Uncertain Graph Research Articles

A Short Note for Hypersoft Rough Graphs

Graph theory, a branch of mathematics, explores relationships among entities using vertices and edges. To address the uncertainties inherent in real-world networks, Uncertain Graph Theory has emerged as a significant extension within this field. Hypersoft Graphs advance traditional graphs further by incorporating multi-attribute nodes, allowing each node to represent multiple attribute values, thus capturing more complex, multi-dimensional relationships. The Soft Rough Set and Soft Rough Graph combine the principles of Soft Sets and Rough Sets to manage uncertainty in a more refined manner. In this paper, we introduce the Hypersoft Rough Graph and analyze its relationships with other graph classes.

Antipodal Turiyam Neutrosophic Graphs

Graph theory, a mathematical field, investigates the relationships between entities through vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model uncertainties in realworld networks. This paper presents the concept of the Antipodal Turiyam Neutrosophic Graph. In an Antipodal Graph, two nodes are connected if their shortest path distance equals the graph's diameter, emphasizing connections between the farthest nodes. Turiyam Neutrosophic Graphs extend traditional graphs by introducing four membership values-truth, indeterminacy, falsity, and liberal state-assigned to each vertex and edge, enabling a more nuanced representation of complex relationships.

Privacy Protection in Mobile Big Data: Challenges and Solutions

The pervasive use of mobile big data has profoundly altered daily life, providing unprecedented convenience and efficiency. However, with the proliferation of mobile devices and the explosive growth of data volume, the issue of user privacy protection has become increasingly severe. Location information and semantic information, as the two core components of mobile big data, can directly reflect users’ behavioral trajectories and thought dynamics, underscoring the importance of privacy protection. Although existing technologies can protect user data to a certain extent, traditional methods struggle to address increasingly sophisticated attack techniques in the face of evolving privacy threats. A comprehensive privacy protection scheme for mobile big data was proposed in this study, with a focus on two main areas: the privacy protection of location-based and semantic-based mobile big data. For location information protection, an uncertain graph model was employed to effectively resist combined attacks by jointly protecting the user layer and the location layer. For semantic information protection, a hypergraph clustering method was used to structurally protect the user layer and the semantic layer, enhancing the privacy security of semantic information. This study not only addresses existing gaps but also provides new solutions for mobile big data privacy protection, offering significant theoretical and practical value.

Truss community search in uncertain graphs

Truss community search in uncertain graphs

Fuzzy Neural Network for Representation Learning on Uncertain Graphs

Fuzzy Neural Network for Representation Learning on Uncertain Graphs

Generic network sparsification via degree- and subgraph-based edge sampling

Network (or graph) sparsification accelerates many downstream analyses. For graph sparsification, sampling methods derived from local heuristic considerations are common in practice, due to their efficiency in generating sparse subgraphs using only local information. Filtering-based edge sampling is the most typical approach in this respect, yet it heavily depends on an appropriate definition of edge importance. Instead, we propose a generalized node-focused edge sampling framework by preserving scaled/expected local node characteristics. Apart from expected degrees, these local node characteristics include the expected number of triangles and the expected number of non-closed wedges associated with a node. From a technical point of view, we adapt a game-theoretic sampling method from uncertain graph generation to obtain sparse subgraphs that approximate the expected local properties. We include a tolerance threshold for much faster convergence. Within this framework, we provide appropriate algorithmic variants for sparsification. Moreover, we propose a network measure called tri-wedge assortativity for the selection of the most suitable variant when sparsifying a given network. Extensive experimental studies on functional climate, observed real-world, and synthetic networks show the effectiveness of our method in preserving overall structural network properties – on average consistently better than the state of the art.

UBlade: Efficient Batch Processing for Uncertainty Graph Queries

The study of uncertain graphs is crucial in diverse fields, including but not limited to protein interaction analysis, viral marketing, and network reliability. Processing queries on uncertain graphs presents formidable challenges due to the vast probabilistic space they encapsulate. While existing systems employ batch processing to address these challenges, their performance is often compromised by the suboptimal selection of parallel graph traversal methods, the excessive costs in random number generation, and additional workloads intrinsic to batch processing. In this paper, we introduce uBlade, an efficient batch-processing framework for uncertain graph queries on multi-core CPUs. uBlade utilizes the work-efficient graph traversal, achieving superior parallelism in the batch processing model. Additionally, our Quasi-Sampling technique reduces the random number generation cost by a factor of B, with O(B) denoting the batch size. We further examine the extra workload resulting from batch processing and introduce an efficient strategy to reorder possible worlds, minimizing this associated overhead. Through comprehensive evaluations, we showcase that uBlade achieves up to two orders of magnitude speedups against the state-of-the-art CPU and GPU-based solutions.

An Uncertain Graph Method Based on Node Random Response to Preserve Link Privacy of Social Networks

An Uncertain Graph Method Based on Node Random Response to Preserve Link Privacy of Social Networks

Finding Antagonistic Communities in Signed Uncertain Graphs

Finding Antagonistic Communities in Signed Uncertain Graphs

Closeness Centrality on Uncertain Graphs

Centrality is a family of metrics for characterizing the importance of a vertex in a graph. Although a large number of centrality metrics have been proposed, a majority of them ignores uncertainty in graph data. In this article, we formulate closeness centrality on uncertain graphs and define the batch closeness centrality evaluation problem that computes the closeness centrality of a subset of vertices in an uncertain graph. We develop three algorithms, MS-BCC , MG-BCC, and MGMS-BCC , based on sampling to approximate the closeness centrality of the specified vertices. All these algorithms require to perform breadth-first searches (BFS) starting from the specified vertices on a large number of sampled possible worlds of the uncertain graph. To improve the efficiency of the algorithms, we exploit operation-level parallelism of the BFS traversals and simultaneously execute the shared sequences of operations in the breadth-first searches. Parallelization is realized at different levels in these algorithms. The experimental results show that the proposed algorithms can efficiently and accurately approximate the closeness centrality of the given vertices. MGMS-BCC is faster than both MS-BCC and MG-BCC because it avoids more repeated executions of the shared operation sequences in the BFS traversals.

Approximating the Value of Collaborative Team Actions for Efficient Multiagent Navigation in Uncertain Graphs

For a team of collaborative agents navigating through an unknown environment, collaborative actions such as sensing the traversability of a route can have a large impact on aggregate team performance. However, planning over the full space of joint team actions is generally computationally intractable. Furthermore, typically only a small number of collaborative actions is useful for a given team task, but it is not obvious how to assess the usefulness of a given action. In this work, we model collaborative team policies on stochastic graphs using macro-actions, where each macro-action for a given agent can consist of a sequence of movements, sensing actions, and actions of waiting to receive information from other agents. To reduce the number of macro-actions considered during planning, we generate optimistic approximations of candidate future team states, then restrict the planning domain to a small policy class which consists of only macro-actions which are likely to lead to high-reward future team states. We optimize team plans over the small policy class, and demonstrate that the approach enables a team to find policies which actively balance between reducing task-relevant environmental uncertainty and efficiently navigating to goals in toy graph and island road network domains, finding better plans than policies that do not act to reduce environmental uncertainty.

A survey on uncertain graph and uncertain network optimization

A survey on uncertain graph and uncertain network optimization

Efficient Influential Community Search in Large Uncertain Graphs

Influential community search aims to find cohesive subgraphs (communities) with considerable influence. It is a fundamental graph management operator that can play a crucial role in biological network analysis, activity organization, and other real-life applications. Existing research on influential community search is mainly focused on deterministic graphs with the assumption that influences between entities are certain. This assumption is invalid in many cases because it ignores the uncertainty which is an inherent property of influence. Against this backdrop, in this paper, we introduce an uncertain influential community model, namely <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential community, based on which the influential community search problem over uncertain graphs is formulated. Furthermore, we propose an online approach by integrating a peeling-pruning strategy that can progressively refine the given uncertain graph to find the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities. To further improve the search performance, two novel indexes, ICU-Index and FICU-Index, are developed to organize the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities at different probabilistic intervals. The indexes decompose the probabilistic interval into multiple subintervals and based on this, the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities are divided into different groups in turn. Compared with ICU-Index, FICU-Index requires considerably less space with the introduction of two optimization strategies. These indexes help obtain results of an influential community search problem more efficiently. Extensive experiments on large real and synthetic datasets demonstrate the efficiency and effectiveness of our proposed algorithms.

Maximal Quasi-Cliques Mining in Uncertain Graphs

Cohesive subgraph mining is a fundamental problem in the field of graph data analysis. Many existing cohesive graph mining algorithms are mainly tailored to deterministic graphs. Real-world graphs, however, are often not deterministic, but uncertain in nature. Applications of such uncertain graphs include protein-protein interactions networks with experimentally inferred links and sensor networks with uncertain connectivity links. In this article, we study the problem of mining cohesive subgraphs from an uncertain graph. Specifically, we introduce a new <inline-formula><tex-math notation="LaTeX">$(\alpha,\gamma)$</tex-math></inline-formula> -quasi-clique model to model the cohesive subgraphs in an uncertain graph, and propose a basic enumeration algorithm to find all maximal <inline-formula><tex-math notation="LaTeX">$(\alpha,\gamma)$</tex-math></inline-formula> -quasi-cliques. We also develop an advanced enumeration algorithm based on several novel pruning rules, including early termination and candidate set reduction. To further improve the efficiency, we propose several optimization techniques. Extensive experiments on five real-world datasets demonstrate that our solutions are almost three times faster than the baseline approach.

Efficient computation of expected motif frequency in uncertain graphs by exploiting possible world marginalization and motif transition

Efficient computation of expected motif frequency in uncertain graphs by exploiting possible world marginalization and motif transition

Improving accuracy of expected frequency of uncertain roles based on efficient ensembling

This study tackles the problem of extracting the node roles in uncertain graphs based on network motifs. Uncertain graphs are useful for modeling information diffusion phenomena because the presence or absence of edges is stochastically determined. In such an uncertain graph, the node role also changes stochastically according to the presence or absence of edges, so approximate calculation using a huge number of samplings is common. However, the calculation load is very large, even for a small graph. We propose a method to extract uncertain node roles with high accuracy and high speed by ensembling a large number of sampled graphs and efficiently searching for all other transitionable roles. This method provides highly accurate results compared to simple sampling and ensembling methods that do not consider the transition to other roles. In our evaluation experiment, we use real-world graphs artificially assigned uniform and non-uniform edge existence probabilities. The results show that the proposed method outperforms an existing method previously reported by the authors, which is the basis of the proposed method, as well as another current method based on the state-of-the-art algorithm, in terms of efficiency and accuracy.

A survey on mining and analysis of uncertain graphs

An uncertain graph (also known as probabilistic graph) is a generic model to represent many real-world networks from social to biological. In recent times, analysis and mining of uncertain graphs have drawn significant attention from the researchers of the data management community. Several noble problems have been introduced, and efficient methodologies have been developed to solve those problems. Hence, there is a need to summarize the existing results on this topic in a self-organized way. In this paper, we present a comprehensive survey on uncertain graph mining focusing on mainly three aspects: (i) different problems studied, (ii) computational challenges for solving those problems, and (iii) proposed methodologies. Finally, we list out important future research directions.

Bond Graph-Based Approach to Modeling Variable-Speed Gearboxes with Multi-Type Clutches

The modeling and simulation of gearboxes is important for analyzing the dynamic characteristics and designing control strategies of transmission systems. Variable-speed gearboxes include compound planetary gear trains and clutches, which complicates dynamic modeling. Here, a procedural bond graph-based modeling method that considers many uncertainties is proposed. The proposed method yields a constant system–structure model. First, bond graph models of the two most common planetary gears were summarized, and were used as sub-models of a compound planetary gear train. Then, the Karnopp friction sub-model of the friction clutch and a relative angular displacement sub-model of the one-way clutch were constructed. Based on the dynamic coupling between the sub-models, the modeling steps of the gearbox, including the compound planetary gear train friction clutch one-way clutch coupling system, are described in detail. Next, the main sources of uncertainties of gearbox were analyzed and the simulation methods were given. Finally, the novel uncertain bond graph model was used to simulate the double planetary gearbox; the transmission ratio before and after the shift was 2.42 and 1.72, compared with the design values of 2.41 and 1.71, respectively; the deviation is within 5.8%; The average rotating speeds of the output shaft fluctuated by 6 and 2.5% respectively, which was within a reasonable range, so the effectiveness of the method is verified.

Connectivity Index of Generalized Uncertain Graph

In the application of classical graph theory, there always are various indeterministic factors. This study studies the indeterministic factors in the connected graph by employing the uncertainty theory. First, this study puts forward two concepts: generalized uncertain graph and its connectivity index. Second, it presents a new algorithm to compute the connectivity index of an uncertain graph and generalized uncertain graph and verify this algorithm with typical examples. In addition, it proposes the definition and algorithm of α-connectivity index of generalized uncertain graph and verifies the stability and efficiency of this new algorithm by employing numerical experiments.

Rough maximal cliques enumeration in incomplete graphs based on partially-known concept learning

The emerging massive noisy and incomplete data is transforming the conventional graph to the uncertain graph. In this paper, we study rough maximal cliques enumeration (RMCE) in incomplete graphs, which we define as the novel problem of enumerating all maximal cliques where some of edges are unknown to users. The hardness of RMCE is proved to NP-complete. To tackle this problem, an efficient framework for obtaining the rough maximal cliques based on Partially-Known Concept Learning (PKCL). With this framework, a given incomplete graph is initially represented as an incomplete formal context. Then, the partially-known SE-ISI concept lattice is generated through the constructed incomplete formal context. Based on the constructed SE-ISI concept lattice, an equivalence theorem between SE-ISI equiconcepts and rough maximal cliques is presented. The detailed topological structural analysis from the point of views of roughness and SE-ISI concept stability of rough maximal cliques are separately discussed. The evaluation results demonstrate that our proposed PKCL algorithm can better identify the rough maximal cliques under different probability distribution models of links compared to the existing baseline algorithms.