Graph Evolution Research Articles

Impact of Black Swan Events on Ethereum blockchain ERC20 token transaction networks

The Ethereum blockchain and its ERC20 token standard have revolutionized the landscape of digital assets and decentralized applications. ERC20 tokens are programmable and interoperable tokens, enabling various applications and token economies. Transaction graphs, representing the flow of the value between wallets within the Ethereum network, have played a crucial role in understanding the system’s dynamics, such as token transfers and the behavior of traders. Here, we explore the evolution of daily transaction graphs of ERC20 token transactions, which sheds light on the trader’s behavior during the Black Swan Events – 2018 crypto crash and the COVID-19 pandemic. By using the tools from network science and differential geometry, we analyze 0.98 billion of ERC20 token transaction data from November 2015 to January 2023. Our analysis reveals an increase in diverse interaction among the traders and a greater adoption of ERC20 tokens in a maturing Ethereum ERC20 financial ecosystem after the Crypto Crash 2018 and the COVID-19 pandemic. Before the crash and the COVID-19 pandemic, most traders interacted with other traders in an isolated or restricted manner, with each trader focusing solely on either buying or selling activities. However, after the crash and during the pandemic, most traders diversely interacted among themselves by participating in both buying and selling activities. In addition, we observe no significant negative impact of the COVID-19 pandemic on user behavior in the financial ecosystem.

Renyi Type Holographic Dark Energy

Dark energy is one of the prominent mysteries of the universe that still awaits a solution. One of the plausible ways to collect data about any formation or understand its information capacity is to investigate the entropy of that formation. In this study, Renyi Holographic Dark Energy (RHDE) matter distribution is analyzed within the framework of General Relativity Theory, considering homogeneous and isotropic Friedmann-Robertson-Walker (FRW) space-time. Hubble parameter and RHDE density were used to obtain exact solutions of Einstein field equations. The analysis of the obtained solutions was performed by drawing evolution graphs for redshift $z$.

Multi-perspective feedback-attention coupling model for continuous-time dynamic graphs

Abstract Representation learning over graph networks has recently gained popularity, with many models showing promising results. However, several challenges remain: (1) most methods are designed for static or discrete-time dynamic graphs; (2) existing continuous-time dynamic graph algorithms focus on a single evolving perspective; and (3) many continuous-time dynamic graph approaches necessitate numerous temporal neighbors to capture long-term dependencies. In response, this paper introduces a Multi-Perspective Feedback-Attention Coupling (MPFA) model. MPFA incorporates information from both evolving and original perspectives to effectively learn the complex dynamics of dynamic graph evolution processes. The evolving perspective considers the current state of historical interaction events of nodes and uses a temporal attention module to aggregate current state information. This perspective also makes it possible to capture long-term dependencies of nodes using a small number of temporal neighbors. Meanwhile, the original perspective utilizes a feedback attention module with growth characteristic coefficients to aggregate the original state information of node interactions. Experimental results on one dataset organized by ourselves and seven public datasets validate the effectiveness and competitiveness of our proposed model.

TSANet: Forecasting traffic congestion patterns from aerial videos using graphs and transformers

Forecasting traffic congestion patterns in lane-less traffic scenarios is a complex task because of the combination of high & irregular vehicle densities, fluctuating speeds, and the presence of environmental obstacles. Existing techniques like vehicle counting and density prediction, which successfully estimate congestion in lane-based traffic, are unsuitable for lane-less traffic scenarios due to the irregular and unpredictable nature of traffic density patterns. To overcome these challenges, we propose traffic states to measure congestion patterns in lane-less traffic scenarios. Each traffic state is characterized by the spatio-temporal distribution of neighbouring road users, including vehicles and motorcyclists. We employ traffic graphs to capture the spatial distribution of neighbouring road users. Also, we propose a novel method for the automated construction of traffic graphs by leveraging the detection and tracking of individual road users in aerial videos. Further, in order to incorporate the temporal distribution, we utilize a transformer model to capture the evolution of spatial traffic graphs over time. This enables us to forecast future spatio-temporal distributions and their associated traffic states. Our proposed model, named Traffic State Anticipation Network (TSANet), can effectively forecast future traffic states by analysing sequences of current traffic graphs, thereby enhancing our understanding of evolving traffic patterns in lane-less scenarios. Also, to address the lack of publicly available lane-less traffic datasets, we introduce EyeonTraffic (EoT), a large-scale lane-less traffic dataset containing three hours of aerial videos captured at three busy intersections in Ahmedabad city, India. Experimental results on the EoT dataset demonstrate the efficacy of our proposed TSANet in effectively anticipating traffic states across diverse spatial regions within an intersection. In addition, we also show that TSANet generalizes well for previously unseen intersections, making it suitable for analysing various traffic scenarios without the need for explicit training, thereby enhancing its practical applicability.

Asymptotic dynamic graph order evolution analysis

In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over time. We focus on generated graphs whose order (number of nodes) varies over time. We use a concept called “sustainability” to qualify the long-term evolution of dynamic graphs. A dynamic graph is considered sustainable if its evolution does not result in a static, empty, or periodic graph. To illustrate how the analysis can be conducted, a parameterized and probability-based generator, named D3G3 (Degree-Driven Dynamic Geometric Graphs Generator), has been introduced in a recent work. From this model, we derive multiple scenarios that correspond to three trends in graph order evolution. Our central contribution lies in a mathematical framework that provides an expectation of the order of the graph at time step t+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t+1$$\\end{document}, given its order at time step t. Nevertheless, our analysis underscores the challenge of characterizing the sustainability of dynamic graphs, even when a formal mathematical model for graph order evolution is known.

Simple evolving random graphs.

We study random graphs densifying by adding edges. In each step, two vertices are randomly chosen, and an edge between these vertices is created if the vertices belong to trees. An edge is added with probability p if only one vertex belongs to a tree and an attempt fails otherwise. Simple random graphs generated by this procedure contain only trees and unicycles. In the thermodynamic limit, the fraction of vertices in unicycles exhibits a phase transition resembling a percolation transition in classical random graphs. In contrast to classical random graphs, where a giant component born at the transition point eventually engulfs all finite components and densifies forever, the evolution of simple random graphs freezes when trees disappear. We quantify simple random graphs in the supercritical phase and the properties of the frozen state.

Knotted 4-regular graphs. II. Consistent application of the Pachner moves

A common choice for the evolution of the knotted graphs in loop quantum gravity is to use the Pachner moves, adapted to graphs from their dual triangulations. Here, we show that the natural way to consistently use these moves is on framed graphs with edge twists, where the Pachner moves can only be performed when the twists, and the vertices the edges are incident on, meet certain criteria. For other twists, one can introduce an algebraic object, which allow any knotted graph with framed edges to be written in terms of a generalized braid group.

TEA+ : A Novel Temporal Graph Random Walk Engine with Hybrid Storage Architecture

Many real-world networks are characterized by being temporal and dynamic, wherein the temporal information signifies the changes in connections, such as the addition or removal of links between nodes. Employing random walks on these temporal networks is a crucial technique for understanding the structural evolution of such graphs over time. However, existing state-of-the-art sampling methods are designed for traditional static graphs, and as such, they struggle to efficiently handle the dynamic aspects of temporal networks. This deficiency can be attributed to several challenges, including increased sampling complexity, extensive index space, limited programmability, and a lack of scalability. In this article, we introduce TEA+ , a robust, fast, and scalable engine for conducting random walks on temporal graphs. Central to TEA+ is an innovative hybrid sampling method that amalgamates two Monte Carlo sampling techniques. This fusion significantly diminishes space complexity while maintaining a fast sampling speed. Additionally, TEA+ integrates a range of optimizations that significantly enhance sampling efficiency. This is further supported by an effective graph updating strategy, skilled in managing dynamic graph modifications and adeptly handling the insertion and deletion of both edges and vertices. For ease of implementation, we propose a temporal-centric programming model, designed to simplify the development of various random walk algorithms on temporal graphs. To ensure optimal performance across storage constraints, TEA+ features a degree-aware hybrid storage architecture, capable of adeptly scaling in different memory environments. Experimental results showcase the prowess of TEA+ , as it attains up to three orders of magnitude speedups compared to current random walk engines on extensive temporal graphs.

A recurrent graph neural network for inductive representation learning on dynamic graphs

Graph representation learning has recently garnered significant attention due to its wide applications in graph analysis tasks. It is well-known that real-world networks are dynamic, with edges and nodes evolving over time. This presents unique challenges that are distinct from those of static networks. However, most graph representation learning methods are either designed for static graphs, or address only partial challenges associated with dynamic graphs. They overlook the intricate interplay between topology and temporality in the evolution of dynamic graphs and the complexity of sequence modeling. Therefore, we propose a new dynamic graph representation learning model, called as R-GraphSAGE, which takes comprehensive considerations for embedding dynamic graphs. By incorporating a recurrent structure into GraphSAGE, the proposed R-GraphSAGE explores structural and temporal patterns integrally to capture more fine-grained evolving patterns of dynamic graphs. Additionally, it offers a lightweight architecture to decrease the computational costs for handling snapshot sequences, achieving a balance between performance and complexity. Moreover, it can inductively process the addition of new nodes and adapt to the situations without labels and node attributes. The performance of the proposed R-GraphSAGE is evaluated across various downstream tasks with both synthetic and real-world networks. The experimental results demonstrate that it outperforms state-of-the-art baselines by a significant margin in most cases.

Enterprise violation risk deduction combining generative AI and event evolution graph

AbstractIn the current realms of scientific research and commercial applications, the risk inference of regulatory violations by publicly listed enterprises has attracted considerable attention. However, there are some problems in the existing research on the deduction and prediction of violation risk of listed enterprises, such as the lack of analysis of the causal logic association between violation events, the low interpretability and effectiveness of the deduction and the lack of training data. To solve these problems, we propose a framework for enterprise violation risk deduction based on generative AI and event evolution graphs. First, the generative AI technology was used to generate a new text summary of the lengthy and complex enterprise violation announcement to realize a concise overview of the violation matters. Second, by fine‐tuning the generative AI model, an event entity and causality extraction framework based on automated data augmentation are proposed, and the UIE (Unified Structure Generation for Universal Information Extraction) event entity extraction model is used to create the event entity extraction for listed enterprises ‘violations. Then, a causality extraction model CDDP‐GAT (Event Causality Extraction Based on Chinese Dictionary and Dependency Parsing of GAT) is proposed. This model aims to identify and analyse the causal links between corporate breaches, thereby deepening the understanding of the event logic. Then, the merger of similar events was realized, and the causal correlation weights between enterprise violation‐related events were evaluated. Finally, the listed enterprise's violation risk event evolution graph was constructed, and the enterprise violation risk deduction was carried out to form an expert system of financial violations. The deduction results show that the method can effectively reveal signs of enterprise violations and adverse consequences.

Revolutionary Strategy for Depicting Knowledge Graphs with Temporal Attributes

In practical applications, the temporal completeness of knowledge graphs is of great importance. However, previous studies have mostly focused on static knowledge graphs, generally neglecting the dynamic evolutionary properties of facts. Moreover, the unpredictable and limited availability of temporal knowledge graphs, together with the complex temporal dependency patterns, make current models inadequate for effectively describing facts that experience temporal transitions. To better represent the evolution of things over time, we provide a learning technique that uses quaternion rotation to describe temporal knowledge graphs. This technique describes the evolution of entities as a temporal rotation change in quaternion space. Compared to the Ermitian inner product in complex number space, the Hamiltonian product in quaternion space is better at showing how things might be connected. This leads to a learning process that is both more effective and more articulate. Experimental results demonstrate that our learning method significantly outperforms existing methods in capturing the dynamic evolution of temporal knowledge graphs, with improved accuracy and robustness across a range of benchmark datasets.

Towards Effective and General Graph Unlearning via Mutual Evolution

With the rapid advancement of AI applications, the growing needs for data privacy and model robustness have highlighted the importance of machine unlearning, especially in thriving graph-based scenarios. However, most existing graph unlearning strategies primarily rely on well-designed architectures or manual process, rendering them less user-friendly and posing challenges in terms of deployment efficiency. Furthermore, striking a balance between unlearning performance and framework generalization is also a pivotal concern. To address the above issues, we propose Mutual Evolution Graph Unlearning (MEGU), a new mutual evolution paradigm that simultaneously evolves the predictive and unlearning capacities of graph unlearning. By incorporating aforementioned two components, MEGU ensures complementary optimization in a unified training framework that aligns with the prediction and unlearning requirements. Extensive experiments on 9 graph benchmark datasets demonstrate the superior performance of MEGU in addressing unlearning requirements at the feature, node, and edge levels. Specifically, MEGU achieves average performance improvements of 2.7%, 2.5%, and 3.2% across these three levels of unlearning tasks when compared to state-of-the-art baselines. Furthermore, MEGU exhibits satisfactory training efficiency, reducing time and space overhead by an average of 159.8x and 9.6x, respectively, in comparison to retraining GNN from scratch.

AeonG: An Efficient Built-in Temporal Support in Graph Databases

Real-world graphs are often dynamic and evolve over time. It is crucial for storing and querying a graph's evolution in graph databases. However, existing works either suffer from high storage overhead or lack efficient temporal query support, or both. In this paper, we propose AeonG, a new graph database with built-in temporal support. AeonG is based on a novel temporal graph model. To fit this model, we design a storage engine and a query engine. Our storage engine is hybrid, with one current storage to manage the most recent versions of graph objects, and another historical storage to manage the previous versions of graph objects. This separation makes the performance degradation of querying the most recent graph object versions as slight as possible. To reduce the historical storage overhead, we propose a novel anchor+delta strategy, in which we periodically create a complete version (namely anchor) of a graph object, and maintain every change (namely delta) between two adjacent anchors of the same object. To boost temporal query processing, we propose an anchor-based version retrieval technique in the query engine to skip unnecessary historical version traversals. Extensive experiments are conducted on both real and synthetic datasets. The results show that AeonG achieves up to 5.73× lower storage consumption and 2.57× lower temporal query latency against state-of-the-art approaches, while introducing only 9.74% performance degradation for supporting temporal features.

Graph Pooling Inference Network for Text-based VQA

Effectively leveraging objects and optical character recognition (OCR) tokens to reason out pivotal scene text is critical for the challenging Text-based Visual Question Answering (TextVQA) task. Graph-based models can effectively capture the semantic relationship among visual entities (objects and tokens) and report remarkable performance in TextVQA. However, previous efforts usually leverage all visual entities and ignore the negative effect of superfluous entities. This article presents a Graph Pooling Inference Network (GPIN), which is an evolutionary graph learning method to purify the visual entities and capture the core semantics. It is observed that the dense distribution of reduplicative objects and the crowd of semantically dependent OCR tokens usually co-exist in the image. Motivated by this, GPIN adopts an adaptive node dropping strategy to dynamically downscale semantically closed nodes for graph evolution and update. To deepen the comprehension of scene text, GPIN is a dual-path hierarchical graph architecture that progressively aggregates the evolved object graph and the evolved token graph semantics into a graph vector that serves as visual cues to facilitate the answer reasoning. It can effectively eliminate object redundancy and enhance the association of semantically continuous tokens. Experiments conducted on TextVQA and ST-VQA datasets show that GPIN achieves promising performance compared with state-of-the-art methods.

Deep graph tensor learning for temporal link prediction

Knowledge discovery on dynamic graphs has received much attention in recent years. As a key task of dynamic graph research, the goal of temporal link prediction is to accurately predict the time-varying links in dynamic networks. Uncertainty in link emergence is a major challenge in this research, as it is not easy to learn stable and reliable link-level feature representations, which are usually readily available on static graphs. In order to adapt to the ever-changing graph structure, this paper proposes to construct a deep graph tensor learning model, which can capture the contextual characteristics of graph evolution from both the graph structure (spatial) mode and the link sequence (temporal) mode. Therefore, compared to link prediction on static graphs, temporal link prediction can benefit more from the link-level embedding representations coupled with spatio-temporal features. The experimental results on seven public dynamic graph datasets show that the prediction accuracy obtained by the new model is overall better than competing models such as GC-LSTM, EvolveGCN, and HTGN. In the meantime, as a result of getting rid of the traditional RNN learning paradigm, the new model is also significantly better than the traditional temporal graph learning model in terms of training efficiency.

Evolution of graphs in hyperbolic space by their Gauss curvature

In this paper, we consider the α-Gauss curvature flow for complete convex graphs over horosphere in the hyperbolic space. We show that for all positive power α>0, if the initial hypersurface is smooth, complete non-compact uniformly convex graph over Rn and bounded by two horospheres, then the solution of the flow exists for all time. Moreover, the evolution of horospheres act as barriers along the flow.

Graph Evolution-Based Vertex Extraction for Hyperspectral Anomaly Detection.

Anomaly detection is a fundamental task in hyperspectral image (HSI) processing. However, most existing methods rely on pixel feature vectors and overlook the relational structure information between pixels, limiting the detection performance. In this article, we propose a novel approach to hyperspectral anomaly detection that characterizes the HSI data using a vertex-and edge-weighted graph with the pixels as vertices. The constructed graph encodes rich structural information in an affinity matrix. A crucial innovation of our method is the ability to obtain internal relations between pixels at multiple topological scales by processing different powers of the affinity matrix. This power processing is viewed as a graph evolution, which enables anomaly detection using vertex extraction formulated as a quadratic programming problem on graphs of varying topological scales. We also design a hierarchical guided filtering architecture to fuse multiscale detection results derived from graph evolution, which significantly reduces the false alarm rate. Our approach effectively characterizes the topological properties of HSIs, leveraging the structural information between pixels to improve anomaly detection accuracy. Experimental results on four real HSIs demonstrate the superior detection performance of our proposed approach compared to some state-of-the-art hyperspectral anomaly detection methods.

A study on the nonlinear relationship between market, subsidy, and income of photovoltaic enterprises based on chaos theory

With the annual promotion of the international “dual carbon” goals, countries attach great importance to the development and innovation of clean energy. The United States, Japan, and China have all created many policies for the research and market development of photovoltaic energy. This article incorporates market dynamic regulation capability into a two-dimensional system of government subsidy policies and photovoltaic revenue, constructs a three-dimensional dynamic nonlinear model based on market dynamic regulation capability, government subsidies, and enterprise revenue, and numerically simulates and analyzes the impact of parameter and initial value changes in the equation on enterprise revenue. The market dynamic regulation capability is obtained from Chaotic attractors and dynamic evolution graphs of the nonlinear evolution between government subsidies and corporate profits in different scenarios. Research has shown that: (1) Rapidly improving the dynamic regulation ability of the market cannot continuously increase the revenue of the photovoltaic industry; (2) The changes in market dynamics affect the dependence of enterprises on government subsidies; (3) The demand for government subsidies by enterprises gradually decreases with the increase of their own profits.

Dynamic Evolution Graph Attention Network for Semi-Supervised Hyperspectral Image Classification

Dynamic Evolution Graph Attention Network for Semi-Supervised Hyperspectral Image Classification

An inductive knowledge graph embedding via combination of subgraph and type information

Conventional knowledge graph representation learn the representation of entities and relations by projecting triples in the knowledge graph to a continuous vector space. The vector representation increases the precision of link prediction and the efficiency of downstream tasks. However, these methods cannot process previously unseen entities during the knowledge graph evolution. In other words, the model trained on the source knowledge graph cannot be applied to the target knowledge graph containing new unseen entities. Recently, a few subgraph-based link prediction models obtained the inductive ability, but they all neglect semantic information. In this work, we propose an inductive representation learning model TGraiL which considers not only the topological structure but also semantic information. First, distance in the subgraph is used to encode the node’s topological structure. Second, the projection matrix is used to encode the entity type information. Finally, both kinds of information are fused for training to acquire the ultimate vector representation of entities. The experimental results indicate that the model’s performance has been significantly improved compared to the existing baseline models, demonstrating the method’s effectiveness and superiority.