Sparse Graphs Research Articles

An Integrated Sparse Gated Graph Density Network Based on Transfer Learning for Multi-Site Probabilistic Forecasting of Renewable Energy

An Integrated Sparse Gated Graph Density Network Based on Transfer Learning for Multi-Site Probabilistic Forecasting of Renewable Energy

Statistical match reports of the 2022 volleyball World Championship in the context of network analysis with Gephi

Background and Study Aim. Modern volleyball teams participating in tournaments provide extensive statistical data about their actions. These data are available for analysis and represent a valuable source for assessing the potential and future success of both individual athletes and teams as a whole. In this context, tools such as Gephi become particularly valuable for visualizing and analyzing events at high-level tournaments. Our study aims to create and analyze network models of interaction among men's volleyball teams during the qualifying matches of the 2022 World Championship using the Gephi software.
 Materials and Methods. For the research, data were obtained from a volleyball statistics website renowned for its extensive database. The study centered on Group C, comprising the teams: Poland, USA, Mexico, and Bulgaria. Data from six matches were extracted into Microsoft Excel tables and then converted into CSV format. The data from these tables were processed using the PyCharm programming environment and Python code. Visualization and analysis of the data were conducted using Gephi.
 Results. The results of the data processing highlight the professional expertise of the teams. The average values for all primary metrics underscore the teams' proficiency in executing fundamental actions at an elevated level. Eigenvector centrality helps determine the significance of nodes in the graph. The graph's density is 0.601, suggesting a relatively dense network of connections within the team. This indicates that volleyball players frequently engage with one another and share information on the court. Such extensive interaction can lead to enhanced coordination and efficiency in team actions. The parameter ε has a value of 1.0E-4, denoting high computational precision. The average interaction degree among volleyball players stands at 46.244. This measure denotes the interaction intensity among team members, hinting at the overall court activity. The modularity measure is 0.483, which signals the structural organization of the graph rooted in modularity. The graph comprises 5 modular communities, hinting at shared characteristics and cohesion among players within these groups. The HITS (Hyperlink-Induced Topic Search) metric assesses the node significance in the graph in terms of hubs and authorities. High HITS values pinpoint pivotal players acting as hubs, signifying their numerous connections with fellow teammates. Such players are crucial for facilitating information flow and coordination within the squad.
 Conclusions. Utilizing statistical match reports in volleyball, combined with the Gephi software, offers a deeper insight into the dynamics of player interactions. This aids in pinpointing key players, refining team strategies, and enhancing court coordination. Coaches are advised to leverage these tools for an in-depth evaluation of gameplay instances and to make informed decisions. Network analysis methodologies might soon be indispensable tools in the contemporary coaching toolkit.

Improved credit risk prediction based on an integrated graph representation learning approach with graph transformation

Accurate credit risk prediction effectively supports decision makings and risk prevention in quantitative management. The general paradigm of previous works usually conducts supervised classification with internal information (credit attributes) of instances, while recent studies have introduced external information like texts, images, relations, to improve predictive accuracy. However, how to improve forecasting without explicit external relations still needs to be explored. Motivated by this and also by the increasing popularity of Graph Neural Network (GNN) with its fast infiltration into other disciplines, we propose an integrated graph representation learning approach to realize improved credit risk prediction. It includes two stages: (i) treat instances as nodes and use kNN to extract and construct edges; (ii) implement GNN models to discriminate risk/default cases by node classification. In this way, both “unsupervised” graph transformation and “supervised” node classification have been integrated to formulate the hybrid kNN–GNN model, and experiments on widely-used credit datasets demonstrate its outperformance over direct classification by conventional machine learning techniques. Sensitivity of hyperparameter k indicating different graph sparsity is also analyzed to reveal its optimal selection. Furthermore, ensemble multi-graphs and introduce edge weights are examined to investigate possible advancements with some enhancements observed for both, providing feasible ways to extend the upper bound of this hybrid model’s performances. Our findings exhibit valid improvements in credit risk prediction under the circumstance of only internal information available, and in depth present the future prospects of innovative integrations and applications of GNN methods in dealing with many other operational research tasks.

Sparse graph matching network for temporal language localization in videos

Temporal language localization in videos aims to retrieve the moment that best matches the text description in the untrimmed video using the query text. Existing methods using graph convolutional networks have been effective in feature representation and cross-modal interaction, but the existing methods do not consider the sparsity constraint of the graph when constructing the graph structure, which can easily cause an increase in computational cost and introduce redundant connections that may adversely affect the accuracy of the results. Therefore, we propose a novel sparse graph matching network for temporal language localization in videos. Specifically, we use graph convolutional networks to learn video features and dynamically construct video graph with constraints on sparsity and connectivity; the complementarity between the sequential context and the syntactic structure of text is used to model the semantic features of text. For cross-modal interaction, we design a sparse graph matching method based on affinity matrix to match video and text graphs, and align cross-modal semantic features. Finally, by fusing the features of the two modalities, candidate moments are generated, and their confidence scores are calculated to locate the moment matching the query. Experimental results on the public datasets TACoS, ActivityNet Caption, and QVHighlights demonstrate the superiority of our method compared to state-of-the-art methods.

From Stars to Diamonds: Counting and Listing Almost Complete Subgraphs in Large Networks

Abstract Listing dense subgraphs is a fundamental task with a variety of network analytics applications. A lot of research has been done focusing on $k$-cliques, i.e. complete subgraphs on $k$ nodes. However, requiring complete connectivity between the nodes of a subgraph may be too restrictive in many real applications. Hence, in this paper, we consider a natural relaxation of cliques, called $k$-diamonds and defined as cliques of size $k$ with one missing edge. We first provide a sequential algorithm that, in $O(nm^{(k-1)/2})$ time, counts and lists all the $k$-diamonds in large graphs, for any constant $k \geq 4$. A parallel extension of the sequential algorithm is then proposed and analyzed in a MapReduce-style model, achieving the same local and total space usage of the state-of-the-art algorithms for $k$-cliques. The running time is optimal on dense graphs and $O(\sqrt{m})$ larger than $k$-clique counting if the graph is sparse. Our algorithms compute induced diamonds by analyzing the structure of directed stars formed by the graph nodes and their neighbors.

Graphformer: Adaptive graph correlation transformer for multivariate long sequence time series forecasting

Accurate long sequence time series forecasting (LSTF) remains a key challenge due to its complex time-dependent nature. Multivariate time series forecasting methods inherently assume that variables are interrelated and that the future state of each variable depends not only on its history but also on other variables. However, most existing methods, such as Transformer, cannot effectively exploit the potential spatial correlation between variables. To cope with the above problems, we propose a Transformer-based LSTF model, called Graphformer, which can efficiently learn complex temporal patterns and dependencies between multiple variables. First, in the encoder’s self-attentive downsampling layer, Graphformer replaces the standard convolutional layer with an dilated convolutional layer to efficiently capture long-term dependencies between time series at different granularity levels. Meanwhile, Graphformer replaces the self-attention mechanism with a graph self-attention mechanism that can automatically infer the implicit sparse graph structure from the data, showing better generality for time series without explicit graph structure and learning implicit spatial dependencies between sequences. In addition, Graphformer uses a temporal inertia module to enhance the sensitivity of future time steps to recent inputs, and a multi-scale feature fusion operation to extract temporal correlations at different granularity levels by slicing and fusing feature maps to improve model accuracy and efficiency. Our proposed Graphformer can improve the long sequence time series forecasting accuracy significantly when compared with that of SOTA Transformer-based models.

Local-global feature-based spatio-temporal wind speed forecasting with a sparse and dynamic graph

Accurate wind speed forecasting can help ensure power-system stability. Many previous studies often neglect spatio-temporal dependence. Therefore, effectively modeling the complex and dynamic spatio-temporal correlations (STCs) between spatially distributed wind speeds and extracting informative spatio-temporal features is very important for boosting forecast accuracy. This study proposes a novel sparse and dynamic graph-based spatio-temporal wind speed forecasting method with local–global features (LGFs). First, a dynamic STC modeling block is designed to learn the dynamic STC degree based on the similarity of wind temporal characteristics. To reduce computational costs, a threshold is set to select the most highly correlated neighboring sites, resulting in a sparse graph. Then, a parallel-structured LGF extraction block including a local feature extraction module and a global feature extraction module is developed. It can capture local features for a single site and global features representing spatio-temporal dependence among neighbor sites according to the obtained graph. The obtained features are fused into the comprehensive LGFs. Finally, accurate wind speed forecasts for multiple sites are generated simultaneously. The proposed model is tested using numerous benchmark models, including temporal, spatio-temporal, static graph-based, and complete graph-based models. The results show that it can effectively learn dynamic STCs and attain the highest accuracy.

Decomposing the percolation backbone reveals novel scaling laws of the current distribution

The distribution of currents on critical percolation clusters is the fundamental quantity describing the transport properties of weakly connected systems. Nevertheless, its finite-size extrapolation is still one of the outstanding open questions concerning disordered media. By hierarchically decomposing the 3-connected components of the backbone, we disclose that the current distribution is determined from two distributions, namely, the one corresponding to the number of bonds in each level and another one corresponding to the factors by which the current is reduced, when going from one level to the next. The first distribution follows a finite-size scaling, while the second is a power law with an exponent consistent with 3/4 in two dimensions. The standard hierarchical model for the backbone is too simple to reproduce this complex scenario. Our new decomposition method of the backbone also allows to calculate much smaller currents than before, attaining a precision of 10−35 and systems of size L = 81922. Moreover, our method is not restricted to electric currents on critical percolation clusters but could also be applied to other transport problems on sparse graphs including fluid flow and car traffic.

Topological Bounds on the Price of Anarchy of Clustering Games on Networks

We consider clustering games in which the players are embedded into a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total utility generated in centralized outcomes and equilibrium outcomes in which players selfishly maximize their utility. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding worst-case Price of Anarchy bounds. More specifically, depending on the type of clustering game, our bounds reveal that the Price of Anarchy depends on the maximum subgraph density or the maximum degree of the graph. Among others, these bounds enable us to derive bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs. Depending on the graph density, these bounds stand in stark contrast to the known worst-case Price of Anarchy bounds. Additionally, we characterize the set of distribution rules that guarantee the existence of a pure Nash equilibrium or the convergence of best-response dynamics. These results are of a similar spirit as the work of Gopalakrishnan et al. [ 19 ] and complement work of Anshelevich and Sekar [ 4 ].

Effects of Cascade Reservoirs on Spatiotemporal Dynamics of the Sedimentary Bacterial Community: Co-occurrence Patterns, Assembly Mechanisms, and Potential Functions.

Dam construction as an important anthropogenic activity significantly influences ecological processes in altered freshwater bodies. However, the effects of multiple cascade dams on microbial communities have been largely overlooked. In this study, the spatiotemporal distribution, co-occurrence relationships, assembly mechanisms, and functional profiles of sedimentary bacterial communities were systematically investigated in 12 cascade reservoirs across two typical karst basins in southwest China over four seasons. A significant spatiotemporal heterogeneity was observed in bacterial abundance and diversity. Co-occurrence patterns in the Wujiang Basin exhibited greater edge counts, graph density, average degree, robustness, and reduced modularity, suggesting more intimate and stronger ecological interactions among species than in the Pearl River Basin. Furthermore, Armatimonadota and Desulfobacterota, identified as keystone species, occupied a more prominent niche than the dominant species. A notable distance-decay relationship between geographical distance and community dissimilarities was identified in the Pearl River Basin. Importantly, in the Wujiang Basin, water temperature emerged as the primary seasonal variable steering the deterministic process of bacterial communities, whereas 58.5% of the explained community variance in the neutral community model (NCM) indicated that stochastic processes governed community assembly in the Pearl River Basin. Additionally, principal component analysis (PCA) revealed more pronounced seasonal dynamics in nitrogen functional compositions than spatial variation in the Wujiang Basin. Redundancy analysis (RDA) results indicated that in the Wujiang Basin, environmental factors and in Pearl River Basin, geographical distance, reservoir age, and hydraulic retention time (HRT), respectively, influenced the abundance of nitrogen-related genes. Notably, these findings offer novel insights: building multiple cascade reservoirs could lead to a cascading decrease in biodiversity and resilience in the river-reservoir ecosystem.

Greedy maximal independent sets via local limits

AbstractThe random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent to any previously added vertex. In this paper, we present a general framework for computing the asymptotic density of the random greedy independent set for sequences of (possibly random) graphs by employing a notion of local convergence. We use this framework to give straightforward proofs for results on previously studied families of graphs, like paths and binomial random graphs, and to study new ones, like random trees and sparse random planar graphs. We conclude by analysing the random greedy algorithm more closely when the base graph is a tree.

Maximum Weighted Independent Set: Effective Reductions and Fast Algorithms on Sparse Graphs

Maximum Weighted Independent Set: Effective Reductions and Fast Algorithms on Sparse Graphs

Exact values for some unbalanced Zarankiewicz numbers

AbstractFor positive integers , , and , the Zarankiewicz number is defined to be the maximum number of edges in a bipartite graph with parts of sizes and that has no complete bipartite subgraph containing vertices in the part of size and vertices in the part of size . A simple argument shows that, for each , when . Here, for large , we determine the exact value of in almost all of the remaining cases where . We establish a new family of upper bounds on which complement a family already obtained by Roman. We then prove that the floor of the best of these bounds is almost always achieved. We also show that there are cases in which this floor cannot be achieved and others in which determining whether it is achieved is likely a very hard problem. Our results are proved by viewing the problem through the lens of linear hypergraphs and our constructions make use of existing results on edge decompositions of dense graphs.

Stable fixed points of combinatorial threshold-linear networks

Combinatorial threshold-linear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent networks have long been used as models for associative memory and pattern completion, with stable fixed points playing the role of stored memory patterns in the network. In prior work, we showed that target-free cliques of the graph correspond to stable fixed points of the dynamics, and we conjectured that these are the only stable fixed points possible [19,8]. In this paper, we prove that the conjecture holds in a variety of special cases, including for networks with very strong inhibition and graphs of size n≤4. We also provide further evidence for the conjecture by showing that sparse graphs and graphs that are nearly cliques can never support stable fixed points. Finally, we translate some results from extremal combinatorics to obtain an upper bound on the number of stable fixed points of CTLNs in cases where the conjecture holds.

Multi-hop path reasoning over sparse temporal knowledge graphs based on path completion and reward shaping

Multi-hop path reasoning plays a crucial role in temporal knowledge graph reasoning, aiming to infer deep complex relationships and obtain interpretable reasoning results. Previous reasoning models primarily focus on designing temporal knowledge graphs with rich paths between entities but struggle to handle path sparsity, known as sparse temporal knowledge graphs. Sparse temporal knowledge graphs store only essential knowledge information, resulting in missing connection paths between certain entities and encountering issues of sparse rewards and information scarcity. To tackle these challenges, this paper proposes a multi-hop path reasoning model over sparse temporal knowledge graph based on path completion and reward shaping (STKGR-PR). STKGR-PR dynamically completes missing paths using a temporal embedding model to alleviate path sparsity. To tackle the issue of sparse rewards caused by reduced hit rates, we propose semantic composition-based reasoning path embeddings derived from relation embeddings and timestamp embeddings for reward shaping. Considering the limited information contained in sparse temporal knowledge graphs, we incorporate time vectors into the embedding and multi-hop path reasoning models to enhance the accuracy of reasoning paths and results. Experimental results conducted on six sparse temporal datasets sampled from ICEWS14 and ICEWS515–05 demonstrate that STKGR-PR outperforms state-of-the-art multi-hop path reasoning models over temporal knowledge graphs across all evaluation metrics, while ensuring interpretability.

On the intersection density of the Kneser graph [formula omitted

A set F⊂Sym(V) is intersecting if any two of its elements agree on some element of V. Given a finite transitive permutation group G≤Sym(V), the intersection densityρ(G) is the maximum ratio |F||V||G| where F runs through all intersecting sets of G. The intersection densityρ(X) of a vertex-transitive graph X=(V,E) is equal to maxρ(G):G≤Aut(X),G transitive. In this paper, we study the intersection density of the Kneser graph K(n,3), for n≥7. The intersection density of K(n,3) is determined whenever its automorphism group contains PSL2(q), with some exceptional cases depending on the congruence of q. We also briefly consider the intersection density of K(n,2) for values of n where PSL2(q) is a subgroup of its automorphism group.

Core microbiota play important roles in maintaining soil multi‐nutrient cycling in lakeshore wetland of plateau lake Caohai

AbstractMicroorganisms play important roles in soil biogeochemical processes, but the relative contributions of different microbial members in soil nutrient cycling and community maintenance are unclear especially in wetland soils with water‐level fluctuation. Here, soil samples, collected from severe inundation zone (SIZ), wet–dry cycling zone (WIZ), and arid zone (NIZ) of the lakeshore wetland of plateau lake Caohai, were used to investigate the relative contributions of core and rare taxa in maintaining nutrient cycling and their associations with microbial network. Results showed that WIZ exhibited higher extracellular enzyme activities including β‐1,4‐N‐acetylglucosaminidase, L‐leucine aminopeptidase, and acid phosphatase, the level of multi‐nutrient cycling and core microbial diversity compared with the NIZ and SIZ. The values of topological features (i.e., links, average degree, clustering coefficient, and graph density) were also higher in the WIZ compared with the NIZ and SIZ. Moreover, the core taxa, specifically their community structures, were the most important driver for multi‐nutrient cycles of wetland soil. Among these taxa, Sphingomonas, Bradyrhizobium, Mortierella, and Fusarium as the most abundant taxa in lakeshore wetlands were significantly positively correlated with most extracellular enzymes. By contrast, rare taxa showed higher degree and its subnetwork complexity than those of core taxa, which potentially serve as the species pool of core taxa to maintaining the microbial community stability. In conclusion, our study suggested that core taxa play dominant roles in soil nutrient cycles, while rare microbiota could greatly influence microbial interaction under hydrological changes.

DYS-SLAM: A real-time RGBD SLAM combined with optical flow and semantic information in a dynamic environment1

Traditional Simultaneous Localization and Mapping application in dynamic situations is constrained by static assumptions. However, the majority of well-known dynamic SLAM systems use deep learning to identify dynamic objects, which creates the issue of trade-offs between accuracy and real-time. To tackle this issue, this work suggests a unique dynamic semantics method(DYS-SLAM) for semantic simultaneous localization and mapping that strikes a trade-off between high accuracy and high real-time performance. We propose M-LK, an enhanced Lucas-Kanade(LK) optical flow method. This technique keeps the continuous motion and greyscale consistency assumptions from the original method while switching out the spatial consistency assumption for a motion consistency assumption, reducing sensitivity to image gradients to identify dynamic feature points and regions efficiently. In order to increase segmentation accuracy while maintaining real-time performance, we develop a segmentation refinement scheme that projects 3D point cloud segmentation results into 2D object detection zones. A dense semantic octree graph is built in the interim to expedite the high-level process. Compared to the four equivalent dynamic SLAM approaches, experiments on the publicly available TUM RGB-D dataset demonstrate that the DYS-SLAM method offers competitive localization accuracy and satisfactory real-time performance in both high and low-dynamic scenarios.

SGA-Net: A Sparse Graph Attention Network for Two-View Correspondence Learning

Establishing reliable correspondences between two images is a fundamental and important task in computer vision. This paper proposes a novel network called Sparse Graph Attention Network (SGA-Net), to capture rich contextual information of sparse graphs for feature matching task. Specifically, a graph attention block is proposed to enhance the representational ability of graph-structured features. The proposed block introduces a novel normalization technique for graph-structured features to embed global information into each edge feature, and it adopts the squeeze-and-excitation mechanism to capture graph-wise contextual information. Meanwhile, to further obtain interesting structural information of sparse graphs, a novel sparse graph transformer is developed based on multi-headed self-attention mechanism, while maintaining permutation-equivariance. Additionally, considering that the graph contexts in shallow layers are not fully exploited, a simple graph-context fusion block is introduced to adaptively capture topological information from different layers by implicitly modeling the interdependence between these graph contexts. The proposed SGA-Net can search dependable candidates among the putative correspondences and simultaneously estimate accurate camera poses for two-view geometry estimation. Extensive experiments on outlier removal and camera pose estimation tasks have demonstrated that the proposed SGA-Net outperforms state-of-the-art methods on both outdoor and indoor benchmarks (i.e., YFCC100M and SUN3D). SGA-Net achieves a mAP5° of 58.88% without RANSAC on the outdoor dataset, and it achieves a precision increase of 13.45% and 7.34% compared with the state-of-the-art result on outdoor and indoor datasets, respectively.

Sparse graph neural network aided efficient decoder for polar codes under bursty interference

In this paper, a sparse graph neural network-aided (SGNN-aided) decoder is proposed for improving the decoding performance of polar codes under bursty interference. Firstly, a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding. To further improve the decoding performance, a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network. This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks. Finally, predictions are generated by feeding the embedding vectors into a readout module. Simulation results are shown that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.