Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automor...
Many challenges in solving large graph coloring through parallel strategies remain unresolved. Previous algorithms based on Pregel-like frameworks, such as Apache Giraph, encounter parallelism bottlenecks due to sequential execution and the need for...
This study aims to investigate the computation of the partition dimension of various anti-myocardial infarction drugs, a graph-theoretical invariant of molecular graphs representing these drugs, for understanding and computationally characterizing st...
OpenMOC-HEX, a neutron transport calculation code with hexagonal modular ray tracing, has the capability of domain decomposition parallelism based on an MPI parallel programming model. In this paper, the optimization of inter-node communication was s...
Recently, numerous graph partitioning approaches have been proposed to distribute a big graph to machines in a cluster for distributed computing. Due to heavy communication overhead, these graph partitioning approaches always suffered from long ingre...
We study partitions (equitable, externally equitable, or other) of graphs that describe physico-chemical systems at the atomic or molecular level; provide examples that show how these partitions are intimately related with symmetries of the systems;...
The concept of metric-related parameters permeates all of graph theory and plays an important role in diverse networks, such as social networks, computer networks, biological networks and neural networks. The graph parameters include an incredible to...
We present a mapping between rooted tree decompositions and node separator based multilevel graph partitions. Significant research into both tree decompositions and graph partitions exists. We hope that our result allows for an easier knowledge trans...
Geospatial knowledge graphs provide critical technology for integrating geographic information and semantic knowledge, which are very useful for geographic data analysis. As the scale of geospatial knowledge graphs continues to grow, the distributed...
The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries o...
The domatic partition problem consists of partitioning a given graph into a maximum number of disjoint dominating sets. This problem is related with the domatic number problem, which consists of quantifying this maximum number of disjoint dominating...
A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the gr...
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algor...
In recent years, graph similarity algorithms have been extensively developed based on neural networks. However, with an increase in the node count in graphs, these models either suffer from a reduced representation ability or face a significant incre...
In time-evolving graphs, the graph changes at each time interval, and the previously computed results become invalid. We addressed this issue for the traveling salesman problem (TSP) in our previous work and proposed an incremental algorithm where th...
The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb in...
RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary st...
The Maximum Colored Cut problem aims to seek a bipartition of the vertex set of a graph, maximizing the number of colors in the crossing edges. It is a classical Max-Cut problem if the host graph is rainbow. Let
Graph clustering has received considerable attention recently, and its applications are numerous, ranging from the detection of social communities to the clustering of computer networks. It is classified as an NP-class problem, and several algorithms...
In this article, the performance indices on consensus problems for three-layered, multiagent systems are studied from the perspective of algebraic graph theory, where the indices can be used as a measurement of the system performance and refer to the...
With the rapid growth of IoT devices, the threat of botnets is becoming increasingly worrying. There are more and more intelligent detection solutions for botnets that have been proposed with the development of artificial intelligence. However, due t...
A novel non-centralised dispatch strategy is presented for wake redirection to optimise large-scale offshore wind farms operation, creating a balanced control between power production and fatigue thrust loads evenly among the wind turbines. This appr...
This article presents ant algorithms for single- and multi-criteria industrial optimization problems. A common factor in these algorithms is the determination of the set with the maximum number of cliques, which represent the solution to multidimensi...
Objectives: Existing motor imagery electroencephalography (MI-EEG) decoding approaches are constrained by their reliance on sole representations of brain connectivity graphs, insufficient utilization of multi-scale information, and lack of adaptabili...
Attack investigation is a crucial technique in proactively defending against sophisticated attacks. Its purpose is to identify attack entry points and previously unknown attack traces through comprehensive analysis of audit data. However, a major cha...
Dynamics always exist in complex systems. Graphs (complex networks) are a mathematical form for describing a complex system abstractly. Dynamics can be learned efficiently from the structure and dynamics state of a graph. Learning the dynamics in gra...
In this article, some properties of the zero-divisor graph
Deduplication in storage systems has gained momentum recently for its capability in reducing data footprint. However, deduplication introduces challenges to storage management as storage objects (e.g., files) are no longer independent from each other...
At present, with the explosive growth of data scale, subgraph matching for massive graph data is difficult to satisfy with efficiency. Meanwhile, the graph index used in existing subgraph matching algorithm is difficult to update and maintain when fa...
The computational tractability of Integrated Information Theory (IIT) is fundamentally constrained by the exponential cost of identifying the Minimum Information Partition (MIP), which is required to quantify integrated information (Φ). Existing...
Accurate forecasting of city-level large-scale traffic flow is crucial for efficient traffic management and effective transport planning. However, previously proposed traffic flow prediction methods model dynamic spatial correlations across entire tr...
Finite Element Method (FEM) is a well known technique extensively studiedfor spatial and temporal modeling of environmental processes, weather predictioncomputations, and intelligent signal processing for wireless sensors. The need for hugecomputatio...
Existing marine sensor networks acquire data from sea areas that are geographically divided, and store the data independently in their affiliated sea area data centers. In the case of marine events across multiple sea areas, the current network struc...
Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency mat...
The Border Gateway Protocol (BGP) is the core protocol for inter-domain routing on the Internet. However, due to its lack of built-in security authentication mechanisms, BGP is highly vulnerable to misconfigurations or malicious route announcements,...
In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties a...
We ask whether there exist non-isomorphic trace monoids over a fixed alphabet that have the same average parallelism. This question is related to the bivariate generating series
Regional protection based on multisource information of a regional power network depends on communication technology. A partition strategy considering communication constraints and implementation techniques must be considered to realize the regional...
In a fuzzy graph
In this work, the concept of equitable partition is applied to molecular graphs to define quantitative descriptors of the symmetry and complexity of molecules, with the ultimate goal of shedding new light on the structure–property relationships...
Spectral clustering algorithms are often used to find clusters in the community detection problem. Recently, a degree-corrected spectral clustering algorithm was proposed. However, it is only used for partitioning graphs which are generated from stoc...
This paper presents a comparative analysis of three partitioning methods, including Fast Greedy, Random Walk, and Metis, which are commonly used to establish the district metered areas (DMAs) in water distribution systems. The performance of the part...
If G is a graph and
At present, the method of using rule set partitioning technology to assist in constructing multiple decision trees for packet classification has been widely recognized. Rule set partitioning demonstrates a unique symmetry-breaking mechanism, systemat...
Intentional islanding is a corrective procedure that aims to protect the stability of the power system during an emergency, by dividing the grid into several partitions and isolating the elements that would cause cascading failures. This paper propos...
Graph learning methods, especially graph convolutional networks, have been investigated for their potential applicability in many fields of study based on topological data. Their topological data processing capabilities have proven to be powerful. Ho...
A diffusion-taking value in probability-measures on a graph with vertex set V,
The article formulates the Dictionary Recognition problem, which is relevant for a wide range of applied problems: word recognition in a noisy audio signal for natural language processing tasks or in a noisy electromagnetic signal, recognition of vis...
This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system’s robustness. Graph oper...
This paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity. By leveraging the connectivity-based metric and employing a heuristic algorithm, we develop...
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