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A spanning k -tree of a connected graph G is a spanning tree in which each vertex admits degree at most k. It is easy to see that a spanning 2-tree is a Hamiltonian path. Hence, a spanning k -tree is an extended concept of a Hamiltonian path. Let Q (G) denote the distance signless Laplacian matrix of a graph G. The largest eigenvalue η 1 (G) of Q (G) is called the distance signless Laplacian spectral radius of G. Liu and Li characterized a connected graph with a perfect matching with respect to the distance signless Laplacian spectral radius (Liu and Li, 2021). Win characterized a connected graph with a spanning k -tree via the number of connected components (Win, 1989). Motivated by Liu and Li's and Win's results, in this paper we investigate the relations between the spanning k -tree and the distance signless Laplacian spectral radius in a connected graph and prove an upper bound for η 1 (G) in a connected graph G to guarantee the existence of a spanning k -tree. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S , and every vertex in V − S is adjacent to a vertex in V − S. The total restrained domination number of G , denoted γ t r (G) , is the smallest cardinality of a total restrained dominating set of G. In this paper we show that if G is a K 1 , ℓ -free graph with δ ≥ ℓ ≥ 3 and δ ≥ 5 , then γ t r (G) ≤ n 1 − (2 δ − 3) (2 δ) δ δ − 1 + o δ (1) . [ABSTRACT FROM AUTHOR]

Diagnosability is a fundamental consideration when designing an interconnected network. The PMC and MM ∗ fault diagnosis models are the two most commonly used models. Both the g -good-neighbour diagnosability and g -extra diagnosability of an interconnection network have been two of the hot topics in the intersectional research areas of Graph theory and Computer Science, which become increasingly attractive for new solutions to real-world problems. However, there are still some problems in the transformation from the concepts of Computer Science to that of mathematics. In this paper, we systematically study such problems and give a strict proof from concepts to mathematical conclusions. In the terms of results, we not only give the relationship between g -good-neighbour diagnosabilities of the network under PMC model and MM ∗ model, but also between g -extra diagnosabilities of the network under PMC and MM ∗ models. To apply our results, we give an application on the enhanced hypercube in the end and derive a lemma explaining whether these are 3-cycles in enhanced hypercubes and how many common neighbours for two vertices of enhanced hypercubes under different values of k in the meantime. [ABSTRACT FROM AUTHOR]

Let k ≥ 2 be an integer. A tree T is called a k-tree if d T (v) ≤ k for each v ∈ V (T) ; that is, the maximum degree of a k-tree is at most k. A k-tree T is a spanning k-tree if T is a spanning subgraph of a connected graph G. Let λ 1 (D (G)) denote the distance spectral radius in G, where D(G) denotes the distance matrix of G. In this paper, we verify an upper bound for λ 1 (D (G)) in a connected graph G to guarantee the existence of a spanning k-tree in G. [ABSTRACT FROM AUTHOR]

A mobile agent, which is an autonomous device navigating in a graph, has to explore a given graph by visiting all of its nodes. We adopt the (arguably) weakest possible model of such a device: a deterministic memoryless automaton (DMA), i.e., a deterministic automaton with a single state. As expected, such a weak machine is incapable of exploring many graphs without marking nodes. Hence we allow the agent to use identical movable pebbles that can be dropped on nodes or picked from them. It turns out that this marking capability significantly enhances the exploration power of the agent. Our goal is to study how the availability of pebbles impacts the class of graphs that a DMA can explore. We first concentrate on finite graphs and show that any finite tree can be explored by a DMA without pebbles but there exist (small) finite graphs that cannot be explored by a DMA without pebbles. Then we turn attention to infinite graphs and fully characterize the class of infinite trees that can be explored by a DMA without pebbles. We also define a large class of infinite trees that can be explored by a DMA with finitely many pebbles. It turns out that many of these trees cannot be explored by a DMA without pebbles. On the other hand, we show a large class of infinite trees that cannot be explored by a DMA with finitely many pebbles. Thus, availability of pebbles yields a strict hierarchy of difficulty of exploration of infinite graphs by a DMA, and this hierarchy is strict even for the class of infinite trees: some trees can be explored without pebbles, some trees can be explored with finitely many pebbles but not without pebbles, and some trees require infinitely many pebbles. Finally, we consider exploration by a DMA with infinitely many pebbles. It turns out that all infinite trees can be explored by a DMA with infinitely many pebbles. By contrast, we construct infinite graphs that cannot be explored by any DMA, even with infinitely many pebbles. [ABSTRACT FROM AUTHOR]

An isolating set in a graph is a set X of vertices such that every edge of the graph is incident with a vertex of X or its neighborhood. The isolation number of a graph, or equivalently the vertex-edge domination number, is the minimum number of vertices in an isolating set. Caro and Hansberg, and independently Żyliński, showed that the isolation number is at most one-third the order for every connected graph of order at least 6. We show that in fact all such graphs have three disjoint isolating sets. Further, using a family introduced by Lemańska, Mora, and Souto-Salorio, we determine all graphs with equality in the original bound. [ABSTRACT FROM AUTHOR]

Given a pair of real symmetric matrices A , B ∈ R n × n with nonzero patterns determined by the edges of any pair of chosen graphs on n vertices, we consider an inverse eigenvalue problem for the structured matrix C = [ A B I O ] ∈ R 2 n × 2 n. We conjecture that C can attain any spectrum that is closed under conjugation. We use a structured Jacobian method to prove this conjecture for A and B of orders at most 4 or when the graph of A has a Hamilton path, and prove a weaker version of this conjecture for any pair of graphs with a restriction on the multiplicities of eigenvalues of C. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph and A (G) be the adjacency matrix of G. A diagonal matrix with diagonal entries ±1 is called a signature matrix. If A (G) is nonsingular and X = S A (G) − 1 S − 1 is entrywise nonnegative for some signature matrix S , then X can be viewed as the adjacency matrix of a unique weighted graph. It is called the inverse of G , denoted by G +. A graph G is said to have the reciprocal eigenvalue property (property(R)) if A (G) is nonsingular, and 1 λ is an eigenvalue of A (G) whenever λ is an eigenvalue of A (G). Further, if λ and 1 λ have the same multiplicity for each eigenvalue λ , then G is said to have the strong reciprocal eigenvalue property (property (SR)). It is known that for a tree T , the following conditions are equivalent: a) T + is isomorphic to T , b) T has property (R), c) T has property (SR) and d) T is a corona tree (it is a tree which is obtained from another tree by adding a new pendant at each vertex). Studies on the inverses, property (R) and property (SR) of bipartite graphs are available in the literature. However, their studies for the non-bipartite graphs are rarely done. In this article, we study the inverse and property (SR) for non-bipartite graphs. We first introduce an operation, which helps us to study the inverses of non-bipartite graphs. As a consequence, we supply a class of non-bipartite graphs for which the inverse graph G + exists and G + is isomorphic to G. It follows that each graph G in this class has property (SR). [ABSTRACT FROM AUTHOR]

The oriented chromatic number of a directed graph G is the minimum order of an oriented graph to which G has a homomorphism. The oriented chromatic number χ o (F) of a graph family F is the maximum oriented chromatic number over any orientation of any graph in F. For the family of hexagonal grids H 2 , Bielak (2006) proved that 5 ≤ χ o (H 2) ≤ 6. Here we close the gap by showing that χ o (H 2) ≥ 6. [ABSTRACT FROM AUTHOR]

Let C k (n) denote the family of all connected graphs of order n with chromatic number k. In this paper we show that the conjecture proposed by Tomescu which if x ≥ k ≥ 4 and G ∈ C k (n) , then P (G , x) ≤ (x) k (x - 1) n - k holds under the additional condition that G has an independent cut-set T of size at most 2 such that the number of components in G \ T is equal to the independence number of G. [ABSTRACT FROM AUTHOR]

The relative fixity of a digraph Γ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of Γ and the number of vertices of Γ . We characterize the vertex-primitive digraphs whose relative fixity is at least 1 3 , and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant. [ABSTRACT FROM AUTHOR]

Purpose. Ensuring the safety of train traffic is a mandatory task in the development of technical equipment of railway transport in Ukraine. To diagnose and verify the performance of such systems, simulation models of overhead devices, in particular, the rail circle, are used. The most commonly used models are in the form of differential equations and in operator form. Unfortunately, they are not fully suitable for solving this problem. In this regard, there is a need to create a mathematical model that is easier to integrate for checking both relay electrical interlocking and microprocessor-based interlocking systems. Methodology. To achieve this goal, the authors proposed to create a mathematical model in the form of a finite discrete automaton. This paper considers the creation of a model of a station rail circuit as a directed graph. During the creation of the model, the input and output values of the model and the states are determined. The tables of inputs and outputs of the automaton are constructed, sequential expressions for the abstract model of the automaton are created, and their minimization is performed. The states of the automaton are coded using trigger circuits. Findings. In the course of the research, a mathematical model of the rail circle in the form of a Moore model finite automaton was created, and its performance was tested in the Proteus software environment. The developed model allows to simulate the operation of a stationary rail circuit at the level of abstraction, which operates with binary signals. This makes it possible to simplify the coordination of the model with microprocessor-based centralization software. In general, it is now possible to more effectively check the performance of microprocessor-based interlocking systems at the design and commissioning stages. Originality. The developed mathematical model makes it possible to determine the response of the microprocessor-based centralization software to the behavior of the rail circuit in various, in particular atypical, operating modes, as well as to determine the response of the station electrical centralization system to individual failures and to the occurrence of several failures simultaneously. Practical value. The proposed mathematical model can be used both to check the operation of microprocessor-based centralization systems at the design and implementation stages and for relay centralization systems when developing diagnostic complexes for monitoring their performance.

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of $ 1 $ or $ 0 $, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multi-criteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices.

Given a graph G and an integer [Formula: see text], a spanning subgraph H of G is called a [Formula: see text]-factor of G if every component of H is a path with at least k vertices. A graph G is [Formula: see text]-factor avoidable if for every edge [Formula: see text], G has a [Formula: see text]-factor excluding e. A graph G is said to be [Formula: see text]-factor critical avoidable if the graph [Formula: see text] is [Formula: see text]-factor avoidable for any [Formula: see text] with [Formula: see text]. Here we study the sharp bounds of toughness and isolated toughness conditions for the existence of [Formula: see text]-factor critical avoidable graphs. In view of graph theory approaches, this paper mainly contributes to verify that (i) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its toughness [Formula: see text]; (ii) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its isolated toughness [Formula: see text].

Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson’s correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R2), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures.

The IOTA Tangle, a Directed Acyclic Graph (DAG)-based distributed ledger, is popular for its scalability and suitability for IoT applications, offering fee-less transactions. A critical component of IOTA’s architecture is the Cumulative Weight Calculation (CWC), essential for its tip selection mechanism. This paper introduces an optimization of the IOTA Reference Implementation (IRI) CWC process originally implemented using Breadth-First Search (BFS) by employing Depth-First Search (DFS) and Iterative Deepening Search (IDS) algorithms. We present a comparative analysis of these methods, demonstrating that DFS and IDS provide significant improvements in computational efficiency, particularly beneficial for IoT devices with limited processing capabilities. Our findings are substantiated through a series of experiments on a Tangle snapshot, highlighting the enhanced performance and reduced resource utilization of the proposed methods. This study contributes to the ongoing development of DAG-based distributed ledgers, offering insights into more efficient algorithmic solutions for large-scale, decentralized networks.

Abstract Pretrained deep learning models self-supervised on large datasets of language, image, and graph representations are often fine-tuned on downstream tasks and have demonstrated remarkable adaptability in a variety of applications including chatbots, autonomous driving, and protein folding. Additional research aims to improve performance on downstream tasks by fusing high dimensional data representations across multiple modalities. In this work, we explore a novel fusion of a pretrained language model, ChemBERTa-2, with graph neural networks for the task of molecular property prediction. We benchmark the MolPROP suite of models on seven scaffold split MoleculeNet datasets and compare with state-of-the-art architectures. We find that (1) multimodal property prediction for small molecules can match or significantly outperform modern architectures on hydration free energy (FreeSolv), experimental water solubility (ESOL), lipophilicity (Lipo), and clinical toxicity tasks (ClinTox), (2) the MolPROP multimodal fusion is predominantly beneficial on regression tasks, (3) the ChemBERTa-2 masked language model pretraining task (MLM) outperformed multitask regression pretraining task (MTR) when fused with graph neural networks for multimodal property prediction, and (4) despite improvements from multimodal fusion on regression tasks MolPROP significantly underperforms on some classification tasks. MolPROP has been made available at https://github.com/merck/MolPROP . Scientific contribution This work explores a novel multimodal fusion of learned language and graph representations of small molecules for the supervised task of molecular property prediction. The MolPROP suite of models demonstrates that language and graph fusion can significantly outperform modern architectures on several regression prediction tasks and also provides the opportunity to explore alternative fusion strategies on classification tasks for multimodal molecular property prediction.

Nowadays, modernizing the data warehouse ecosystem is a key challenge in decision support systems. This modernization is crucial for ensuring scalability and meeting evolving business requirements, especially with the advent of big data. A promising solution involves implementing data warehouses with contemporary data stores, such as NoSQL. In this context, we introduce in this paper a framework that leverages Model-Driven Architecture (MDA) to design and implement modern data warehouses across NoSQL data stores. Our MDA approach aims to offer a collaborative, dynamic, and reusable process for developing NoSQL-oriented data warehouses tailored to specific project requirements. It facilitates the automatic and dynamic generation of a hybrid data warehouse model from its conceptual model, which encompasses structural, domain, and access parameters. Moreover, our framework includes the generation of implementation code for the data warehouse, along with a set of files to validate, document, and illustrate the data warehouse schema on a target platform. Finally, we present a detailed case study to highlight the effectiveness of our MDA framework. [JJCIT 2024; 10(2.000): 214-230]

The major concerns of e-commerce are the optimization of order dispatch operations and delivery time prediction. Finding the optimal path is considered an important problem in logistics systems. Efficient order distribution is crucial for enhancing logistic operations, especially in urban environments like the city of Tetovo. Therefore, proper prediction and optimization for delivery operations are required for optimal logistics management. This study proposes a novel approach to optimize order distribution utilizing Dijkstra’s Algorithm, a wellestablished method in graph theory and network analysis. To ensure better visibility of the logistics activities and avoid possible obstacles it is suitable to adopt a graph-based method. By modeling Tetovo city’s road network as a graph, with intersections as nodes and roads as edges, the algorithm calculates the shortest paths between various distribution points, such as warehouses and delivery destinations. From the drop points, we will get the information and data about the delivery address, weight of goods packages, and number of customer packages carried by a courier in one delivery transfer by truck delivery logistics. In the meantime, the data about the distance from the distribution points to the delivery destinations will be obtained from the Open Street Maps applications. All the data above will be used to construct a connected weight graph as an initial model graph. Using a methodology based on Dijkstra’s Algorithm, we will determine the shortest or fastest route for delivery service in logistics distribution. By denoting the location of a drop point as a starting point of the route and the road connecting two locations as an edge where the distance traveled from the drop point to the customers or from one customer to another will represent the weight in the graph, we can apply the Dijkstra’s algorithm to optimize the mileage of the delivery packages. The optimization process aims to reduce delivery time and minimize costs while maximizing resource utilization and customer satisfaction. The implementation of Dijkstra’s Algorithm in this context involves factors like traffic congestion, road conditions, and delivery priorities. This algorithm works by finding the lowest cost path with various costs associated with the edges enabling the most efficient way of completing an order within a factory or warehouse. We represent a JavaScript implementation of this algorithm. Through simulation and empirical validation, the proposed approach demonstrates significant improvements in order distribution efficiency compared to traditional methods. This research contributes to the advancement of logistic optimization techniques and provides practical insights for enhancing urban delivery systems in the city of Tetovo and similar metropolitan areas. [ABSTRACT FROM AUTHOR]

Whole-tissue transcriptomic analyses have been helpful to characterize molecular subtypes of hepatocellular carcinoma (HCC). Metabolic subtypes of human HCC have been defined, yet whether these different metabolic classes are clinically relevant or derive in actionable cancer vulnerabilities is still an unanswered question. Publicly available gene sets or gene signatures have been used to infer functional changes through gene set enrichment methods. However, metabolism-related gene signatures are poorly co-expressed when applied to a biological context. Here, we apply a simple method to infer highly consistent signatures using graph-based statistics. Using the Cancer Genome Atlas Liver Hepatocellular cohort (LIHC), we describe the main metabolic clusters and their relationship with commonly used molecular classes, and with the presence of TP53 or CTNNB1 driver mutations. We find similar results in our validation cohort, the LIRI-JP cohort. We describe how previously described metabolic subtypes could not have therapeutic relevance due to their overall downregulation when compared to non-tumoral liver, and identify N-glycan, mevalonate and sphingolipid biosynthetic pathways as the hallmark of the oncogenic shift of the use of acetyl-coenzyme A in HCC metabolism. Finally, using DepMap data, we demonstrate metabolic vulnerabilities in HCC cell lines. [ABSTRACT FROM AUTHOR]

Let G be a connected graph of order n, where n is a positive integer. A spanning subgraph F of G is called a path-factor if every component of F is a path of order at least 2. A P ≥ k -factor means a path-factor in which every component admits order at least k ( k ≥ 2 ). The distance matrix D (G) of G is an n × n real symmetric matrix whose (i, j)-entry is the distance between the vertices v i and v j . The distance signless Laplacian matrix Q (G) of G is defined by Q (G) = T r (G) + D (G) , where Tr(G) is the diagonal matrix of the vertex transmissions in G. The largest eigenvalue η 1 (G) of Q (G) is called the distance signless Laplacian spectral radius of G. In this paper, we aim to present a distance signless Laplacian spectral radius condition to guarantee the existence of a P ≥ 2 -factor in a graph and claim that the following statements are true: (i) G admits a P ≥ 2 -factor for n ≥ 4 and n ≠ 7 if η 1 (G) < θ (n) , where θ (n) is the largest root of the equation x 3 - (5 n - 3) x 2 + (8 n 2 - 23 n + 48) x - 4 n 3 + 22 n 2 - 74 n + 80 = 0 ; (ii) G admits a P ≥ 2 -factor for n = 7 if η 1 (G) < 25 + 161 2 . [ABSTRACT FROM AUTHOR]

For a graph G = (V G , E G) , a degree-based graphical index G I d takes the general form G I d = ∑ x y ∈ E G ϕ (d x , d y) , where ϕ is a symmetric map and d i is the degree of i ∈ V G . For α ∈ R , if ϕ = (d x d y) α (resp. ϕ = (d x + d y) α ), the index is called the general product-connectivity R α (resp. general sum-connectivity S C I α ) index. In this paper, by formulating an optimization problem, we determine the value(s) of α , for which the linear/multiple correlation coefficient of R α and S C I α with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area. [ABSTRACT FROM AUTHOR]

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. [ABSTRACT FROM AUTHOR]

Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph H = (V , E) . Graphs possessing the property of being 1-extendable are termedas Berge graphs. This introduction gave rise to the notion of well-covered graphs and well-dominated graphs. A graph is categorized as well-covered if each of its maximal independent sets is, in fact, a maximum independent set. Similarly, a graph attains the classification of well-dominated if every minimal dominating set (DS) within it is a minimum dominating set. In alignment with the concept of k-extendable graphs, the framework of (k , γ) -endowed graphs and symmetric (k , γ) -endowed graphs are established. In these graphs, each DS of size k encompasses a minimum DS of the graph. In this article, a study of γ -endowed dominating sets is initiated. Various results providing a deep insight into γ -endowed dominating sets in graphs such as those characterizing the ones possessing a unique minimum DS are proven. We also introduce and study the symmetric γ -endowed graphs and minimality of dominating sets in them. In addition, we give a solution to an open problem in the literature. which seeks to find a domination-based parameter that has a correlation coefficient of ρ > 0.9967 with the total π -electronic energy of lower benzenoid hydrocarbons. We show that the upper dominating number Γ (H) studied in this paper delivers a strong prediction potential. [ABSTRACT FROM AUTHOR]

We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool is a connection between polar sets in such boundaries and null sets of paths. This connection relies on suitably diverging functions of finite energy. [ABSTRACT FROM AUTHOR]

In this paper, we study the quenching phenomenon related to the ω-diffusion equation on graphs with a potential and a singular source ut(x, t) = Δωu(x, t) + b(x)(1 - u(x, t))-p, where Δω is called the discrete weighted Laplacian operator. Under some appropriate hypotheses, we prove the existence and uniqueness of the local solution via Banach fixed point theorem. We also show that the solution of the problem quenches in a finite time and that the time-derivative blows up at the quenching time. Moreover, we estimate the quenching time and the quenching rate. Finally, we verify our results through some numerical examples. [ABSTRACT FROM AUTHOR]

Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and viruses. Several methods have emerged to pinpoint these influential entities in networks, represented as graphs. In these graphs, nodes correspond to individuals and edges indicate their connections. This study focuses on centrality measures, prized for their straightforwardness and effectiveness. We divide structural centrality into two categories: local, considering a node's immediate vicinity, and global, accounting for overarching path structures. Some techniques blend both centralities to highlight nodes influential at both micro and macro levels. Our paper presents a novel centrality measure, accentuating node degree and incorporating the network's broader features, especially paths of different lengths. Through Spearman and Pearson correlations tested on seven standard datasets, our method proves its merit against traditional centrality measures. Additionally, we employ the susceptible–infected–recovered (SIR) model, portraying virus spread, to further validate our approach. The ultimate influential node is gauged by its capacity to infect the most nodes during the SIR model's progression. Our results indicate a notable correlative efficacy across various real-world networks relative to other centrality metrics. [ABSTRACT FROM AUTHOR]

Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson's correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R2), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures. [ABSTRACT FROM AUTHOR]