Distributed Triangle Approximately Counting Algorithms in Simple Graph Stream

Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, the problem of counting global and local triangles in a graph stream has been widely studied, and numerous triangle counting steaming algorithms have emerged. To improve the throughput and scalability of streaming algorithms, many researches of distributed streaming algorithms on multiple machines are studied. In this article, we first propose a framework of distributed streaming algorithm based on the Master-Worker-Aggregator architecture. The two core parts of this framework are an edge distribution strategy, which plays a key role to affect the performance, including the communication overhead and workload balance, and aggregation method, which is critical to obtain the unbiased estimations of the global and local triangle counts in a graph stream. Then, we extend the state-of-the-art centralized algorithm TRIÈST into four distributed algorithms under our framework. Compared to their competitors, experimental results show that DVHT-i is excellent in accuracy and speed, performing better than the best existing distributed streaming algorithm. DEHT-b is the fastest algorithm and has the least communication overhead. What’s more, it almost achieves absolute workload balance.

A novel method for identifying influential nodes in complex networks based on gravity model

How to identify influential nodes in complex networks is an essential issue in the study of network characteristics. A number of methods have been proposed to address this problem, but most of them focus on only one aspect. Based on the gravity model, a novel method is proposed for identifying influential nodes in terms of the local topology and the global location. This method comprehensively examines the structural hole characteristics and K-shell centrality of nodes, replaces the shortest distance with a probabilistically motivated effective distance, and fully considers the influence of nodes and their neighbors from the aspect of gravity. On eight real-world networks from different fields, the monotonicity index, susceptible-infected-recovered (SIR) model, and Kendall's tau coefficient are used as evaluation criteria to evaluate the performance of the proposed method compared with several existing methods. The experimental results show that the proposed method is more efficient and accurate in identifying the influence of nodes and can significantly discriminate the influence of different nodes.

Research on Local Topology Tracking of Power Grid Based on Graph Theory

Power network topology identification, judgment, and tracking are the basic functional components of power system guarantee system and security management system. They can provide basic network structure data for other application software programs of power system. However, the traditional power grid topology method is not easy to implement and provides less relevant data that can be accurately analyzed, so that relevant personnel cannot fully understand the state of the power grid and give accurate commands, resulting in serious power accidents. Therefore, this paper proposes the research of power grid local topology tracking based on graph theory and constructs the power grid local topology tracking algorithm based on graph theory. The experimental results show that the local topology tracking algorithm based on graph theory can track the local topology of power grid quickly and effectively. Compared with the traditional method based on priority search, although the first power grid topology takes a relatively long time, it greatly improves the search and processing time after each time and has high efficiency in local topology. This shows that the local topology tracking algorithm based on graph theory needs less computation when carrying out the local topology of power grid. At the same time, the theory of power grid local topology tracking algorithm based on graph theory is relatively simple and easy to time, which is more practical than the traditional method.

Study on Discovery Method of Cooperative Research Team Based on Improved Louvain Algorithm

According to the needs of scientific research project research and development, the research of cooperative team excavation methods was carried out. Aiming at the current difficulties in accurately and reliably defining and identifying cooperative research teams from co-author network, an improved Louvain algorithm that integrates core node recognition was proposed: Louvain-LSCR algorithm. Based on the analysis of the Louvain algorithm, considering the local topology of the node in the network and the communication range of the node, a new algorithm LSCR for core node identification was constructed. The LSCR algorithm and Louvain algorithm were merged to obtain a new and improved algorithm, Louvain-LSCR. In this algorithm, the leaf nodes in phase 1 of Louvain algorithm were first pruned to reduce calculations; then, seed nodes were selected according to the LSCR algorithm in phase 2. The experimental results on related datasets show that LSCR algorithm has certain advantages in identifying core nodes. The modularity of Louvian-LSCR algorithm is better than other algorithms, and the community structure is more reasonable. It was verified that the algorithm can mine potential cooperative research teams in co-author network.

Local topology and bifurcation hot-spots in proteins with SARS-CoV-2 spike protein as an example

Novel topological methods are introduced to protein research. The aim is to identify hot-spot sites where a bifurcation can alter the local topology of the protein backbone. Since the shape of a protein is intimately related to its biological function, a substitution that causes a bifurcation should have an enhanced capacity to change the protein’s function. The methodology applies to any protein but it is developed with the SARS-CoV-2 spike protein as a timely example. First, topological criteria are introduced to identify and classify potential bifurcation hot-spot sites along the protein backbone. Then, the expected outcome of asubstitution, if it occurs, is estimated for a general class of hot-spots, using a comparative analysis of the surrounding backbone segments. The analysis combines the statistics of structurally commensurate amino acid fragments in the Protein Data Bank with general stereochemical considerations. It is observed that the notorious D614G substitution of the spike protein is a good example of a bifurcation hot-spot. A number of topologically similar examples are then analyzed in detail, some of them are even better candidates for a bifurcation hot-spot than D614G. The local topology of the more recently observed N501Y substitution is also inspected, and it is found that this site is proximal to a different kind of local topology changing bifurcation.

Multi-Channel Pooling Graph Neural Networks

Graph pooling is a critical operation to downsample a graph in graph neural networks. Existing coarsening pooling methods (e.g. DiffPool) mostly focus on capturing the global topology structure by assigning the nodes into several coarse clusters, while dropping pooling methods (e.g. SAGPool) try to preserve the local topology structure by selecting the top-k representative nodes. However, there lacks an effective method to integrate the two types of methods so that both the local and the global topology structure of a graph can be well captured. To address this issue, we propose a Multi-channel Graph Pooling method named MuchPool, which captures the local structure, the global structure, and node feature simultaneously in graph pooling. Specifically, we use two channels to conduct dropping pooling based on the local topology and node features respectively, and one channel to conduct coarsening pooling. Then a cross-channel convolution operation is designed to refine the graph representations of different channels. Finally, the pooling results are aggregated as the final pooled graph. Extensive experiments on six benchmark datasets present the superior performance of MuchPool. The code of this work is publicly available at Github.

PointLIE: Locally Invertible Embedding for Point Cloud Sampling and Recovery

Point Cloud Sampling and Recovery (PCSR) is critical for massive real-time point cloud collection and processing since raw data usually requires large storage and computation. This paper addresses a fundamental problem in PCSR: How to downsample the dense point cloud with arbitrary scales while preserving the local topology of discarded points in a case-agnostic manner (i.e., without additional storage for point relationships)? We propose a novel Locally Invertible Embedding (PointLIE) framework to unify the point cloud sampling and upsampling into one single framework through bi-directional learning. Specifically, PointLIE decouples the local geometric relationships between discarded points from the sampled points by progressively encoding the neighboring offsets to a latent variable. Once the latent variable is forced to obey a pre-defined distribution in the forward sampling path, the recovery can be achieved effectively through inverse operations. Taking the recover-pleasing sampled points and a latent embedding randomly drawn from the specified distribution as inputs, PointLIE can theoretically guarantee the fidelity of reconstruction and outperform state-of-the-arts quantitatively and qualitatively.