzy logic. After that Karcı and Shannon entropies were compared based on experimental results. Moreover, Karcı entropy was compared to traditional centrality measures. If Karcı entropy definition is considered as a set of entropies, Shannon entropy can be regarded as an element of this set. Accordingly, it can be concluded that Karcı entropy is superior to Shannon entropy. • Applying graph entropy to identify influential nodes instead of traditional centrality measures. • Karcı entropy was applied to graph entropy for the first time. • Karcı entropy's α value was determined by using fuzzy α selection algorithm. • Karcı entropy is a promised method for identifying influential node in social networks. • Karcı entropy is more universal with respect to Shannon entropy. [ABSTRACT FROM AUTHOR]

The advent of borophene sheets and their nanoribbons has inspired significant experimental and theoretical research on the 2D-sheets and nanoribbons of boron, wonder materials of the future with the potential to replace graphene. As a result of the electron deficient nature of boron compounds, borophenes exhibit multiple phases with contrasting network structures. The present study employs novel graph theoretical techniques based on neighborhood degree-sum parameters that provide refined bond partitions to characterize the different phases of borophene nanoribbons. We have applied these techniques to the β 12 and χ 3 phases of borophene nanoribbons. We have also employed computer-assisted combinatorial techniques to generate the boron NMR spectra of different phases of the borophene nanoribbons. • Novel graph theoretical techniques are utilized to compute the topological properties of two phases of borophenes. • Phases of boron nanoribbons, encompassing various boundary configurations, are contrasted by their topological properties. • Degree-sum topological indices and entropies of different phases of borophenes are juxtaposed to show their efficacy. • Machine-generated combinatorial 11B NMR spectra of two phases of borophenes show that 11B NMR can be a powerful tool. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel framework of computing the Quantum-based Entropic Representations (QBER) for un-attributed graphs, through the Continuous-time Quantum Walk (CTQW). To achieve this, we commence by transforming each original graph into a family of k -level neighborhood graphs, where each k -level neighborhood graph encapsulates the connected information between each vertex and its k -hop neighbor vertices, providing a fine representation to reflect the multi-level topological information for the original global graph structure. To further capture the complicated structural characteristics of the original graph through its neighborhood graphs, we propose to characterize the structure of each neighborhood graph with the Average Mixing Matrix (AMM) of the CTQW, that encapsulates the time-averaged behavior of the CTQW evolved on the neighborhood graph. More specifically, we show how the AMM matrix allows us to compute a Quantum Shannon Entropy for each vertex, and thus compute an entropic signature for each neighborhood graph by measuring the averaged value or the Jensen–Shannon Divergence between the entropies of its vertices. For each original graph, the resulting QBER is defined by gauging how the entropic signat ures vary on its k -level neighborhood graphs with increasing k , reflecting the multi-dimensional entropy-based structure information of the original graph. Experiments on standard graph datasets demonstrate the effectiveness of the proposed QBER approach in terms of the classification accuracies. The proposed approach can significantly outperform state-of-the-art entropic complexity measuring methods, graph kernel methods, as well as graph deep learning methods. • We propose a novel framework of computing Quantum-based Entropic Representations (QBER) for un-attributed graphs. • The proposed QBER approaches are based on measuring how the entropic signatures vary on the family of the k-level neighborhood graphs. • The entropic signatures are computed through the Average Mixing Matrix (AMM) of the Continuous-time Quantum Walk (CTQW). • The proposed QBER can simultaneously capture both global and local structural characteristics through the AMM matrix of the CTQW. • Experiments on standard graph datasets demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The constantly and rapidly increasing amount of the biological data gained from many different high-throughput experiments opens up new possibilities for data- and model-driven inference. Yet, alongside, emerges a problem of risks related to data integration techniques. The latter are not so widely taken account of. Especially, the approaches based on the flux balance analysis (FBA) are sensitive to the structure of a metabolic network for which the low-entropy clusters can prevent the inference from the activity of the metabolic reactions. In the following article, we set forth problems that may arise during the integration of metabolomic data with gene expression datasets. We analyze common pitfalls, provide their possible solutions, and exemplify them by a case study of the renal cell carcinoma (RCC). Using the proposed approach we provide a metabolic description of the known morphological RCC subtypes and suggest a possible existence of the poor-prognosis cluster of patients, which are commonly characterized by the low activity of the drug transporting enzymes crucial in the chemotherapy. This discovery suits and extends the already known poor-prognosis characteristics of RCC. Finally, the goal of this work is also to point out the problem that arises from the integration of high-throughput data with the inherently nonuniform, manually curated low-throughput data. In such cases, the over-represented information may potentially overshadow the non-trivial discoveries.

A fullerene is a cubic three-connected graph whose faces are entirely composed of pentagons and hexagons. Entropy applied to graphs is one of the significant approaches to measuring the complexity of relational structures. Recently, the research on complex networks has received great attention, because many complex systems can be modelled as networks consisting of components as well as relations among these components. Information—theoretic measures have been used to analyze chemical structures possessing bond types and hetero-atoms. In the present article, we reviewed various entropy-based measures on fullerene graphs. In particular, we surveyed results on the topological information content of a graph, namely the orbit-entropy Ia(G), the symmetry index, a degree-based entropy measure Iλ(G), the eccentric-entropy Ifσ(G) and the Hosoya entropy H(G).

Under the fierce competition and budget constraints, most mobile apps are launched without sufficient tests. Thus, there exists a great demand for automated app testing. Recent developments in various machine learning techniques have made automated app testing a promising alternative to manual testing. This work proposes novel approaches for one of the core functionalities of automated app testing: the detection of changes in usage-phases of a mobile app. Because of the flexibility of app development languages and the lack of standards, each mobile app is very different from other apps. Furthermore, the graphical user interfaces for similar functionalities are rarely consistent or similar. Thus, we propose methods detecting usage-phase changes through object recognition and metrics utilizing graphs and generative models. Contrary to the existing change detection methods requiring learning models, the proposed methods eliminate the burden of training models. This elimination of training is suitable for mobile app testing whose typical usage-phase is composed of less than 10 screenshots. Our experimental results on commercial mobile apps show promising improvement over the state-of-the-practice method based on SIFT (scale-invariant feature transform).