Node Ranking Research Articles

A flexible method for parameterizing ranked nodes in Bayesian networks using Beta distributions.

When novice modelers first attempt to build a Bayesian network, they are often impressed with the intuitive graphical structures that capture their causal understanding. This favorable impression evaporates on proceeding to parameterization. Conditional probability tables (CPT) require parameters for often hundreds of very similar scenarios and specifying them in the absence of data can be overwhelming. The problem is even more severe when eliciting parameters from experts with limited time. Often, there is local structure with fewer parameters that better describes the relationship. Such structures include the Noisy OR, decision trees, and equations. These work well for modelers, but can be an issue for experts and particularly groups of experts. An alternative approach is to elicit only a few CPT rows and interpolate the remainder. This is a promising approach, as it can handle unknown structures and multiple experts, but existing techniques can be limited. Here, we present a flexible approach called InterBeta for performing CPT interpolation with ordered nodes. In the simplest case, just two CPT rows are needed, but this can be easily augmented with further information. The basic approach assumes input independence, but allows dependencies to be reintroduced as required, and can also be combined with other local structures such as decision trees or equations, leaving the interpolator to fill in the gaps. We explain the InterBeta method, describe its capabilities and limitations and how it compares to similar approaches and show how it can trade-off elicitation effort against faithfully representing expertunderstanding.

Complex Traffic Network Analysis Method Based on a Multiscale Aggregation Model

Identifying the aggregation characteristics of the geospatial network is an important aspect of analyzing highway traffic networks. Based on the complex network theory, this paper studies the block aggregation characteristics of the highway traffic network and proposes an Improved PageRank Spectral Clustering (IPSC) Algorithm to divide the functional blocks of highway traffic networks. Firstly, the theoretical model of a highway traffic network is constructed by adding location attribute weight, geographical distance weight, road grade weight, and dynamic traffic congestion weight. Secondly, the improved PageRank algorithm is used to get the ranking of key nodes of the highway traffic network. The clustering center and the number of clusters are determined by the ranking of key nodes and the shortest path distance. Then the improved spectral clustering algorithm is used to divide the functional blocks of the highway transportation network and identify the special common blocks of the highway transportation network. Finally, the IPSC Algorithm is used to analyze the aggregation mode of complex traffic networks at city and district scales. Crossing the limit of administrative division, the division results of special common blocks of highway transportation networks are obtained. Maintaining the connectivity between blocks can improve the overall efficiency of highway transportation networks.

Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks.

Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in recent years to layer-coupled multiplex networks. The layers of these networks can reflect different relationships and interactions between entities or changing interactions over time. We use the supra-adjacency matrix as network representation, which has already been used to generalize eigenvector centrality to temporal and multiplex networks. With a suitable choice of edge weights, the definition of single-layer matrix function-based centrality measures in terms of walks on networks carries over naturally to the multilayer case. In contrast to other walk-based centralities, matrix function-based centralities are parameterized measures, which have been shown to interpolate between (local) degree and (global) eigenvector centrality in the single-layer case. As the explicit evaluation of the involved matrix function expressions becomes infeasible for medium to large-scale networks, we present highly efficient approximation techniques from numerical linear algebra, which rely on Krylov subspace methods, Gauss quadrature, and stochastic trace estimation. We present extensive numerical studies on synthetic and real-world multiplex transportation, communication, and collaboration networks. The comparison with established multilayer centrality measures shows that our framework produces meaningful rankings of nodes, layers, and node-layer pairs. Furthermore, our experiments corroborate the linear computational complexity of the employed numerical methods in terms of the network size that is theoretically indicated under the assumption of sparsity in the supra-adjacency matrix. This excellent scalability allows the efficient treatment of large-scale networks with the number of node-layer pairs of order 10^{7} or higher.

Efficient learning for decomposing and optimizing random networks

In this study, we consider the problem of node ranking in a random network. A Markov chain is defined for the network, and its transition probability matrix is unknown but can be learned by sampling random interactions among nodes. Our objective is to decompose the Markov chain into several ergodic classes and select the best node in each ergodic class. We propose a dynamic sampling procedure, which gives a probability guarantee on correct decomposition and maximizes a weighted probability of correct selection of the best node in each ergodic class. Numerical experiment results demonstrate the efficiency of the proposed sampling procedure.

Diffusion delay centrality: decelerating diffusion processes across networks

AbstractThis paper presents a new measure (the diffusion delay centrality—DDC) to identify agents who should be put into isolation to decelerate a diffusion process spreading throughout a network. We show that DDC assigns a high rank to agents acting as the gatekeepers of the fringe of the network. We also show that the ranking of nodes obtained from the DDC is predicted by the difference in the values of betweenness and eigenvector centrality of network agents. The findings presented might constitute a useful tool to reduce diffusion processes both for policy makers and for corporate managers in the organization of production.

A Grade Identification Method of Critical Node in Urban Road Network Based on Multi-Attribute Evaluation Correction

Accurately identifying the key nodes of the road network and focusing on its management and control is an important means to improve the robustness and invulnerability of the road network. In this paper, a classification and identification method of key nodes in urban road networks based on multi-attribute evaluation and modification was proposed. Firstly, the emergency function guarantee grade of road network nodes was divided by comprehensively considering the importance of road network nodes, the consequences of failure, and the degree of difficulty of recovery. The evaluation indexes were selected according to the local attributes, global attributes, and functional attributes of the road network topology. The spatial distribution patterns of the evaluation indexes of the nodes were analyzed. The dynamic classification method was used to cluster the attributes of the road network nodes, and the TOPSIS method was used to comprehensively evaluate the importance ranking of the road network nodes. Attribute clustering of road network nodes by dynamic classification method (DT) and the TOPSIS method was used to comprehensively evaluate the ranking of the importance of road network nodes. Then, combined with the modification of the comprehensive evaluation and ranking of the importance of the road network nodes, the emergency function support classification results of the road network nodes were obtained. Finally, the method was applied to the road network within the second Ring Road of Beijing. It was compared with the clustering method of self-organizing competitive neural networks. The results show that this method can identify the key nodes of the road network more accurately. The first-grade key nodes are all located at the more important intersections on expressways and trunk roads. The spatial distribution pattern shows a “center-edge” pattern, and the important traffic corridors of the road network show a “five vertical and five horizontal” pattern.

An Inverse-Free Block-SOR Method With Randomly Sampling for Temporal Multiplex PageRank Problems

Ranking nodes in a multiplex network is one of the most pressing and challenging tasks in network analysis. Generalizing centrality measures to multiplex networks is an active area of research. The Multiplex PageRank model is an extension of Google's PageRank, which introduces a new centrality measure to extend the usual PageRank to multiplex networks. In this work, we focus on the Multiplex PageRank problem. First, based on the special structure of the Multiplex PageRank problem, we propose an inverse-free block-SOR method. Second, with the help of randomly sampling, we propose a new strategy for estimating the optimal relaxation parameter. Specifically, the multiplex network is frequently updated in real world applications, and we have to deal with temporal Multiplex PageRank problems including the incremental and the decremental Multiplex PageRank problems. To the best of our knowledge, however, there are few efficient algorithms for solving these type of problems. To fill-in this gap, the third contribution of this work is to propose both incremental and decremental algorithms for solving the temporal Multiplex PageRank problems. Comprehensive numerical experiments are performed to illustrate the numerical behavior of the proposed algorithms, and show the effectiveness of our new strategies.

A Node Ranking Method Based on Multiple Layers for Dynamic Protein Interaction Networks

Constructing dynamic protein interaction networks (DPIN) is a common way to improve identification accuracy of essential proteins. The existing methods usually aggregate DPIN into a single-layer network and in which all nodes are sorted by their importance. This makes the dynamic information about proteins in multiple layers lost in the single layer, and thus affects the identification accuracy of essential proteins. This paper proposes a node ranking method based on multiple layers for DPIN to address the problem. First, we calculate the centrality values of all nodes for each time-specific layer, then work out the centrality score of each node by dividing the total of its centrality values across all layers by its layer activity, and finally sort the importance of all nodes by their centrality scores. Different from the methods based on single layer, our method makes full use of centrality values of each protein in time-specific layers, and thus can more effectively utilize the dynamic information of proteins than those methods based on single layer. To evaluate the effectiveness of the node ranking method based on multiple layers, we apply ten network-based centrality methods on multiple layers and compare the results with those on a single layer. Then the predictive performance of the ten centrality methods are validated in terms of sensitivity, specificity, positive predictive value, negative predictive value, F-measure and accuracy. The experimental results for the identification of essential proteins show that the node ranking method based on multiple layers is superior to those based on a single layer and can help to identify essential proteins more accurate.

Fault-Tolerant Embedding Algorithm for Node Failure in Airborne Tactical Network Virtualization

Airborne tactical networks (ATNs) are driving the promising development of Internet of Battle things by enabling efficient information sharing, which is impeded by the network ossification problem that is deep-rooted in the tightly coupled network architecture. As a solution, network virtualization (NV) can break the tight coupling between applications and network infrastructure, providing a more flexible and scalable architecture for ATNs. With complex interference and malicious attacks, the application of NV is challenged by network failures when instantiating multiple virtual networks on a shared substrate network, which is known as survivable virtual network embedding (SVNE). However, existing SVNE algorithms, mostly designed for wired networks, are not necessarily optimal for the virtualization of ATNs due to the complex wireless interference. To this end, a fault-tolerant SVNE algorithm, termed SVNE-FT, is proposed to recover virtual networks from single node failure (end or switching node failure) under the wireless interference. To end node failure, SVNE-FT firstly adopts a novel node ranking approach to select reliable substrate nodes for virtual nodes and then remaps the failed virtual nodes, affected by node failure, by releasing part of the substrate paths to improve the resource utilization. In addition, to switching node failure, it adopts the improved pre-configured cycle (p-Cycle) technology to augment the reliable link mapping with differentiated p-Cycles that protect switching node from node failure and reduce the resource consumption of backups. Numerical simulation results reveal that SVNE-FT outperforms typical and latest heuristic SVNE algorithms under the complex interference of ATNs. For instance, average acceptance ratio of virtual networks improves at least 12%.

A New Model for Predicting and Dismantling a Complex Terrorist Network

The perennial nature of terrorist attacks in recent times has ushered in a new wave of study in the field of terrorism known as social network analysis (SNA). Terrorist groups operate as a social network stealthily to enhance their efficacy rate, thereby making sure their activities are cloaked. This study proposes a new method to uncover and dismantle a terror network by applying a 4-centrality measure. After establishing link prediction using centrality measures, we dismantle the network based on Galton-Watson extinction probability. This study examines the 9/11 incident and measures the link prediction of the M-19 network. In curbing terrorist network activities, the elimination of a highly ranked node in the network is a condition sine qua non.We further examine the lethality of the network as well as network bonding to obtain the degree of cohesiveness, which is a crucial determinant for network survival. Our experimental results indicate that link prediction is vital in uncloaking a terror network, which is the core of counterterrorism.

Enabling fast path delay measurement using closeness centrality

As one of the key performance metrics, path delay is of great significance for network policy making. Existing work has focused too much on the accuracy of delay measurement and neglected its timeliness. In response, in this paper, we propose a fast path delay measurement scheme using closeness centrality for software‐defined network. First, the node ranking method using closeness centrality is used to select the initial point for the delay measurement to enable fast forwarding of probe packets. On this basis, we assign link weights according to the delay measurement results, and readjust the measurement points to optimize the performance. A series of simulation experiments on different topologies and network state verifies the advantage of the proposed scheme in this paper in terms of time overhead for delay measurement, compared to existing work.

Characterizing cycle structure in complex networks

A cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. An in-depth understanding of which cycles are important and what role they play on network structure and dynamics, however, is still lacking. In this paper, we define the cycle number matrix, a matrix enclosing the information about cycles in a network, and the cycle ratio, an index that quantifies node importance. Experiments on real networks suggest that cycle ratio contains rich information in addition to well-known benchmark indices. For example, node rankings by cycle ratio are largely different from rankings by degree, H-index, and coreness, which are very similar indices. Numerical experiments on identifying vital nodes for network connectivity and synchronization and maximizing the early reach of spreading show that the cycle ratio performs overall better than other benchmarks. Finally, we highlight a significant difference between the distribution of shorter cycles in real and model networks. We believe our in-depth analyses on cycle structure may yield insights, metrics, models, and algorithms for network science.

Novel centrality measures and applications to underground networks

Two novel centrality indices, PathRank and Icentr, are defined. PathRank is a generalization of the PageRank algorithm, suitable to rank nodes of undirected graphs according to number and weight of paths in the graph. Icentr ranks the nodes of the graph by means of a combination of the weights of nodes and edges, scaled according to the distance from each node, one at a time. We apply the two novel indices to underground transportation networks, since these networks represent an infrastructural backbone for the transportation system of most big cities over the world. The characterization of the most important components of those networks and the simulation of their responses when they stop working properly, are vital for maintaining the mobility service at a desirable level. Since there are different ways to associate a graph to an underground network according to the degree of detail and aims of the study, we describe the methodology we adopted to associate a graph to such a network. The methodology was applied to 34 underground networks of worldwide cities, and the resulting graphs constitute the reference dataset. A detailed study of both Boston network and the dataset is proposed as prototypal for either a graph alone or all graphs in a dataset. Results show how different features of graphs are revealed by the two novel indices.

Simulating systematic bias in attributed social networks and its effect on rankings of minority nodes

Network analysis provides powerful tools to learn about a variety of social systems. However, most analyses implicitly assume that the considered relational data is error-free, and reliable and accurately reflects the system to be analysed. Especially if the network consists of multiple groups (e.g., genders, races), this assumption conflicts with a range of systematic biases, measurement errors and other inaccuracies that are well documented in the literature. To investigate the effects of such errors we introduce a framework for simulating systematic bias in attributed networks. Our framework enables us to model erroneous edge observations that are driven by external node attributes or errors arising from the (hidden) network structure itself. We exemplify how systematic inaccuracies distort conclusions drawn from network analyses on the task of minority representations in degree-based rankings. By analysing synthetic and real networks with varying homophily levels and group sizes, we find that the effect of introducing systematic edge errors depends on both the type of edge error and the level of homophily in the system: in heterophilic networks, minority representations in rankings are very sensitive to the type of systematic edge error. In contrast, in homophilic networks we find that minorities are at a disadvantage regardless of the type of error present. We thus conclude that the implications of systematic bias in edge data depend on an interplay between network topology and type of systematic error. This emphasises the need for an error model framework as developed here, which provides a first step towards studying the effects of systematic edge-uncertainty for various network analysis tasks.

Urban Environment during Post-War Reconstruction: Architectural Dominants and Nodal Points as Measures of Changes in an Urban Landscape

Modernist planners were given the opportunity to apply the idea of the Modern Movement in the implementation of cities transforming after the World War II blitz, which was not possible before in long-term evolving structures. However, they could not alter everything: some urban and even architectural elements were necessary to be preserved. As a result, the elements of the ancient landscapes of these cities—historical objects and spaces—necessary for the continuity of evidence of history and identity were preserved, often being completely reconstructed. Finally, in some of these cities, both old and new elements contribute to the contemporary urban landscape. The aim of the research is to examine two key categories of urban structure in this perspective: (1) architectural dominants (landmarks) and (2) urban network nodes. For this purpose, (1) the changes in the number and rank of the spaces through which the landmarks expositions were carried out are compared, and (2) the changes in the rank of nodes in the urban structure, both these in the pre-war and in the present structures, as well as changes in their distribution and concentration areas are analyzed. The number of individual elements is compared and the changes in the structure of their arrangement are analyzed with the use of a polygon grid. A medium-scale European city (Bialystok) is used as the case study. Results of our analysis indicate that the post-war reconstruction led to a decrease in the number of elements of the urban grid (streets, nodal points), especially those of low rank. The rank of many others also decreased: 57% of all nodal points within the historical grid of the selected area does not exist in the post-war structure. The number of main rank directions of exposition decreased by 18% and in the subordinate group by 38%. The research is an attempt to construct a new criteria of evaluating changes in the quality of the cityscape, which is described in the article.

An ensemble feature selection algorithm based on PageRank centrality and fuzzy logic

One of the crucial processes in machine learning algorithms to improve the performance as well as, in some cases, to reduce the computational cost is feature selection. In other words, when there are many features, some are irrelevant; thus, irrelevant features will badly affect the learning process, so selecting the most fitting features can lead to increasing the accuracy of models in high-dimensional datasets. Recent researches benefit from an integration of various feature selection methods to find relevant features more accurately. Despite the fact that applying several feature selection methods can be efficient, the accuracy of current methods and combining the ranks of different feature selection methods are still challenging problems. In this paper, a novel ensemble of feature selection based on weighted PageRank and fuzzy logic, named EFSPF, is proposed to overcome these drawbacks. First, an M×M matrix, called Euclidean Distance Matrix (EDM), is set up, where M is the number of features. Secondly, a fuzzy Type-I is applied individually to tackle uncertainties in ranks. In other words, to specify a reliability rate for each feature, fuzzy Type-I is utilized. Then, EFSPF forms a reliable weighted graph where each feature is considered as a node. Furthermore, the weight between two nodes expresses a combination of their Euclidean Distance in EDM and the calculated reliability rates through fuzzy Type-I. Finally, the rank of each graph node is calculated via the PageRank algorithm. To demonstrate the performance of EFSPF, we have compared it with five ensemble algorithms and eight primary feature selection algorithms. The proposed method is evaluated based on Accuracy, Precision, Recall, and F1 score metrics. The analysis results show that the proposed method outperforms its rivals. The source code of the proposed method is accessible from https://github.com/mehdijoodaki/EFSPF.

Deep node ranking for neuro‐symbolic structural node embedding and classification

Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Deep Node Ranking (DNR) algorithm are competitive or better classification performance, significantly higher learning speed and lower space requirements when compared to state-of-the-art approaches on 15 real-life node classification benchmarks. Furthermore, it enables exploration of the relationship between symbolic and the derived sub-symbolic node representations, offering insights into the learned node space structure. To avoid the space complexity bottleneck in a direct node classification setting, DNR computes stationary distributions of personalized random walks from given nodes in mini-batches, scaling seamlessly to larger networks. The scaling laws associated with DNR were also investigated on 1488 synthetic Erd\H{o}s-R\'enyi networks, demonstrating its scalability to tens of millions of links.

Modelling COVID-19 Hotspot Using Bipartite Network Approach

COVID-19 causes a jarring impact on the livelihoods of people in Malaysia and globally. To prevent an outbreak in the community, identifying the likely sources of infection (hotspots) of COVID-19 is important. The goal of this study is to formulate a bipartite network model of COVID-19 transmissions by incorporating patient mobility data to address the assumption on population homogeneity made in the conventional models and focus on indirect transmission. Two types of nodes – human and location – are the main concern in the research scenario. 21 location nodes and 31 human nodes are identified from a patient’s pre-processed mobility data. The parameters used in this study for location node and human node quantifications are the ventilation rate of a location and the environmental properties of the location that affect the stability of the virus such as temperature and relative humidity. The summation rule is applied to quantify all nodes in the network and the link weight between the human node and the location node. The ranking of location and human nodes in this network is computed using a web search algorithm. This model is considered verified as the error obtained from the comparison made between the benchmark model and the COVID-19 bipartite network model is small. As a result, the higher ranking of the location is denoted as a hotspot in this study, and for a human node attached to this node will be ranked higher in the human node ranking. Consequently, the hotspot has a higher risk of transmission compared to other locations. These findings are proposed to provide a framework for public health authorities to identify the sources of infection and high-risk groups of people in the COVID-19 cases to control the transmission at the initial stage.

Algorithmic bias amplification via temporal effects: The case of PageRank in evolving networks

Biases impair the effectiveness of algorithms. For example, the age bias of the widely-used PageRank algorithm impairs its ability to effectively rank nodes in growing networks. PageRank’s temporal bias cannot be fully explained by existing analytic results that predict a linear relation between the expected PageRank score and the indegree of a given node. We show that in evolving networks, under a mean-field approximation, the expected PageRank score of a node can be expressed as the product of the node’s indegree and a previously-neglected age factor which can “amplify” the indegree’s age bias. We use two well-known empirical networks to show that our analytic results explain the observed PageRank’s age bias and, when there is an age bias amplification, they enable estimates of the node PageRank score that are more accurate than estimates based solely on local structural information. Accuracy gains are larger in degree–degree correlated networks, as revealed by a growing directed network model with tunable assortativity. Our approach can be used to analytically study other kinds of ranking bias.

EM-based smooth graphon estimation using MCMC and spline-based approaches

This paper proposes the estimation of a smooth graphon model for network data analysis using principles of the EM algorithm. The approach considers both variability with respect to ordering the nodes of a network and smooth estimation of the graphon by nonparametric regression. To do so, (linear) B-splines are used, which allow for smooth estimation of the graphon, conditional on the node ordering. This provides the M-step. The true ordering of the nodes arising from the graphon model remains unobserved and MCMC techniques are employed to obtain position samples conditional on the network. This yields the E-step. Combining both steps gives an EM-based approach for smooth graphon estimation. Unlike common other methods, this procedure does not require the restriction of a monotonic marginal function. The proposed graphon estimate allows to explore node-ordering strategies and therefore to compare the common degree-based node ranking with the ordering conditional on the network. Variability and uncertainty are taken into account relying on the MCMC sequences. Examples and simulation studies support the applicability of the approach.