Time Variant Node Ranking Technique for Chatbot Neural Graph

In contrast to wireless sensor networks (WSN), Internet of things (IoT) applications are supported by global IP connectivity and two-way data communication between low power wireless sensor nodes of lossy area networks. The Internet Engineering Task Force (IETF) has proposed the routing protocol for low power and lossy area networks (RPL). The RPL constructs a destination oriented directed acyclic graph (DODAG) that is grounded at the root node. The DODAG is constructed by using an objective function (OF) to compute the rank of each sensor node. The IETF has proposed two objective functions that are OF0 and MRHOF. Subsequently, with the help of the rank of nodes, a parent-child relationship is established between nodes to construct the DODAG. In this paper, we have proposed an OF named ‘EEQ’ that protects the node which has already excessively consumed its energy for forwarding sensed data towards the root node. The EEQ computes the rank of a node using three energy related parameters: i) expected number of transmissions, ii) consumed energy, and iii) active queue length. Under low and high intensity traffic loads, we have simulated various scenarios for OF0, MRHOF, and EEQ. The simulation results show that for high intensity traffic, EEQ has less overhead of control messages as compared to OF0 and MRHOF, resulting in energy conservation.

Compared with the traditional static network, the temporal networks can describe the events in the network in more detail and comprehensively. The static network only considers the connection between nodes and ignores the process of network development, while the temporal network lacks the process of finding important nodes in the network. In real life, many networks can be described as temporal networks, such as communication networks, infectious disease transmission networks, and the activation of neurons inside the brain. An important node of a temporal network is that it can affect the structure and function of the network to a greater extent than other nodes of the network. This paper conducts research and analysis on the ranking of important nodes in temporal networks. This article summarizes several prioritization methods of node importance in temporal networks and compares them with the importance ranking of nodes in static networks. Finally, this paper proposes two methods for ranking the importance of nodes in the time network: eigenvalue centrality and growth-based centrality. The experiment is conducted on two real datasets, one is social networking college message and another one is based on real human contact network.

The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a group (color), we provide a framework to model multiple natural fairness aspects. We seek to find short paths in which the number of occurrences of each color is within some given lower and upper bounds. Among other results, we prove the introduced problems to be computationally intractable (NP-hard and parameterized hard with respect to the number of colors) even in very restricted settings (such as each color should appear with exactly the same frequency), while also presenting an encouraging algorithmic result ("fixed-parameter tractability") related to the length of the sought solution path for the general problem.

The basis of Google's acclaimed PageRank is an artificial mixing of the Markov chain representing the connectivity structure of the network under study with a maximally connected network where every node is connected to every other node. The rate with which the original network is mixed with the strongly connected one is called damping factor. The choice of the damping factor can influence the ranking of the nodes. As we show in this paper, the ranks of transient nodes, i.e., nodes not belonging to a strongly connected component without outgoing links in the original network, tend to zero as the damping factor increases. In this paper we develop a new methodology for obtaining a meaningful ranking of nodes without having to resort to mixing the network with an artificial one. Our new ranking relies on an adjusted definition of the ergodic projector of the Markov chain representing the original network. We will show how the new ergodic projector leads to a more structural way of ranking (transient) nodes. Numerical examples are provided to illustrate the impact of this new ranking approach.

Node ranking in heterogeneous graphs, which quantifies the relative importance of nodes, can often be improved by incorporating information from relevant paths. Graph database and heterogeneous graph neural network (HGNN) are two main approaches to better solve this problem. Graph databases support efficient path queries for flexible path types but require manual design to combine results for node ranking. Conversely, current HGNNs can automatically integrate semantic information from multiple linear path types for accurate node ranking. However, our experiments show that they fail to outperform a multi-layer perceptron model that utilizes features extracted from multiple nonlinear conditional paths, which can be handled by graph databases. Therefore, we aim to enable HGNN to take advantage of these path types for better performance. However, HGNNs require a generalized path schema to define the structure of input paths, and incorporating each additional path type will significantly increase the required system memory and sampling time for HGNNs. To address these limitations, we introduce CompNode, a novel framework based on a new unified path schema definition called Complex-path, which is used to describe all the required path types, including nonlinear conditional path types. Then, we design a pre-aggregation method to reduce the required system memory and sampling time by pre-aggregating the same type of complex-path. Furthermore, we develop a model that combines semantic information from all aggregated complex-paths for accurate node ranking. Real-world experiments on identifying top potential high-value customers show CompNode outperforms state-of-the-art HGNNs by 20% in average precision and the previously deployed graph database method by 252% in success rate.

Influence maximization for opinion formation (IMOF) in social networks is an important problem, which is used to determine some initial nodes and propagate the most ideal opinions to the whole network. The existing researches focus on improving the opinion formation models to compute the opinion of each node. However, little work has been done to describe the IMOF process mathematically, and the current researches cannot provide an effective mechanism to deal with the IMOF. In this paper, the IMOF is formulated mathematically and solved by an iterative framework. At first, we describe the IMOF as a constrained optimization problem. Then, based on node influence and neighbor coordination, the weighted coordination model is proposed to compute the opinions of network nodes with the change of iterations. In particular, in order to determine top- $k$ influential nodes (i.e., seed nodes), an iterative framework for the IMOF, called IIMOF is presented. Based on the framework, the score and rank of each node by Iterative 2-hop algorithm, i.e., SRI2 is proposed to compute the influence score of each node. Based on small in-degree and high out-degree, one-hop measure is proposed to better reflect the rank of all initial nodes. We also prove that IIMOF converges to a stable order set within the finite iterations. The simulation results show that IIMOF has superior average opinions than the comparison algorithms.

Disruptive coefficient and 2-step disruptive coefficient: Novel measures for identifying vital nodes in complex networks

The increasing complexity and dynamics of the stock trading market are major challenges for the financial industry and are primary dilemmas for all countries nowadays. In addition, the stock trading market has a considerable impact on the global economy, and its importance is self-evident. To cope with the complexity and dynamics of a stock trading market, this paper applies complex network theory and model to explore the topology of the global stock trading network. First, this paper collects stock trading data from 74 countries from 1999 to 2020. It converts the collected stock trading data of these countries into a complex network using a type of algorithm based on the time series visibility graph (VG) algorithm. Then, the data are analyzed by a complex network model, and six analytical metrics are obtained. Finally, the six metrics are analyzed by the entropy weight method to identify the key nodes in the network and to obtain the ranking of each country’s stock trading data. This paper is an effective application of complex network and entropy weight method in stock trend analysis, which mainly includes two contributions. First, the VG algorithm provides a novel research perspective for modeling the global stock trading trend. Second, key nodes in the network are analyzed and identified based on the entropy weight method, and the ranking of key nodes in the stock trading network is obtained, which provides a new method for further research on the stock trading trend, investment portfolio, and stock return forecasting.

Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social networks where people are involved in different types of relationships and interact through various forms of communication media. The ranking of nodes in multiplex networks is one of the most pressing and challenging tasks that research on complex networks is currently facing. When pairs of nodes can be connected through multiple links and in multiple layers, the ranking of nodes should necessarily reflect the importance of nodes in one layer as well as their importance in other interdependent layers. In this paper, we draw on the idea of biased random walks to define the Multiplex PageRank centrality measure in which the effects of the interplay between networks on the centrality of nodes are directly taken into account. In particular, depending on the intensity of the interaction between layers, we define the Additive, Multiplicative, Combined, and Neutral versions of Multiplex PageRank, and show how each version reflects the extent to which the importance of a node in one layer affects the importance the node can gain in another layer. We discuss these measures and apply them to an online multiplex social network. Findings indicate that taking the multiplex nature of the network into account helps uncover the emergence of rankings of nodes that differ from the rankings obtained from one single layer. Results provide support in favor of the salience of multiplex centrality measures, like Multiplex PageRank, for assessing the prominence of nodes embedded in multiple interacting networks, and for shedding a new light on structural properties that would otherwise remain undetected if each of the interacting networks were analyzed in isolation.

How to identify influential nodes in complex networks continues to be an open issue. A number of centrality measures have been presented to address this problem. However, these studies focus only on a centrality measure and each centrality measure has its own shortcomings and limitations. To solve the above problems, in this paper, a novel method is proposed to identify influential nodes based on combining of the existing centrality measures. Because information flow spreads in different ways in different networks, in the specific network, the appropriate centrality measures should be selected to calculate the ranking of nodes. Then, an interval can be generated for the ranking of each node, which includes the upper limit and lower limit obtained from different centrality measures. Next, the final ranking of each node can be determined based on the median of the interval. In order to illustrate the effectiveness of the proposed method, four experiments are conducted to identify vital nodes simulations on four real networks, and the superiority of the method can be demonstrated by the results of comparison experiments.

Multilayer networks are described as complex networks in which each node is related to all other nodes in distinct layers. These layers form a class of cooperating and interacting networks. Examples of such multilayer networks are transport networks, where people can move from one city to another through various modes of transportation. The ranking of nodes in multilayer networks is one of the most challenging and demanding tasks on complex networks. Since pairs of nodes are related through various types of links in multilayers, the ranking of nodes should inevitably reveal the weights of nodes in all corresponding layers. In this paper, we exploit the concept of populations’ random migration in a multiplex transport network to propose a new Multiplex PageRank centrality measure, where the effects of influence and feedback between networks on the centrality of nodes are directly considered. We apply the proposed measure to an artificial duplex network. Findings indicate that considering the network with multilayers helps uncover the rankings of nodes, which are different from the rankings in a monotonous network. Moreover, the Multiplex PageRank centrality measure of dynamical network models is discussed for further practical application and applied to an urban transport network. The results demonstrate the effectiveness of our measure in the dynamical network.

The problem of improving structural properties of artificial discrete neural networks is investigated. The structure of the neural network is regarded as a theoretical graph. Cyclical substructures can occur in this structure under certain conditions, e.g., when there is feedback among neural network layers. Some properties of cycles in the graphs corresponding to neural networks have a significant effect not only on the rate of convergence to the (stable) solutions of the problems posed by network users, but also on the very possibility of obtaining these solutions. These properties include the negativity of some circuits (simple cycles) in neural network graphs. We propose an algorithm that makes it possible to eliminate negative circuits from neural network graphs under certain constraints formulated in this paper. It increases the chances of finding correct solutions to the problems for which neural networks were developed. An illustrative example is presented.

Ranking nodes in networks according to a defined measure of importance is an extensively studied task, with applications in ecology, economic trade networks, and social networks. This paper introduces a method based on a non-linear iterative map to evaluate node relevance in bipartite networks. By tuning a single parameter γ, the method captures different concepts of node importance, including established measures like degree centrality, eigenvector centrality and the fitness-complexity ranking. The algorithm’s flexibility allows for efficient ranking optimization tailored to specific tasks, outperforming state-of-the-art algorithms. We apply this method to ecological mutualistic networks, where ranking quality can be assessed by the extinction area - the rate at which the system collapses when species are removed in a certain order. The map with the optimal γ value surpasses existing ranking methods on this task. Additionally, our method excels in evaluating nestedness, another crucial structural property of ecological systems, requiring specific node rankings. Finally, we explore theoretical aspects of the map, revealing a phase transition at a critical γ dependent on the data structure that can be characterized analytically for random networks. Near the critical point, the map exhibits unique features and a distinctive “triangular” packing pattern of the incidence matrix.

Detecting influential spreaders had become a challenging and crucial topic so far due to its practical application in many areas, such as information propagation inhibition and disease dissemination control. Some traditional local based evaluation methods had given many discussions on ranking important nodes. In this paper, ranking nodes of networks continues to be discussed. A semilocal structures method for ranking nodes based on the degree and the neighbors’ connections of the node is presented. The semilocal structures are regarded as the number of neighbors of the nodes and the connections between the node and its neighbors. We combined the triangle structure and the degree information of the neighbors to define the inner‐outer spreading ability of the nodes and then summed the node neighbors’ inner‐outer spreading ability to be used as the local triangle structure centrality (LTSC). The LTSC avoids the defect “pseudo denser connections” in measuring the structure of neighbors. The performance of the proposed LTSC method is evaluated by comparing the spreading ability on both real‐world and synthetic networks with the SIR model. The simulation results of the discriminability and the correctness compared with pairs of ranks (one is generated by SIR model and the others are generated by central nodes measures) show that LTSC outperforms some other local or semilocal methods in evaluating the node’s influence in most cases, such as degree, betweenness, H‐index, local centrality, local structure centrality, K‐shell, and S‐shell. The experiments prove that the LTSC is an efficient and accurate ranking method which provides a more reasonable evaluating index to rank nodes than some previous approaches.

Influential nodes ranking in complex networks: An entropy-based approach