Generalized Commuting Graph of Dihedral, Semi-dihedral and Quasi-dihedral Groups

Commuting graphs are characterized by vertices that are non-central elements of a group where two vertices are adjacent when they commute. In this paper, the concept of commuting graph is extended by defining the generalized commuting graph. Furthermore, the generalized commuting graph of the dihedral groups, the quasi-dihedral groups and the semi-dihedral groups are presented and discussed. The graph properties including chromatic and clique numbers are also explored.

Understanding MOF nucleation from solution with Evolving Graphs

Molecular modeling is ordinarily employed to understand the synthesis of complex materials. In this work, we investigate the collective assembly of building units that have been experimentally observed to initiate Metal-Organic Framework (MOF) nucleation. MOFs exhibit attractive characteristics such as remarkable surface area and diverse porosities, however, a mechanistic understanding of their synthesis and scale-up remains underexplored due to the complicated nature of the building block interactions. Here, we tackle this problem with large-scale molecular dynamics simulations under a variety of synthesis conditions and mixture compositions. We observe that the connectivity of building units, as well as their level of crystalline order and fractal dimension, largely vary depending on the synthesis conditions. However, these properties naturally emerge when interpreting the self-assembly process of MOF nuclei as the time-evolution of an undirected graph. The results show that solution-induced conformational complexity and ionic concentration have a dramatic effect on the morphology of clusters emerging during assembly, such diversity is captured by key features of the graph representation. Principal Component Analysis (PCA) on graph properties successfully deconvolutes MOF self-assembly to be characterized by a small number of molecular descriptors, such as average coordination number between half-secondary building units (half-SBUs) and fractal dimension, which can be followed by time-resolved spectroscopy. We conclude that graph theory can be used to understand complex processes such as MOF nucleation by providing molecular descriptors accessible by both simulation and experiment.

Annotation and Classification of Graphs of Property Values Reported in Material Science Literature

Building a system for extracting information from the scientific literature is an important research topic in the field of inorganic materials science. However, conventional extraction systems have a limitation in that they do not extract characteristic values from nontextual components, such as charts, diagrams, and tables, which provide key information in many scientific documents. Although there have been several studies on identifying the characteristic values of graphs in the literature, there is no general method that classifies graphs according to the property conditions of the values in the field of materials science. Therefore, in this study, we focus on graphs that are figures representing graphically numerical data, such as a bar graph and line graph, as the first step toward developing a framework for extracting material property information from such noncontextual components. We propose deep-learning-based classification models for identifying the types of graph properties, such as temperature and time, by combining graph images, text in graphs, and captions in neural networks. To train and evaluate the models, we construct a material graph dataset with different types of material properties from a large collection of data from journals in the field of materials science. By using cloud sourcing, we annotate 16,668 images. Our experimental results demonstrate that the best model can achieve high performance with a microaveraged F-score of 0.961.

Clustering in preferential attachment random graphs with edge-step

We prove concentration inequality results for geometric graph properties of an instance of the Cooper–Frieze [5] preferential attachment model with edge-steps. More precisely, we investigate a random graph model that at each time $t\in \mathbb{N}$ , with probability p adds a new vertex to the graph (a vertex-step occurs) or with probability $1-p$ an edge connecting two existent vertices is added (an edge-step occurs). We prove concentration results for the global clustering coefficient as well as the clique number. More formally, we prove that the global clustering, with high probability, decays as $t^{-\gamma(p)}$ for a positive function $\gamma$ of p, whereas the clique number of these graphs is, up to subpolynomially small factors, of order $t^{(1-p)/(2-p)}$ .

Privacy Preservation in Online Social Networks Using Multiple-Graph-Properties-Based Clustering to Ensure k-Anonymity, l-Diversity, and t-Closeness

As per recent progress, online social network (OSN) users have grown tremendously worldwide, especially in the wake of the COVID-19 pandemic. Today, OSNs have become a core part of many people’s daily lifestyles. Therefore, increasing dependency on OSNs encourages privacy requirements to protect users from malicious sources. OSNs contain sensitive information about each end user that intruders may try to leak for commercial or non-commercial purposes. Therefore, ensuring different levels of privacy is a vital requirement for OSNs. Various privacy preservation methods have been introduced recently at the user and network levels, but ensuring k-anonymity and higher privacy model requirements such as l-diversity and t-closeness in OSNs is still a research challenge. This study proposes a novel method that effectively anonymizes OSNs using multiple-graph-properties-based clustering. The clustering method introduces the goal of achieving privacy of edge, node, and user attributes in the OSN graph. This clustering approach proposes to ensure k-anonymity, l-diversity, and t-closeness in each cluster of the proposed model. We first design the data normalization algorithm to preprocess and enhance the quality of raw OSN data. Then, we divide the OSN data into different clusters using multiple graph properties to satisfy the k-anonymization. Furthermore, the clusters ensure improved k-anonymization by a novel one-pass anonymization algorithm to address l-diversity and t-closeness privacy requirements. We evaluate the performance of the proposed method with state-of-the-art methods using a “Yelp real-world dataset”. The proposed method ensures high-level privacy preservation compared to state-of-the-art methods using privacy metrics such as anonymization degree, information loss, and execution time.

Optimal Incomplete-Block Designs with Low Replication: A Unified Approach Using Graphs

An incomplete-block design defines both a concurrence graph and a Levi graph. Properties of either graph can be used to compare designs with respect to D-optimality and with respect to A-optimality. In this paper, we show that optimality of the design implies strong conditions on connectivity properties of the graph, and use this to classify the optimal designs when the number of observational units is close to minimal.

You Only Traverse Twice: A YOTT Placement, Routing, and Timing Approach for CGRAs

Coarse-grained reconfigurable architecture (CGRA) mapping involves three main steps: placement, routing, and timing. The mapping is an NP-complete problem, and a common strategy is to decouple this process into its independent steps. This work focuses on the placement step, and its aim is to propose a technique that is both reasonably fast and leads to high-performance solutions. Furthermore, a near-optimal placement simplifies the following routing and timing steps. Exact solutions cannot find placements in a reasonable execution time as input designs increase in size. Heuristic solutions include meta-heuristics, such as Simulated Annealing (SA) and fast and straightforward greedy heuristics based on graph traversal. However, as these approaches are probabilistic and have a large design space, it is not easy to provide both run-time efficiency and good solution quality. We propose a graph traversal heuristic that provides the best of both: high-quality placements similar to SA and the execution time of graph traversal approaches. Our placement introduces novel ideas based on “you only traverse twice” (YOTT) approach that performs a two-step graph traversal. The first traversal generates annotated data to guide the second step, which greedily performs the placement, node per node, aided by the annotated data and target architecture constraints. We introduce three new concepts to implement this technique: I/O and reconvergence annotation, degree matching, and look-ahead placement. Our analysis of this approach explores the placement execution time/quality trade-offs. We point out insights on how to analyze graph properties during dataflow mapping. Our results show that YOTT is 60.6 , 9.7 , and 2.3 faster than a high-quality SA, bounding box SA VPR, and multi-single traversal placements, respectively. Furthermore, YOTT reduces the average wire length and the maximal FIFO size (additional timing requirement on CGRAs) to avoid delay mismatches in fully pipelined architectures.