Edge Deletion Research Articles

IMCSN: An improved neighborhood aggregation interaction strategy for multi-scale contrastive Siamese networks

Graph contrastive learning is an effective method for enhancing graph representation by maximizing the similarity of representations between analogous graphs while minimizing the similarity between dissimilar ones. A common approach to improve the representation capabilities of graphs involves data augmentation, which generates additional training samples through transformations applied to the original graphs. However, traditional data augmentation techniques, such as random deletion of nodes or edges, often compromise the structural integrity of graphs, result in loss of crucial information, and lead to representation instability. To overcome these drawbacks, this study introduces a novel data augmentation paradigm, the integration of directed random noise (IDR), which incorporates controlled random noise to optimize the augmentation objectives. IDR enhances the diversity and robustness of representations without sacrificing the structural integrity of the graphs. This approach significantly improves the performance of graph contrastive learning, avoiding the common issues of graph structure damage and information loss associated with conventional methods. To further refine the model, this paper proposes an improved multiscale contrastive Siamese network framework that employs three Siamese networks to process different views of input graphs. It utilizes cross-network and cross-view contrastive learning objectives to optimize graph representations, leveraging the complementary information between different views to maximize the consistency of representations among similar graphs. This enhancement improves the quality and generalizability of graph representations. Additionally, the introduction of a self-supervised loss function based on graph reconstruction within the loss framework capitalizes on the structural similarity between the original and reconstructed graphs to further refine graph representations. This loss function ensures that the global view retains more structural information from the original graph, thus enhancing the complementarity between the global and local views. The effectiveness and stability of this research framework are demonstrated through node classification tasks and visualizations on six real-world datasets, comparing favorably against existing methods such as MERIT and GraphVAT. The proposed model achieves accuracy improvements of 3.21 % and 3.71 % on the Cora dataset and 1.12 % and 1.42 % on the CiteSeer dataset. Additionally, it ranks first in an average accuracy comparison across six datasets, with scores of 80.6 % and 52.67 %. These results underscore the robustness and efficacy of the proposed model in self-supervised graph representation learning, offering substantial advancements over existing techniques.

Fuzzy Outerplanar Graphs and Its Applications

The concept of a crisp graph is essential in the study of outerplanar graphs because outerplanar graphs are a unique type of planar graphs containing special characteristics. One of the core concepts of crisp graphs, the notion of a subgraph, is utilized primarily to solve difficult data problems. In this paper, researching outerplanar graphs in fuzzy graphs is the main aim of the work. By allowing edges connecting vertices to have varying levels of membership or fuzziness, a fuzzy graph is a mathematical framework that develops on the concept of crisp graphs. Because of their capacity to describe unclear or imprecise relationships between items, fuzzy outerplanar graphs might have potential applications. The subgraphs of fuzzy outerplanar graphs are revealed by eliminating specific vertices or edges from the fuzzy graphs. Furthermore, maximum, and maximal fuzzy outerplanar subgraphs defined for both vertex and edge deletion are examined using examples. Some of the connections between the concepts discussed are represented as theorems and conclusions. An application for the layout of a bypass road is discussed using the proposed concepts.

Research on personalised knowledge graph recommendation algorithm based on self-supervised learning

A recommendation algorithm that integrates generative graph self-supervised learning and contrastive graph self-supervised learning is proposed in this paper to address the issues of noisy data and graph incompleteness in knowledge graphs. Firstly, implicit semantics are captured by the self-supervised generative learning method through the masking and reconstruction of the edges of knowledge graph triples. Secondly, a multi-level contrastive learning method is proposed, which includes strategies for edge deletion and feature dropout in the graph structure and embedding layers, respectively.Finally, a contrastive loss function is introduced for contrastive learning to improve the quality of the embedded representations, and the BPR loss is incorporated and combined with the loss from the graph self-supervised learning module to optimize the overall performance of the recommender system. The results demonstrate that on the Last.fm, MovieLens, and Yelp2018 datasets, the model proposed in this paper significantly improves Recall and NDCG evaluation metrics compared to other traditional methods.

Edge Deletion based Subgraph Hiding

Extracting subgraphs from graph data is a challenging and important subgraph mining task since they reveal valuable insights in many domains. However, in the data sharing scenario, some of the subgraphs might be considered as sensitive by the data owner and require hiding before publishing the data. Therefore, subgraph hiding is applied to the data so that when subgraph mining algorithms, such as frequent subgraph mining, subgraph counting, or subgraph matching, are executed on this published data, sensitive subgraphs will not appear. While protecting the privacy of the sensitive subgraphs through hiding, the side effects should be kept at a minimum. In this paper, we address the problem of hiding sensitive subgraphs on graph data and propose an Edge deletion-based heuristic (EDH) algorithm. We evaluate our algorithm using three graph datasets and compare the results with the previous vertex masking heuristic algorithms in terms of execution time and side effects in the context of frequent subgraph hiding. The experimental results demonstrate that the EDH is competitive concerning execution time and outperforms the existing masking heuristic algorithms in terms of side effects by reducing information loss of non-sensitive patterns significantly and not creating fake patterns.

Incremental Sliding Window Connectivity over Streaming Graphs

We study index-based processing for connectivity queries within sliding windows on streaming graphs. These queries, which determine whether two vertices belong to the same connected component, are fundamental operations in real-time graph data processing and demand high throughput and low latency. While indexing methods that leverage data structures for fully dynamic connectivity can facilitate efficient query processing, they encounter significant challenges with deleting expired edges from the window during window updates. We introduce a novel indexing approach that eliminates the need for physically performing edge deletions. This is achieved through a unique bidirectional incremental computation framework, referred to as the BIC model. The BIC model implements two distinct incremental computations to compute connected components within the window, operating along and against the timeline, respectively. These computations are then merged to efficiently compute queries in the window. We propose techniques for optimized index storage, incremental index updates, and efficient query processing to improve BIC effectiveness. Empirically, BIC achieves a 14× increase in throughput and a reduction in P95 latency by up to 3900× when compared to state-of-the-art indexes.

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.

Modification and completion of geological structure knowledge graph based on pattern matching

As a knowledge representation method, knowledge graph is widely used in intelligent question answering systems and recommendation systems. At present, the research on knowledge graph mainly focuses on information query and retrieval based on knowledge graph. In some domain knowledge graphs, specific subgraph structures (patterns) have specific physical meanings. Aiming at this problem, this paper proposes a method and framework of knowledge graph pattern mining based on gat. Firstly, the patterns with specific physical meaning were transformed into subgraph structures containing topological structures and entity attributes. Secondly, the subgraph structure of the pattern is regarded as the query graph, and the knowledge graph is regarded as the data graph, so that the problem is transformed into an approximate subgraph matching problem. Then, the improved relational graph attention network is used to fuse the adaptive edge deletion mechanism to realize the approximate subgraph matching of subgraph structure and attribute, so as to obtain the best matching subgraph. The proposed method is trained in an end-to-end manner. The approximate subgraph matching is realized on the existing data set, and the research work of key pattern mining of complex geological structure knowledge graph is carried out.

On Breaking Truss-based and Core-based Communities

We introduce the general problem of identifying a smallest edge subset of a given graph whose deletion makes the graph community-free. We consider this problem under two community notions that have attracted significant attention: k -truss and k -core. We also introduce a problem variant where the identified subset contains edges incident to a given set of nodes and ensures that these nodes are not contained in any community: k -truss or k -core, in our case. These problems are directly applicable in social networks: The identified edges can be hidden by users or sanitized from the output graph; or in communication networks: the identified edges correspond to vital network connections. We present a series of theoretical and practical results. On the theoretical side, we show through non-trivial reductions that the problems we introduce are NP-hard and, in fact, hard to approximate. For the k -truss-based problems, we also show exact exponential-time algorithms, as well as a non-trivial lower bound on the size of an optimal solution. On the practical side, we develop a series of heuristics that are sped up by efficient data structures that we propose for updating the truss or core decomposition under edge deletions. In addition, we develop an algorithm to compute the lower bound. Extensive experiments on 11 real-world and synthetic graphs show that our heuristics are effective, outperforming natural baselines, and also efficient (up to two orders of magnitude faster than a natural baseline), thanks to our data structures. Furthermore, we present a case study on a co-authorship network and experiments showing that the removal of edges identified by our heuristics does not substantially affect the clustering structure of the input graph. This work extends a KDD 2021 paper, providing new theoretical results as well as introducing core-based problems and algorithms.

Community Deception in Large Networks: Through the Lens of Laplacian Spectrum

Many complex networks in the real world have community structures. Typical examples include online social networks and ecology networks. While the identification of communities bears numerous practical applications, with the increasing awareness of data security and privacy concerns, the need to protect the community affiliations of individuals from disclosing by attackers emerges. This raises the community deception (CD) problem, that is, the opposite of community detection, which asks for ways to minimally perturb the network structures by rewiring nodes so that the target communities maximally hide themself from community detection algorithms. To this end, we investigate the CD problem through a Laplacian spectrum lens and propose a method named <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathtt{ComDeceptor}$</tex-math> </inline-formula> to hide a flexible target set of communities, which is more universal than most existing methods that either focus on hiding the entire communities or a single community. The key idea of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathtt{ComDeceptor}$</tex-math> </inline-formula> is to first allocate the resources of perturbations fairly and effectively. By proving that hiding communities through intercommunity edge addition and intracommunity edge deletion correspond to maximizing the second smallest eigenvalue <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda_2$</tex-math> </inline-formula> and minimizing the largest eigenvalue <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda_n$</tex-math> </inline-formula> of the graph Laplacian, respectively, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathtt{ComDeceptor}$</tex-math> </inline-formula> then incorporates efficient heuristics for approximately solving the problems, thus selecting the appropriate edge to perturb. Experimental results over nine real-world networks and six community detection algorithms not only demonstrate the efficiency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathtt{ComDeceptor}$</tex-math> </inline-formula> , but also the superior performance on obfuscating community structures over the baselines.

Recognizing when a preference system is close to admitting a master list

A preference system I is an undirected graph where vertices have preferences over their neighbors, and I admits a master list if all preferences can be derived from a single ordering over all vertices. We study the problem of deciding whether a given preference system I is close to admitting a master list based on three different distance measures. We determine the computational complexity of the following questions: can I be modified by (i) k swaps in the preferences, (ii) k edge deletions, or (iii) k vertex deletions so that the resulting instance admits a master list? We investigate these problems in detail from the viewpoint of parameterized complexity and of approximation. We also present two applications related to stable and popular matchings.

An FPT Algorithm for Directed Co-Graph Edge Deletion

In the directed co-graph edge-deletion problem, we are given a directed graph and an integer k, and the question is whether we can delete, at most, k edges so that the resulting graph is a directed co-graph. In this paper, we make two minor contributions. Firstly, we show that the problem is NP-hard. Then, we show that directed co-graphs are fully characterized by eight forbidden structures, each having, at most, six edges. Based on the symmetry properties and several refined observations, we develop a branching algorithm with a running time of O(2.733k), which is significantly more efficient compared to the brute-force algorithm, which has a running time of O(6k).

Minimum Strongly Connected Subgraph Collection in Dynamic Graphs

Real-world directed graphs are dynamically changing, and it is important to identify and maintain the strong connectivity information between nodes, which is useful in numerous applications. Given an input graph G , we study a new problem, minimum strongly connected subgraph collection (MSCSC), which asks for a complete collection of subgraphs, each of which contains a maximal set of nodes that are strongly connected to each other via minimum number of edges in G. MSCSC is NP-hard, and its computation and maintenance are challenging, especially on large-scale dynamic graphs. Thus, we resort to approximate MSCSC with theoretical guarantees. We develop a series of approximate MSCSC methods for both static and dynamic graphs. Specifically, we first develop a static MSCSC method MSC that only needs one scan of the graph G , runs in linear time w.r.t. , the number of edges, and provides rigorous approximation guarantees. Then, based on MSC, we leverage a reduced directed acyclic graph of G to design incremental MSCSC method MSC i with two variants to handle edge insertions efficiently. We further develop MSC d that updates MSCSC under edge deletions by efficiently scanning only locally affected subgraphs. Moreover, to demonstrate the high utility, we conduct two use case studies to apply our MSCSC methods to boost the efficiency of dynamic strongly connected component (SCC) maintenance and dynamic SCC-based reachability index maintenance. Extensive experiments on 8 large graphs, including 3 billion-edge graphs, validate the superior efficiency of our methods.

Cluster Editing Parameterized above Modification-disjoint P 3 -packings

Given a graph G =( V,E ) and an integer k , the Cluster Editing problem asks whether we can transform G into a union of vertex-disjoint cliques by at most k modifications (edge deletions or insertions). In this paper, we study the following variant of Cluster Editing . We are given a graph G = ( V,E ), a packing ℋ of modification-disjoint induced P 3 s (no pair of P 3 s in ℋ share an edge or non-edge) and an integer ℓ. The task is to decide whether G can be transformed into a union of vertex-disjoint cliques by at most ℓ +|ℋ| modifications (edge deletions or insertions). We show that this problem is NP-hard even when ℓ = 0 (in which case the problem asks to turn G into a disjoint union of cliques by performing exactly one edge deletion or insertion per element of ℋ) and when each vertex is in at most 23 P 3 s of the packing. This answers negatively a question of van Bevern, Froese, and Komusiewicz (CSR 2016, ToCS 2018), repeated by C. Komusiewicz at Shonan meeting no. 144 in March 2019. We then initiate the study to find the largest integer c such that the problem remains tractable when restricting to packings such that each vertex is in at most c packed P 3 s. Here packed P 3 s are those belonging to the packing ℋ. Van Bevern et al. showed that the case c = 1 is fixed-parameter tractable with respect to ℓ and we show that the case c = 2 is solvable in | V | 2ℓ + O (1) time.

Algorithms for 2-club cluster deletion problems using automated generation of branching rules

In the 2-Club Cluster Vertex Deletion (resp., 2-Club Cluster Edge Deletion) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices (resp., edges) whose removal from G results in a graph in which the diameter of every connected component is at most 2. In this paper we give algorithms for 2-Club Cluster Vertex Deletion and 2-Club Cluster Edge Deletion whose running times are O⁎(3.104k) and O⁎(2.562k), respectively. Our algorithms were obtained using automated generation of branching rules. Our results improve the previous O⁎(3.303k)-time algorithm for 2-Club Cluster Vertex Deletion [Liu et al., FAW-AAIM 2012] and the O⁎(2.695k)-time algorithm for 2-Club Cluster Edge Deletion [Abu-Khzam et al., TCS 2023].

Efficient Core Maintenance in Large Bipartite Graphs

As an important cohesive subgraph model in bipartite graphs, the (α, β)-core (a.k.a. bi-core) has found a wide spectrum of real-world applications, such as product recommendation, fraudster detection, and community search. In these applications, the bipartite graphs are often large and dynamic, where vertices and edges are inserted and deleted frequently, so it is costly to recompute (α, β)-cores from scratch when the graph has changed. Recently, a few works have attempted to study how to maintain (α, β)-cores in the dynamic bipartite graph, but their performance is still far from perfect, due to the huge size of graphs and their frequent changes. To alleviate this issue, in this paper we present efficient (α, β)-core maintenance algorithms over bipartite graphs. We first introduce a novel concept, called bi-core numbers, for the vertices of bipartite graphs. Based on this concept, we theoretically analyze the effect of inserting and deleting edges on the changes of vertices' bi-core numbers, which can be further used to narrow down the scope of the updates, thereby reducing the computational redundancy. We then propose efficient (α, β)-core maintenance algorithms for handling the edge insertion and edge deletion respectively, by exploiting the above theoretical analysis results. Finally, extensive experimental evaluations are performed on both real and synthetic datasets, and the results show that our proposed algorithms are up to two orders of magnitude faster than the state-of-the-art approaches.

Large Coherent States Formed from Disordered k-Regular Random Graphs.

The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs.

Some novel concepts of interval-valued picture fuzzy graphs with applications toward the Transmission Control Protocol and social networks

The Transmission Control Protocol usually involves incomplete and imperfect network states for which sophisticated analysis is needed. Fuzzy logic could be more helpful for the analysis of network state more accurately. The interval-valued picture fuzzy set being the most generalized form of fuzzy set has more capacity to analyze the network state more intelligently. In this manuscript, we present the concepts of interval-valued picture fuzzy graphs (IVPFGs) as an extension of interval-valued fuzzy graphs and picture fuzzy graphs. Since interval-valued picture fuzzy sets are the most advanced form of fuzzy sets, IVPFGs would be a more efficient tool for handling data containing uncertainties. First, basic concepts such as degree, order, and size are discussed, followed by operations such as union, intersection, Cartesian product, composition, and the ring sum of IVPFGs. Then, we provide a few relationships between the ring sum and edge deletion of IVPFGs. Special types of IVPFGs including complete IVPFGs, regular IVPFGs, complement IVPFGs, and strong IVPFGs are introduced. Concepts such as the strength of arcs, path sequence, strength of the path, and connectedness are explored in IVPFGs. Different types of strengths of connectedness are discussed based on specific types of arcs. We also provide a few structural properties of IVPFGs through these arcs. Finally, we give a clue about the potential implementation of IVPFGs, an extension of the fuzzy logic-based Transmission Control Protocol and toward social networking.

The Hamiltonian Cycle and Travelling Salesperson problems with traversal-dependent edge deletion

Variants of the well-known Hamiltonian Cycle and Travelling Salesperson problems have been studied for decades. Existing formulations assume either a static graph or a temporal graph in which edges are available based on some function of time. In this paper, we introduce a new variant of these problems inspired by applications such as open-pit mining, harvesting and painting, in which some edges become deleted or untraversable depending on the vertices that are visited. We formally define these problems and provide both a theoretical and experimental analysis of them in comparison with the conventional versions. We also propose two solvers, based on an exact backward search and a meta-heuristic solver, and provide an extensive experimental evaluation.

A fuzzy planar subgraph formation model for partitioning very large-scale integration networks

This study focuses on forming planar subgraphs in fuzzy graphs where the planarity value is not equal to 1. The paper commences by introducing the concepts of vertex-deletion (VD) and edge-deletion (ED) operations applied to fuzzy graphs. These operations aim to derive the fuzzy planar subgraphs and extensively examine the consequential significant findings. Additionally, maximal and maximum planar subgraphs in vertex-deletion (VD) and edge-deletion (ED) are presented alongside illustrative examples. A novel approach called the Planar Partition subgraph (PP subgraph) is introduced for identifying the fuzzy planar subgraphs from a fuzzy graph with an algorithm rooted in PP subgraphs for enhanced efficiency. Furthermore, the concept of thickness value in fuzzy graphs is constructed using PP-subgraphs is introduced. The discussion involves the thickness value of a fuzzy planar graph and its connection to the planarity value, supported by illustrative examples. Finally, an application made on PP subgraphs where the network needs to be partitioned into a finite number of subgraphs is demonstrated in a very large-scale integration network.

Entropy-Aware Time-Varying Graph Neural Networks with Generalized Temporal Hawkes Process: Dynamic Link Prediction in the Presence of Node Addition and Deletion

This paper addresses the problem of learning temporal graph representations, which capture the changing nature of complex evolving networks. Existing approaches mainly focus on adding new nodes and edges to capture dynamic graph structures. However, to achieve more accurate representation of graph evolution, we consider both the addition and deletion of nodes and edges as events. These events occur at irregular time scales and are modeled using temporal point processes. Our goal is to learn the conditional intensity function of the temporal point process to investigate the influence of deletion events on node representation learning for link-level prediction. We incorporate network entropy, a measure of node and edge significance, to capture the effect of node deletion and edge removal in our framework. Additionally, we leveraged the characteristics of a generalized temporal Hawkes process, which considers the inhibitory effects of events where past occurrences can reduce future intensity. This framework enables dynamic representation learning by effectively modeling both addition and deletion events in the temporal graph. To evaluate our approach, we utilize autonomous system graphs, a family of inhomogeneous sparse graphs with instances of node and edge additions and deletions, in a link prediction task. By integrating these enhancements into our framework, we improve the accuracy of dynamic link prediction and enable better understanding of the dynamic evolution of complex networks.