NE-FLGC: Network Embedding Based on Fusing Local (First-Order) and Global (Second-Order) Network Structure with Node Content

Network embedding aims to learn distributed vector representations of nodes in a network. The problem of network embedding is fundamentally important. It plays crucial roles in many applications, such as node classification, link prediction, and so on. As the real-world networks are often sparse with few observed links, many recent works have utilized the local and global network structure proximity with shallow models for better network embedding. In reality, each node is usually associated with rich attributes. Some attributed network embedding models leveraged the node attributes in these shallow network embedding models to alleviate the data sparsity issue. Nevertheless, the underlying structure of the network is complex. What is more, the connection between the network structure and node attributes is also hidden. Thus, these previous shallow models fail to capture the nonlinear deep information embedded in the attributed network, resulting in the suboptimal embedding results. In this paper, we propose a deep attributed network embedding framework to capture the complex structure and attribute information. Specifically, we first adopt a personalized random walk-based model to capture the interaction between network structure and node attributes from various degrees of proximity. After that, we construct an enhanced matrix representation of the attributed network by summarizing the various degrees of proximity. Then, we design a deep neural network to exploit the nonlinear complex information in the enhanced matrix for network embedding. Thus, the proposed framework could capture the complex attributed network structure by preserving both the various degrees of network structure and node attributes in a unified framework. Finally, empirical experiments show the effectiveness of our proposed framework on a variety of network embedding-based tasks.

Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have as accurate a model as possible. As a result, new techniques and models for analyzing and modeling real-world networks have recently been introduced. One example of large and complex networks involves protein-protein interaction (PPI) networks. We analyze PPI networks of yeast Saccharomyces cerevisiae and fruitfly Drosophila melanogaster using a newly introduced measure of local network structure as well as the standardly used measures of global network structure. We examine the fit of four different network models, including Erdos-Renyi, scale-free and geometric random network models, to these PPI networks with respect to the measures of local and global network structure. We demonstrate that the currently accepted scale-free model of PPI networks fails to fit the data in several respects and show that a random geometric model provides a much more accurate model of the PPI data. We hypothesize that only the noise in these networks is scale-free. We systematically evaluate how well-different network models fit the PPI networks. We show that the structure of PPI networks is better modeled by a geometric random graph than by a scale-free model. Supplementary information is available at http://www.cs.utoronto.ca/~juris/data/data/ppiGRG04/

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

The U.S. Inter-Sector Network Dynamics and Its Effects on Technology Adoption

In online social networks, identifying influential users is crucial for maintaining network stability and accelerating information dissemination. However, most of the existing research evaluate the influence of users according to the topological structure of local or global networks, which ignores the historical information and social interactions of users. In this work, we introduce a novel algorithm called MADS‐UC to pinpoint the influential super‐spreaders of information. Specifically, three kinds of activation influence between each pair of users are defined to better portray the mutual interactions with each other, and the proposed measure makes full consideration of the topological and historical information of networks, and the social interactions of users. Then, a hybrid multi‐attribute decision‐making algorithm is put forward to evaluate the influence of users, while the obtained three kinds of activation influence are introduced as basic indicators, and the weight for each indicator is determined from both subjective and objective dimensions. Finally, to achieve a good balance between algorithm accuracy and time complexity, the influential users are identified by considering the interactions between a user and other users within its influence range. We collect seven real‐world datasets from the Sina Weibo platform in 2024 about mobile product Honor, and a series of experiments is conducted to validate the effectiveness of the MADS‐UC algorithm. Experimental results show that MADS‐UC surpasses six widely used algorithms in robustness, sensitivity analysis, and distinguishing capability, which is useful in accelerating the dissemination of information in the product marketing process.

The railway plays an essential role in urban and intercity transport of goods and people. Intercity and urban rail transit infrastructures contribute to the economic and environmental sustainability of global economies. Those infrastructures can be modeled as complex networks, so that we can evaluate system properties of the network structure. This stream of research has focused on the topological analysis of global network structure, but little research exists that examines how local network structures affect system properties. The local structure of complex networks can be examined with network motif analysis, as those network motifs are the building blocks of networked systems. Nevertheless, there has been scarce attention given to local network properties in rail transit networks. We contribute to covering this gap in the literature with a literature review of motif analysis research and its application to weighted and unweighted rail transit networks, also covering the current state-of-the-art of network motif decomposition and analysis. We demonstrate that network motif analysis is not only applicable, but also beneficial for the design and planning of rail transit networks, enhancing their sustainability by improving efficiency, reducing environmental impact, and optimizing resource allocation. Based on our findings, we propose future research directions that involve applying motif analysis to enhance the sustainability features of both unweighted and weighted rail transit networks.

As an important data type, the demand of network analysis and learning is increasingly prominent. A key problem of network analysis is to study how to reasonably represent the feature information in the network, that is network embedding. However, in the study of network embedding, only the first-order proximity relationship of nodes is characterized, while the second-order proximity relationship hidden in the network nodes is ignored. Therefore, we propose an algorithm, called SINE, to realize the representation learning of nodes in the network which fuses the first-order and second-order proximity of nodes in the original network. Through applying SINE to three real networks, we obtain the feature representation of the nodes in the networks and cluster the nodes based on these features. Comparing with the existing network embedding learning methods-Node2vec, Large-Scale Information Network Embedding (LINE) and Structural Deep Network Embedding (SDNE), the SINE algorithm showed better performance in clustering tasks.

Effects of Global and Local Network Structure on Number of Driver Nodes in Complex Networks

Learning representations for network has aroused great research interests in recent years. Existing approaches embed vertices into a low dimensional continuous space which encodes local or global network structures. While these methods show improvements over traditional representations, they do not utilize the label information until the learned embeddings are used for training classifier. That is, the process of representation learning is separated from the labels and thus is unsupervised. In this paper, we propose a novel method which learns the embeddings for vertices under the supervision of labels. The key idea is to regard the label as the context of a vertex. More specifically, we attach a true or virtual label node for each training or test sample, and update the embeddings for vertices and labels to maximize the probability of both the neighbors and their labels in the context. We conduct extensive experiments on three real datasets. Results demonstrate that our method outperforms the state-of-the-art approaches by a large margin.

This study investigates the dynamic interdependencies among key sectors of Borsa Istanbul-industrial, services, technology, banking, and electricity-using a novel network-geometric framework. Daily closure prices from 2022 to 2024 are transformed into logarithmic returns and analyzed via a sliding window approach. In each window, mutual information is computed to construct weighted networks that are filtered using Triangulated Maximally Filtered Graphs (TMFG) to isolate the most significant links. Forman-Ricci curvature is then calculated at the node level, and entropy measures over k-neighborhoods (k=1,2,3) capture the complexity of both local and global network structures. Cross-correlation, Granger causality, and transfer entropy analyses reveal that sector responses to macroeconomic shocks-such as inflation surges, interest rate hikes, and currency depreciation-vary considerably. The services sector emerges as a critical intermediary, transmitting shocks between the banking and both the industrial and technology sectors, while the electricity sector displays robust, stable interconnections. These findings demonstrate that curvature-based metrics capture nuanced network characteristics beyond traditional measures. Future work could incorporate high-frequency data to capture finer interactions and empirically compare curvature metrics with conventional indicators.

Internet of Things (IoT) symbolic formula is given. The analysis of management technologies both in the network structures of infocommunications, based on the NSMP, and on local networks of the Io T. Two approaches for implementing the management process in infocommunication networks are shown: one is based on creating special software tools, the second is based on the working with data describing the network device. The basic operations of SNMP are given. Four levels of IoT in local network structure are described: smart sensors, network vehicles, services, and applications. Structure of local network of IoT which includes smart sensors, transport environment, services and applications information representation in network use semantic web are considered.The structure of multi-agent system (MAS) of milk farms analyzing in Leban (MASMFA) for monitoring of production quality. MASMFA structure has many agents such as quality milk sensors, agents of communications, data base, analysis of the information received from sensor agents, decision-making. This system implements the functions to ensure the required class of milk quality and based on IoT local network construction. The information algorithm processing in such IoT is proposed. Milk sensor shell be periodically queried, their values will be recorded in the server database. The decisionmaking subsystem will issue data on milk quality to the farm administrator on a mobile device. The server structure will be implemented using a cloud service. Implementation this Internet of things network is being developed using LTE technology.

Plant specialization and pollination network structure play important roles in community assembly. Floral traits can mediate plant-pollinator interactions and thus have important impacts on nestedness and modularity of pollination network. When such traits are phylogenetically conserved, therefore, phylogeny and traits should predict network structure to similar degrees. Moreover, conserved network structures were also found attributed to pollination syndrome or pollination system. However, we still know little about the relation between pollination syndrome and pollination network, especially under a phylogenetic framework. Herein, we established a phylogenetic framework including five floral traits (flower density, floral size, floral shape, floral symmetry, and floral color) and five species-level metrics (species strength, weighted closeness, specialization d', nestedness contribution, and modularity contribution) to test how floral traits could directly or indirectly influence species' specialization and network structure in central China. Phylogenetic signals were found in all floral traits except flower density. Structural equation model and phylogenetic structural equation model results showed that both floral size and floral density affected plant specialization and its contribution to network modularity indirectly. However, compared with phylogenetic independent flower density, phylogenetic conserved floral size had much more complexed influences, having a direct influence both on species' specialization and on modularity contribution. In this nested and modular network, abundant species with larger flowers tend to be more central and had larger values of z. Floral shape, symmetry, and color could act as co-flowering filters in pollination sharing and help to shape network modularity. Our results emphasize that phylogenetically conserved traits partially represent pollination syndrome and are important drivers for modular structure of local pollination network. This study may improve the understanding how the evolutionary history and ecological process drive local network structure and dynamics.

Link prediction based on bipartite networks can not only mine hidden relationships between different types of nodes, but also reveal the inherent law of network evolution. Existing bipartite network link prediction is mainly based on the global structure that cannot analyze the role of the local structure in link prediction. To tackle this problem, this paper proposes a deep link-prediction (DLP) method by leveraging the local structure of bipartite networks. The method first extracts the local structure between target nodes and observes structural information between nodes from a local perspective. Then, representation learning of the local structure is performed on the basis of the graph neural network to extract latent features between target nodes. Lastly, a deep-link prediction model is trained on the basis of latent features between target nodes to achieve link prediction. Experimental results on five datasets showed that DLP achieved significant improvement over existing state-of-the-art link prediction methods. In addition, this paper analyzes the relationship between local structure and link prediction, confirming the effectiveness of a local structure in link prediction.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms for mining communities have focused on global graph structure, and often run in time proportional to the size of the entire graph. As we explore networks with millions of vertices and find communities of size in the hundreds, it becomes important to shift our attention from macroscopic structure to microscopic structure in large networks. A growing body of work has been adopting local expansion methods in order to identify communities from a few exemplary seed members. In this article, we propose a novel approach for finding overlapping communities called L emon ( L ocal E xpansion via M inimum O ne N orm). Provided with a few known seeds , the algorithm finds the community by performing a local spectral diffusion. The core idea of L emon is to use short random walks to approximate an invariant subspace near a seed set, which we refer to as local spectra . Local spectra can be viewed as the low-dimensional embedding that captures the nodes’ closeness in the local network structure. We show that L emon ’s performance in detecting communities is competitive with state-of-the-art methods. Moreover, the running time scales with the size of the community rather than that of the entire graph. The algorithm is easy to implement and is highly parallelizable. We further provide theoretical analysis of the local spectral properties, bounding the measure of tightness of extracted community using the eigenvalues of graph Laplacian. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the seed set quality and quantity would affect the performance are provided.

Network embedding is an effective method to learn a low-dimensional feature vector representation for each node of a given network. In this paper, we propose a deep network embedding model with aggregated proximity preserving (DNE-APP). Firstly, an overall network proximity matrix is generated to capture both local and global network structural information, by aggregating different k-th order network proximities between different nodes. Then, a semi-supervised stacked auto-encoder is employed to learn the hidden representations which can best preserve the aggregated proximity in the original network, and also map the node pairs with higher proximity closer to each other in the embedding space. With the hidden representations learned by DNE-APP, we apply vector-based machine learning techniques to conduct node classification and link label prediction tasks on the real-world datasets. Experimental results demonstrate the superiority of our proposed DNE-APP model over the state-of-the-art network embedding algorithms.