Node Ranking Research Articles

The topology, stability, and instability of learning-induced brain network repertoires in schizophrenia.

There is a paucity of graph theoretic methods applied to task-based data in schizophrenia (SCZ). Tasks are useful for modulating brain network dynamics, and topology. Understanding how changes in task conditions impact inter-group differences in topology can elucidate unstable network characteristics in SCZ. Here, in a group of patients and healthy controls (n = 59 total, 32 SCZ), we used an associative learning task with four distinct conditions (Memory Formation, Post-Encoding Consolidation, Memory Retrieval, and Post-Retrieval Consolidation) to induce network dynamics. From the acquired fMRI time series data, betweenness centrality (BC), a metric of a node's integrative value was used to summarize network topology in each condition. Patients showed (a) differences in BC across multiple nodes and conditions; (b) decreased BC in more integrative nodes, but increased BC in less integrative nodes; (c) discordant node ranks in each of the conditions; and (d) complex patterns of stability and instability of node ranks across conditions. These analyses reveal that task conditions induce highly variegated patterns of network dys-organization in SCZ. We suggest that the dys-connection syndrome that is schizophrenia, is a contextually evoked process, and that the tools of network neuroscience should be oriented toward elucidating the limits of this dys-connection.

АЛГОРИТМ РАНЖИРОВАНИЯ УЗЛОВ БЕСПРОВОДНОЙ СЕНСОРНОЙ СЕТИ ПРИ ИХ СЛУЧАЙНОМ ПРОСТРАНСТВЕННОМ РАСПРЕДЕЛЕНИИ

The method of making a decision on the ranking of sensor nodes in a wireless sensor network randomly distributed on a certain plane, which operates in a constantly changing network environment, is considered. As a priori information about the network environment, expertise is used, framed in the form of a matrix of utility relations. The given matrix is filled with integer point estimates. The solution to the ranking of base stations is a calculated a posteriori fuzzy set. A numerical example of solving the problem is considered.

An improved RPL algorithm for low-power and lossy networks

The routing protocol for low-power and lossy networks (RPL), standardized by Internet Engineering Task Force (IETF), is mainly designed to use for Low-power and Lossy Networks (LLNs). To solve the problems of several important routing metrics are not evaluated, the optimal path may contain long single hop links, lack of scientific multi-routing metrics evaluation method and mechanism to balance the parent child number (especially the parent with one hop away from root), this paper proposes an improved RPL algorithm for LLN (I-RPL). First of all, we propose the evaluated routing metrics: child number of parent, candidate parent number, hop count, ETX and energy consumption index. Meanwhile, we improve the path ETX calculation method to avoid selecting optimal path containing long single hop links. Then we design a novel lexical method to synthetically evaluate candidate parents. Meanwhile, based on the evaluation results of candidate parents, we design a novel objective function and a new calculation node rank method which can also be used for selecting the optimal path. Finally, evaluation results show that I-RPL outperforms ETXOF and several other improvements in terms of packet delivery ratio, latency, etc.

Unsupervised Learning-based New Seed-Expanding Approach using Influential Nodes for Community Detection in Social Networks

Several recent studies focus on community structure due to its importance in analyzing and understanding complex networks. Communities are groups of nodes highly connected with themselves and not much connected to the rest of the network. Community detection helps us to understand the properties of the dynamic process within a network. In this paper, we propose a novel seed-centric approach based on TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) and k-means algorithm to find communities in a social network. TOPSIS is used to find the seeds within this network using the benefits of multiple measure centralities. The use of a single centrality to determine seeds within a network, like in classical algorithms of community detection, doesn’t succeed in the majority of cases to reach the best selection of seeds. Therefore, we consider all centrality metrics as a multi-attribute of TOPSIS and we rank nodes based on the TOPSIS’ relative closeness. The Top-K nodes extracted from TOPSIS will be considered as seeds in the proposed approach. Afterwards, we apply the k-means algorithm using these seeds as starting centroids to detect and construct communities within a social network. The proposed approach is tested on Facebook ego network and validated on the famous dataset having the ground-truth community structure Zachary karate club. Experimental results on Facebook ego network show that the dynamic k-means provides reasonable communities in terms of distribution of nodes. These results are confirmed using Zachary karate club. Two detected communities are detected with higher normalized mutual information NMI and Adjusted Rand Index ARI compared to other seed centric algorithms such as Yasca, LICOD, etc. The proposed method is effective, feasible, and provides better results than other available state-of-the-art community detection algorithms.

The performance of modern centrality measures on different information models and networks

For the last few years networks became integral parts of our everyday life. They are used in communication, transportation, marketing, and the list goes on. They are also becoming bigger, and more complex and dynamic networks also start to appear more. In light of this, the problem of finding the most influential node in the network remains of high interest however, it is getting more and more difficult to find these nodes. It is hard to grasp the true meaning of what is really being the most influential node means. There are several approaches to define what the most vital nodes are like having the most edges connected to them or having the shortest paths running through them. They can be also identified by calculating the influence of their neighbors, or evaluating how they contribute to the whole of the network. Over recent years various new centrality measures were proposed to order the importance of the nodes of a network. In this paper, we evaluate the performance of three modern centrality measures, namely Local Fuzzy Information Centrality (LFIC), Local Clustering H-index Centrality (LCH), and Global Structure Model (GSM) on different information models, and compare them with conventional centrality measures. In our experiments, we investigate the similarity between the top-n ranking nodes of the measures, the influential capacity of these nodes as well as the frequency of the nodes with the same centrality value.

A comparison of node vaccination strategies to halt SIR epidemic spreading in real-world complex networks.

We compared seven node vaccination strategies in twelve real-world complex networks. The node vaccination strategies are modeled as node removal on networks. We performed node vaccination strategies both removing nodes according to the initial network structure, i.e., non-adaptive approach, and performing partial node rank recalculation after node removal, i.e., semi-adaptive approach. To quantify the efficacy of each vaccination strategy, we used three epidemic spread indicators: the size of the largest connected component, the total number of infected at the end of the epidemic, and the maximum number of simultaneously infected individuals. We show that the best vaccination strategies in the non-adaptive and semi-adaptive approaches are different and that the best strategy also depends on the number of available vaccines. Furthermore, a partial recalculation of the node centrality increases the efficacy of the vaccination strategies by up to 80%.

WINNER: A network biology tool for biomolecular characterization and prioritization.

In network biology, molecular functions can be characterized by network-based inference, or "guilt-by-associations." PageRank-like tools have been applied in the study of biomolecular interaction networks to obtain further the relative significance of all molecules in the network. However, there is a great deal of inherent noise in widely accessible data sets for gene-to-gene associations or protein-protein interactions. How to develop robust tests to expand, filter, and rank molecular entities in disease-specific networks remains an ad hoc data analysis process. We describe a new biomolecular characterization and prioritization tool called Weighted In-Network Node Expansion and Ranking (WINNER). It takes the input of any molecular interaction network data and generates an optionally expanded network with all the nodes ranked according to their relevance to one another in the network. To help users assess the robustness of results, WINNER provides two different types of statistics. The first type is a node-expansion p-value, which helps evaluate the statistical significance of adding "non-seed" molecules to the original biomolecular interaction network consisting of "seed" molecules and molecular interactions. The second type is a node-ranking p-value, which helps evaluate the relative statistical significance of the contribution of each node to the overall network architecture. We validated the robustness of WINNER in ranking top molecules by spiking noises in several network permutation experiments. We have found that node degree-preservation randomization of the gene network produced normally distributed ranking scores, which outperform those made with other gene network randomization techniques. Furthermore, we validated that a more significant proportion of the WINNER-ranked genes was associated with disease biology than existing methods such as PageRank. We demonstrated the performance of WINNER with a few case studies, including Alzheimer's disease, breast cancer, myocardial infarctions, and Triple negative breast cancer (TNBC). In all these case studies, the expanded and top-ranked genes identified by WINNER reveal disease biology more significantly than those identified by other gene prioritizing software tools, including Ingenuity Pathway Analysis (IPA) and DiAMOND. WINNER ranking strongly correlates to other ranking methods when the network covers sufficient node and edge information, indicating a high network quality. WINNER users can use this new tool to robustly evaluate a list of candidate genes, proteins, or metabolites produced from high-throughput biology experiments, as long as there is available gene/protein/metabolic network information.

Ranking locations in a city via the collective home-work relations in human mobility data

Human mobility has long been a hot topic of research in complex systems. An intra-urban network treats a specific set of locations within a city as nodes and the various connections between locations at different spatial scales as edges. Human mobility is one of the direct responses to the connection of locations. Thus, human mobility data can be used to study the importance of locations in intra-urban networks, which has practical applications in urban layout. However, the datasets used in existing studies have shortcomings such as low temporal resolution and narrow range of covered users. Therefore, these kind of datasets only capture partial human mobility behavior. In this paper, a 4G communication data of 1.7million users in Shijiazhuang, a city in northern China, is used to investigate the mobility patterns of users. Our dataset covers a large proportion of the population in the city. We can also identify the location of a user to a high frequency of every second. Then two kinds of directed weighted networks, which consist of links separately from home to workplace and from home to weekend-stay, are respectively constructed based on the users’ mobility record. By analyzing the statistical properties of these networks and their skeleton networks, we find that although most users leave home to work and spend weekends, they prefer to live and work within the same district. To identify important locations in the city, we use the weighted PageRank algorithm to rank nodes in the intra-urban network. We find that the locations in the central area ranked highest, but the ranking is still different from the simple ranking based on population. Finally, using housing prices in the entire urban area of the city, and locations on Zhongshan road, a traditional commercial road in the city, as well as locations on the first ring area, which is the most densely populated area in the city, we verify that in identifying essential locations, PageRank is more effective than only using in-strength, which represents the frequency of a location is visited.

Optimizing Intermodal Transport and Hub Location Problem for ECOWAS in the Context of Improving Intra-African Trade

Trade within Africa is at an all-time low, with a lack of an optimal intermodal transportation network and a high cost of business serving as a deterrent to trade. This research studies Intra-African Trade within ECOWAS using a hierarchical spatial aggregation process to identify 27 nodes. Distance-based weighted centrality measures employed TOPSIS to model a ranked node centrality of Economic Community of West African States (ECOWAS) intermodal transport of railway, road, and waterway networks. The ten highest-ranking nodes identified from the mixed-integer linear program adopted as candidate hubs, thus selecting Ibeshe ferry terminal in Lagos and Tema Harbour in Accra for waterway; Thies, Ibadan, Conakry, Monrovia and Thies for railway; and Thies and Ibadan for road. We conclude with sensitivity analysis and a discussion of management implications for ECOWAS. This paper demonstrated that a limited number of transshipment hubs would encourage interregional trade and cut point-to-point transportation costs and lead to economic growth and development.

Cross-graph reference structure based pruning and edge context information for graph matching

Graph matching (GM) plays a vital role in solving various computer vision tasks by establishing a node-to-node correspondence between graph-structured data. In this study, we propose a novel method based on affinity matrix for solving GM tasks. Specifically, a pruning strategy is proposed to remove inconsistent edges from an association graph that formulates the GM problem into a node ranking and selection problem. Moreover, an edge context information with respect to a cross-graph reference structure is proposed and combined with the local distance information to compute the affinities among the graphs’ nodes. Then, the re-weighted random walk technique is utilized to simulate random walks on the association graph and compute a quasi-stationary distribution in an iterative manner. Finally, the Hungarian algorithm is used to discretize the distribution and obtain an approximate matching between two graphs. The experimental results indicate that our proposed GM method is able to produce promising results in the presence of outliers and deformation noise as compared with other methods.

A novel integration of MCDM methods and Bayesian networks: the case of incomplete expert knowledge

In this study, we propose an effective integration of multi criteria decision making methods and Bayesian networks (BN) that incorporates expert knowledge. The novelty of this approach is that it provides decision support in case the experts have partial knowledge. We use decision-making trial and evaluation laboratory (DEMATEL) to elicit the causal graph of the BN based on the causal knowledge of the experts. BN provides the evaluation of alternatives based on the decision criteria which make up the initial decision matrix of the technique for order of preference by similarity to the ideal solution (TOPSIS). We then parameterize BN using Ranked Nodes which allows the experts to submit their knowledge with linguistic expressions. We propose the analytical hierarchy process to determine the weights of the decision criteria and TOPSIS to rank the alternatives. A supplier selection case study is conducted to illustrate the effectiveness of the proposed approach. Two evaluation measures, namely, the number of mismatches and the distance due to the mismatch are developed to assess the performance of the proposed approach. A scenario analysis with 5% to 20% of missing values with an increment of 5% is conducted to demonstrate that our approach remains robust as the level of missing values increases.

Structural importance and evolution: An application to financial transaction networks

A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static networks, that do not change over time, but does not consider the dynamics of the network. Here we propose instead to measure the importance of a node based on how much a change to its strength will impact the global structure of the network, which we measure in terms of the spectrum of its adjacency matrix. We apply our method to the identification of important nodes in equity transaction networks and show that, while it can still be computed from a static network, our measure is a good predictor of nodes subsequently transacting. This implies that static representations of temporal networks can contain information about their dynamics.

Understanding percolation phase transition behaviors in complex networks from the macro and meso-micro perspectives

Over the most recent twenty years, network science has bloomed and impacted different fields such as statistical physics, computer science, sociology, and so on. Studying the percolation behavior of a network system has a very important role in vital nodes identification, ranking, network resilience, and propagation behavior of networks. When a network system undergoes failures, network connectivity is broken. In this perspective, the percolation behavior of the giant connected component and finite-size connected components is explored in depth from the macroscopic and meso-microscopic views, respectively. From a macro perspective, a single network system always shows second-order phase transitions, but for a coupled network system, it shows rich percolation behaviors for various coupling strength, coupling patterns and coupling mechanisms. Although the giant component accounts for a large proportion in the real system, it cannot be neglected that when the network scale is large enough, the scale of finite-size connected components has an important influence on network connectivity. We here systematically analyze the phase transition behaviors of finite-size connected components that are different from the giant component from a meso-microscopic perspective. Studying percolation behaviors from the macro and meso-micro perspectives is helpful for a comprehensive understanding of many fields of network science, such as time-series networks, adaptive networks, and higher-order networks. The intention of this paper is to provide a frontier research progress and promising research direction of network percolation from the two perspectives, as well as the essential theory of percolation transitions on a network system.

Interictal Connectivity Revealed by Granger Analysis of Stereoelectroencephalography: Association With Ictal Onset Zone, Resection, and Outcome.

Stereoelectroencephalography (sEEG) facilitates electrical sampling and evaluation of complex deep-seated, dispersed, and multifocal locations. Granger causality (GC), previously used to study seizure networks using interictal data from subdural grids, may help identify the seizure-onset zone from interictal sEEG recordings. To examine whether statistical analysis of interictal sEEG helps identify surgical target sites and whether surgical resection of highly ranked nodes correspond to favorable outcomes. Ten minutes of extraoperative recordings from sequential patients who underwent sEEG evaluation were analyzed (n = 20). GC maps were compared with clinically defined surgical targets using rank order statistics. Outcomes of patients with focal resection/ablation with median follow-up of 3.6 years were classified as favorable (Engel 1, 2) or poor (Engel 3, 4) to assess their relationship with the removal of highly ranked nodes using the Wilcoxon rank-sum test. In 12 of 20 cases, the rankings of contacts (based on the sum of outward connection weights) mapped to the seizure-onset zone showed higher causal node connectivity than predicted by chance ( P ≤ .02). A very low aggregate probability ( P < 10 -18 , n = 20) suggests that causal node connectivity predicts seizure networks. In 8 of 16 with outcome data, causal connectivity in the resection was significantly greater than in the remaining contacts ( P ≤ .05). We found a significant association between favorable outcome and the presence of highly ranked nodes in the resection ( P < .05). Granger analysis can identify seizure foci from interictal sEEG and correlates highly ranked nodes with favorable outcome, potentially informing surgical decision-making without reliance on ictal recordings.

An Internet-Oriented Multilayer Network Model Characterization and Robustness Analysis Method.

The Internet creates multidimensional and complex relationships in terms of the composition, application and mapping of social users. Most of the previous related research has focused on the single-layer topology of physical device networks but ignored the study of service access relationships and the social structure of users on the Internet. Here, we propose a composite framework to understand how the interaction between the physical devices network, business application network, and user role network affects the robustness of the entire Internet. In this paper, a multilayer network consisting of a physical device layer, business application layer and user role layer is constructed by collecting experimental network data. We characterize the disturbance process of the entire multilayer network when a physical entity device fails by designing nodal disturbance to investigate the interactions that exist between the different network layers. Meanwhile, we analyze the characteristics of the Internet-oriented multilayer network structure and propose a heuristic multilayer network topology generation algorithm based on the initial routing topology and networking pattern, which simulates the evolution process of multilayer network topology. To further analyze the robustness of this multilayer network model, we combined a total of six target node ranking indicators including random strategy, degree centrality, betweenness centrality, closeness centrality, clustering coefficient and network constraint coefficient, performed node deletion simulations in the experimental network, and analyzed the impact of component types and interactions on the robustness of the overall multilayer network based on the maximum component change in the network. These results provide new insights into the operational processes of the Internet from a multi-domain data fusion perspective, reflecting that the coupling relationships that exist between the different interaction layers are closely linked to the robustness of multilayer networks.

Medical Data Storage Model Based on an Alliance Chain

Aiming at the problems of centralized storage, low sharing efficiency, and the security and privacy of traditional medical data, a medical data storage model based on a consortium chain is proposed. First, the Distance algorithm is designed based on the geographical relationship of nodes, which reduces the amount of communication between nodes, improves the communication efficiency between A nodes, and ensures the efficiency and reliability of grouping. Second, the dynamic election is combined with the Distance algorithm to design the election strategy of the primary node, which realizes the scientific and reasonable ranking of the medical nodes, improves the reliability of the selection of the primary node, and ensures the efficiency of the medical nodes in the alliance chain to quickly reach consensus when the medical data are uploaded to the chain. Finally, the model designs a method of information separation, which combines the distributed database IPFS (InterPlanetary File System) with the blockchain, which greatly reduces the pressure of medical data storage in the blockchain and improves the operation efficiency. The experimental results show that the medical data storage model can effectively improve the problem of the sharp increase in the amount of communication between medical nodes in the network and reduce the impact of malicious consensus nodes.

Beyond preferential attachment: falling of stars and survival of superstars.

Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the ‘degree ladder’, causing high-degree nodes to be prone for attachment of new edges and for detachment of existing ones. Despite the extensive study of node degrees (absolute popularity), many domains consider node ranks (relative popularity) as of greater importance. This raises intriguing questions—what dynamics are expected to emerge when observing the ranking of network nodes over time? Does the ranking of nodes present similar monotonous patterns to the dynamics of their corresponding degrees? In this paper, we show that surprisingly the answer is not straightforward. By performing both theoretical and empirical analyses, we demonstrate that preferential principles do not apply to the temporal changes in node ranking. We show that the ranking dynamics follows a non-monotonous curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. These findings provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability.

Graph Pointer Neural Networks

Graph Neural Networks (GNNs) have shown advantages in various graph-based applications. Most existing GNNs assume strong homophily of graph structure and apply permutation-invariant local aggregation of neighbors to learn a representation for each node. However, they fail to generalize to heterophilic graphs, where most neighboring nodes have different labels or features, and the relevant nodes are distant. Few recent studies attempt to address this problem by combining multiple hops of hidden representations of central nodes (i.e., multi-hop-based approaches) or sorting the neighboring nodes based on attention scores (i.e., ranking-based approaches). As a result, these approaches have some apparent limitations. On the one hand, multi-hop-based approaches do not explicitly distinguish relevant nodes from a large number of multi-hop neighborhoods, leading to a severe over-smoothing problem. On the other hand, ranking-based models do not joint-optimize node ranking with end tasks and result in sub-optimal solutions. In this work, we present Graph Pointer Neural Networks (GPNN) to tackle the challenges mentioned above. We leverage a pointer network to select the most relevant nodes from a large amount of multi-hop neighborhoods, which constructs an ordered sequence according to the relationship with the central node. 1D convolution is then applied to extract high-level features from the node sequence. The pointer-network-based ranker in GPNN is joint-optimized with other parts in an end-to-end manner. Extensive experiments are conducted on six public node classification datasets with heterophilic graphs. The results show that GPNN significantly improves the classification performance of state-of-the-art methods. In addition, analyses also reveal the privilege of the proposed GPNN in filtering out irrelevant neighbors and reducing over-smoothing.

A Deep Contextual Bandit-Based End-to-End Slice Provisioning Approach for Efficient Allocation of 5G Network Resources

5G networks have been experiencing challenges in handling the heterogeneity and influx of user requests brought upon by the constant emergence of various services. As such, network slicing is considered one of the critical technologies for improving the performance of 5G networks. This technology has shown great potential for enhancing network scalability and dynamic service provisioning through the effective allocation of network resources. This paper presents a Deep Reinforcement Learning-based network slicing scheme to improve resource allocation in 5G networks. First, a Contextual Bandit model for the network slicing process is created, and then a Deep Reinforcement Learning-based network slicing agent (NSA) is developed. The agent’s goal is to maximize every action’s reward by considering the current network state and resource utilization. Additionally, we utilize network theory concepts and methods for node selection, ranking, and mapping. Extensive simulation has been performed to show that the proposed scheme can achieve higher action rewards, resource efficiency, and network throughput compared to other algorithms.

Learning to rank complex network node based on the self-supervised graph convolution model

Node ranking in complex networks is of great value in many fields, such as identifying opinion leaders in social networks and risky institutions in financial networks. However, traditional ranking methods are built on heuristic rules and may be effective in certain datasets and fail in others. To address the issues, we formulate node ranking on complex networks as a learning to rank problem, and propose a novel model based on self-supervised learning and graph convolution model to rank nodes based on integrated information from node features and network structure. (1) We develop a self-supervised pretext task to extract information about node location and global topology from complex networks. (2) To train the model more efficiently, multi-task learning is adopted, which includes ranking task and regression task besides the self-supervised pretext task. Our model works well with only a small number of nodes that have ranking labels. Comprehensive experiments on different datasets demonstrate that it outperforms the existing state-of-the-art methods, which verify the effectiveness and robustness of the proposed approach.