Vertices In Network Research Articles

Network Embedding on Hierarchical Community Structure Network

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.

Correlation bounds, mixing and m-dependence under random time-varying network distances with an application to Cox-processes

We will consider multivariate stochastic processes indexed either by vertices or pairs of vertices of a dynamic network. Under a dynamic network, we understand a network with a fixed vertex set and an edge set which changes randomly over time. We will assume that the spatial dependence-structure of the processes conditional on the network behaves in the following way: Close vertices (or pairs of vertices) are dependent, while we assume that the dependence decreases conditionally on that the distance in the network increases. We make this intuition mathematically precise by considering three concepts based on correlation, β-mixing with time-varying β-coefficients and conditional independence. These concepts allow proving weak-dependence results, for example, an exponential inequality, which might be of independent interest. In order to demonstrate the use of these concepts in an application, we study the asymptotics (for growing networks) of a goodness of fit test in a dynamic interaction network model based on a Cox-type model for counting processes. This model is then applied to bike-sharing data.

SAKE

Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE , a S ampling-based A lgorithm for fast K atz centrality E stimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.

On using the modularity of recurrence network communities to detect change-point behaviour

The behaviour of a dynamical system can be examined from time series using the technique of recurrence plots through visualization and quantification methods. One such method is the quadrant scan in which a recurrence plot of a time series is converted into a second time series whose local maxima can be identified and interpreted as possible transitions in dynamic behaviour. A recurrence plot can also be represented as a complex network. A quadrant scan can similarly be thought of as a partition of the network vertices into two communities. Here, we argue that different dynamic behavioural regimes can be realized as network communities and the quality of such partitions can be assessed using modularity. Thereby, community modularity can be used as an alternative to the quadrant scan. We investigate this correspondence with respect to two promising arenas for quadrant scan uptake, namely, concept drift detection from machine learning and tipping point or failure and damage monitoring in system maintenance. We also examine two additional data sets to highlight the potential of the methods. These are a geophysical time series of earth tremor data and a physiological time series of an electrocardiogram.

Protein Complexes Detection Based on Semi-Supervised Network Embedding Model.

A protein complex is a group of associated polypeptide chains which plays essential roles in the biological process. Given a graph representing protein-protein interactions (PPI) network, it is critical but non-trivial to detect protein complexes, the subsets of proteins that are tightly coupled, from it. Network embedding is a technique to learn low-dimensional representations of vertices in networks. It has been proved quite useful for community detection in social networks in recent years. However, unlike social networks, PPI network does not contain rich metadata, so that existing network embedding methods cannot fully capture the network structure of PPI to improve the effect of protein complexes detection significantly. We propose a semi-supervised network embedding model by adopting graph convolutional networks to detect densely connected subgraphs effectively. We compare the performance of our model with state-of-the-art approaches on three popular PPI networks with various data sizes and densities. The experimental results show that our approach significantly outperforms other approaches on all three PPI networks.

Anomaly detection by discovering bipartite structure on complex networks

Anomaly detection is a classic problem on complex networks. An anomaly detection method based on network projection is proposed in this study on networks with fundamental bipartite connection relationships and repeated interactions, such as the Internet and computer networks. First of all, two network partition algorithms are advanced to discover the bipartite structure of the network. Then, put forward a similarity metric based on the cosine similarity function to construct the projection network. Finally, the metrics of vertices in the projection network are used as input of the one-class SVM algorithm to detect anomalies. Experiments on simulation datasets and real datasets illustrate that our method achieves higher precision in identifying anomalous addresses than traditional approaches for large-scale Internet and computer networks with the bipartite structure.

ICS-GNN

Searching a community containing a given query vertex in an online social network enjoys wide applications like recommendation, team organization, etc. When applied to real-life networks, the existing approaches face two major limitations. First, they usually take two steps, i.e. , crawling a large part of the network first and then finding the community next, but the entire network is usually too big and most of the data are not interesting to end users. Second, the existing methods utilize hand-crafted rules to measure community membership, while it is very difficult to define effective rules as the communities are flexible for different query vertices. In this paper, we propose an Interactive Community Search method based on Graph Neural Network (shortened by ICS-GNN) to locate the target community over a subgraph collected on the fly from an online network. Specifically, we recast the community membership problem as a vertex classification problem using GNN, which captures similarities between the graph vertices and the query vertex by combining content and structural features seamlessly and flexibly under the guide of users' labeling. We then introduce a k -sized Maximum-GNN-scores (shortened by kMG ) community to describe the target community. We next discover the target community iteratively and interactively. In each iteration, we build a candidate subgraph using the crawled pages with the guide of the query vertex and labeled vertices, infer the vertex scores with a GNN model trained on the subgraph, and discover the kMG community which will be evaluated by end users to acquire more feedback. Besides, two optimization strategies are proposed to combine ranking loss into the GNN model and search more space in the target community location. We conduct the experiments in both offline and online real-life data sets, and demonstrate that ICS-GNN can produce effective communities with low overhead in communication, computation, and user labeling.

Centrality measures in transportation networks for Unpad campus route

Centrality measurement still becomes an interesting research topic recently, including its relation to transportation’s effectiveness and efficiency. A transportation network can be expressed in the form of a graph so that even a level of centrality for each vertex of a complex transportation network can be simply analyzed. There have been various developments/modifications of methods on centrality measures in transportation networks. The offered methods show the different points of view regarding which vertices are most important in the transport network. In this research, the study of some centrality measures in the transportation network is discussed. A numerical experiment of some centrality measures implemented to Universitas Padjadjaran (Unpad) campus route as a network is given. The comparisons are done to explore the performance of each method. The calculation is done using Python software with NetworkX library. The results for Unpad campus route show that some vertices (locations) are more prior than another.

On Fault‐Tolerant Resolving Sets of Some Families of Ladder Networks

In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an arbitrary vertex stopped working and selected vertices still remain the resolving set, then the chosen set is called as the fault‐tolerant resolving set. The least number of vertices in such resolving sets is called the fault‐tolerant metric dimension of the network. Because of the variety of applications of the metric dimension in different areas of sciences, many generalizations were proposed, and fault tolerant is one of them. In this paper, we computed the fault‐tolerant metric dimension of triangular snake, ladder, Mobius ladder, and hexagonal ladder networks. It is important to observe that, in all these classes of networks, the fault‐tolerant metric dimension and metric dimension differ by 1.

Modeling the morphology of the intercity road network

Many aspects of the functioning of the transport network and its impact on the socioeconomic development of a territory significantly depend on its morphology. In particular, the morphological features of the network underlie the network effects, which can lead to significant changes in transport costs (both downward and upward) with minor modifications to the network. The article analyzes the factors most significant for the morphology of the intercity transport network and presents a mathematical description of the mechanisms for the realization of their influence. It is shown that the key factor is the location of network vertices in space, and a two-parameter family of models is proposed that can generate networks close to real ones, only based on information about the spatial location of their vertices. Implementation of the proposed model is demonstrated using the intercity highway network in Belarus. For this network, the optimal parameter values were selected, and it was shown that the resulting model is quite close to the original network.

Identifying transition states of chemical kinetic systems using network embedding techniques.

Many chemical and biochemical systems can be intuitively modeled using networks. Due to the size and complexity of many biochemical networks, we require tools for efficient network analysis. Of particular interest are techniques that embed network vertices into vector spaces while preserving important properties of the original graph. In this article, we {introduce a new method for generating low-dimensional node embeddings for directed graphs, using random walk sampling methods for feature learning on networks. Additionally, we demonstrate the usefulness of this method for identifying transition states of stochastic chemical reacting systems.} Network representations of chemical systems are typically given by weighted directed graphs, and are often complex and high dimensional. In order to deal with networks representing these chemical systems, therefore, we modified objective functions adopted in existing random walk based network embedding methods to handle directed graphs and neighbors of different degrees. Through optimization via gradient ascent, we embed the weighted graph vertices into a low-dimensional vector space $ {\mathbb{R}}^d $ while preserving the neighborhood of each node. These embeddings may then be used to detect relationships between nodes and study the structure of the original network. We then demonstrate the effectiveness of our method on dimension reduction through several examples regarding identification of transition states of chemical reactions, especially for entropic systems.

HSNR: A Network Representation Learning Algorithm Using Hierarchical Structure Embedding

Vertices in the same group tend to connect densely, and usually share common attributes. Groups of different sizes reflect the relations of vertices in different ranges, and also reflect the features of different orders of the network. In this work, we propose a novel network representation learning algorithm by introducing group features of vertices of different orders to learn more discriminative network representations, named as network representation learning algorithm using Hierarchical structure embedding (HSNR). HSNR algorithm firstly constructs hierarchical relations of network structures of different orders based on greedy algorithm and modularity. In order to introduce hierarchical features into the network representation learning model, HSNR algorithm then introduces the idea of multi-relational modeling from knowledge representation, and converts the hierarchical relations into the triplet form between vertices. Finally, HSNR proposes a joint learning model embedding vertex triplets into the network representations. The experimental results show that the HSRN algorithm presented has an excellent performance in network vertex classification task on three real-world datasets.

Dynamic network embedding via incremental skip-gram with negative sampling

Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large graph. Most existing methods focus on learning the structural representations of vertices in a static network, but cannot guarantee an accurate and efficient embedding in a dynamic network scenario. The fundamental problem of continuously capturing the dynamic properties in an efficient way for a dynamic network remains unsolved. To address this issue, we present an efficient incremental skip-gram algorithm with negative sampling for dynamic network embedding, and provide a set of theoretical analyses to characterize the performance guarantee. Specifically, we first partition a dynamic network into the updated, including addition/deletion of links and vertices, and the retained networks over time. Then we factorize the objective function of network embedding into the added, vanished and retained parts of the network. Next we provide a new stochastic gradient-based method, guided by the partitions of the network, to update the nodes and the parameter vectors. The proposed algorithm is proven to yield an objective function value with a bounded difference to that of the original objective function. The first order moment of the objective difference converges in order of $$\mathbb{O}(\frac{1}{n^{2}})$$ , and the second order moment of the objective difference can be stabilized in order of $$\mathbb{O}(1)$$ . Experimental results show that our proposal can significantly reduce the training time while preserving the comparable performance. We also demonstrate the correctness of the theoretical analysis and the practical usefulness of the dynamic network embedding. We perform extensive experiments on multiple real-world large network datasets over multi-label classification and link prediction tasks to evaluate the effectiveness and efficiency of the proposed framework, and up to 22 times speedup has been achieved.

Coupling network vertex representation learning based on network embedding method

Network representation learning is a basic problem in network data analysis. By learning network representation vectors, network vertices can be represented more accurately. With the development of deep learning, embedding methods have been widely used for network vertex representation learning. Providing that network data have changed in terms of their scale and modality, the research focus gradually shifted from single network mining to coupling network mining. This paper first analyzes the research status of embedding methods for single networks and then compares their advantages and disadvantages. Furthermore, the paper presents a model called CWCNE for coupling network embedding. The random walk and training algorithms of the proposed model are improved to adapt to coupling network features. The validity of the proposed model was verified using social, academic, film, poetry, and work coupling network data. Good results were obtained on community detection, entity recognition, and label classification tasks.

Finite-time synchronization of multi-coupling stochastic fuzzy neural networks with mixed delays via feedback control

In this paper, the finite-time synchronization problem for multi-coupling fuzzy cellular neural networks (FCNNs) with stochastic perturbations and mixed delays is addressed. Compared with exponential synchronization and asymptotic synchronization in existing literature, finite-time synchronization of stochastic FCNNs is studied for the first time, which is of better significance. Combining graph-theoretical technique and Lyapunov method, under the framework of feedback control, some finite-time synchronization conditions are derived. Besides, from the perspective of the connectedness of FCNNs, we just demand at least one directed path on the digraph between different vertices in networks, instead of each sub-network. Then, the convergence time is explicitly proposed, which is connected with the parameters of control and topological structure of networks. Eventually, a numerical example is also carried out to demonstrate the practicability and validity of our proposed results. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results.

Tunable strain soliton networks confine electrons in van der Waals materials

Sliding and twisting van der Waals layers with respect to each other gives rise to moir\'e structures with emergent electronic properties. Electrons in these moir\'e structures feel weak potentials that are typically in the tens of millielectronvolt range when the moir\'e structures are smooth at the atomic scale. Here we report a facile technique to achieve deep, deterministic trapping potentials via strain-based moir\'e engineering in van der Waals bilayers. We use elasto-scanning tunneling microscopy to show that uniaxial strain drives a commensurate-incommensurate lattice transition in a multilayer MoSe$_2$ system. In the incommensurate state, the top monolayer is partially detached from the bulk through the spontaneous formation of topological solitons where stress is relieved. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of the honeycomb network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Honeycomb soliton networks thus provide a unique path to engineer an array of identical deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials.

Upper and Lower Bounds for the Kirchhoff Index of the n-Dimensional Hypercube Network

The hypercube Qn is one of the most admirable and efficient interconnection network due to its excellent performance for some practical applications. The Kirchhoff index KfG is equal to the sum of resistance distances between any pairs of vertices in networks. In this paper, we deduce some bounds with respect to Kirchhoff index of hypercube network Qn.

Метод формалізації даних при вирішенні задач розпізнавання повітряних об'єктів

В роботі розроблена методика формалізації структур даних ознак повітряних об’єктів яка враховує характеристики точності і достовірності джерел інформації з нестохастичною невизначеністю і рекурентними правилами узагальнення оцінок значень ознак при багаторазовому спостереженні повітряних об’єктів. В основу розробленої методики були покладені методи формалізації процесу розпізнавання, оцінки ступеня істинності різнорідних ознак, об'єднання незалежних результатів розпізнавання, пошуку рішень про класи розпізнаваних повітряних об'єктів з урахуванням неповноти і надмірності даних про ознаки. Розроблений метод формалізації процесу розпізнавання повітряних об’єктів на основі описів класів різнорідними ознаками, відрізняється від відомих використанням ієрархічної функціональної мережі. Удосконалення методу об'єднання незалежних результатів розпізнавання на основі правила Демпстера полягає в попередньому перетворенні одного з неузгоджених розподілів можливостей класів алфавіту в розподіл ймовірностей. Це дозволяє проводити коректне об'єднання неузгоджених розподілів можливостей класів алфавіту з використанням правила Демпстера. Проведено дослідження застосовності розробленого правила при об'єднанні неузгоджених розподілів ймовірностей класів алфавіту. Розроблений метод пошуку рішень про класи розпізнаваних об'єктів на графі функціональної мережі відрізняється від відомих розробленим способом отримання інтервальної оцінки ступеня істинності класів в умовах відсутності даних щодо окремих ознак повітряних об’єктів і запропонованим евристичним правилом, що дозволяє скоротити розмірність безлічі вершин мережі, які перебираються при пошуку рішення про клас повітряних об’єктів. Метод дозволяє проводити пошук рішень про класи повітряних об’єктів в умовах неповноти і надмірності даних про ознаки.

A novel method for determining research groups from co-authorship network and scientific fields of authors.

Large networks not only have a large number of vertices but also have a large number of edges. Usually such networks are dense and difficult to visualise, even locally. This paper considers the case where large weights on edges represent proximity of the corresponding end-vertices. We follow two main ideas in this paper. The first one is \emph{network pruning}, that is removal of edges that makes the resulting network more manageable while keeping the main characteristic of the original network. The other idea is to partition the network vertex set in such a way that the induced connected components represent groups of network elements that fit together. Furthermore, we assume that the vertices of the network are labeled by \emph{types}. In this paper we apply our approach to co-authorship network of researchers in Slovenia in order to identify research groups, finding group leaders and the degree of inter-disciplinarity of the group. For the network pruning phase we use a pathfinder network and for vertex partition appropriate line-cuts. Each cluster is assigned a distribution of types. A measure of inter-disciplinarity of research group is derived from such a distribution.

Finding Community of Brain Networks Based on Neighbor Index and DPSO with Dynamic Crossover

Background: : The brain networks can provide us an effective way to analyze brain function and brain disease detection. In brain networks, there exist some import neural unit modules, which contain meaningful biological insights. Objective:: Therefore, we need to find the optimal neural unit modules effectively and efficiently. Method:: In this study, we propose a novel algorithm to find community modules of brain networks by combining Neighbor Index and Discrete Particle Swarm Optimization (DPSO) with dynamic crossover, abbreviated as NIDPSO. The differences between this study and the existing ones lie in that NIDPSO is proposed first to find community modules of brain networks, and dose not need to predefine and preestimate the number of communities in advance. Results: : We generate a neighbor index table to alleviate and eliminate ineffective searches and design a novel coding by which we can determine the community without computing the distances amongst vertices in brain networks. Furthermore, dynamic crossover and mutation operators are designed to modify NIDPSO so as to alleviate the drawback of premature convergence in DPSO. Conclusion: The numerical results performing on several resting-state functional MRI brain networks demonstrate that NIDPSO outperforms or is comparable with other competing methods in terms of modularity, coverage and conductance metrics.