Multiple Types Of Links Research Articles

A network community detection method with integration of data from multiple layers and node attributes

AbstractMultilayer networks are in the focus of the current complex network study. In such networks, multiple types of links may exist as well as many attributes for nodes. To fully use multilayer—and other types of complex networks in applications, the merging of various data with topological information renders a powerful analysis. First, we suggest a simple way of representing network data in a data matrix where rows correspond to the nodes and columns correspond to the data items. The number of columns is allowed to be arbitrary, so that the data matrix can be easily expanded by adding columns. The data matrix can be chosen according to targets of the analysis and may vary a lot from case to case. Next, we partition the rows of the data matrix into communities using a method which allows maximal compression of the data matrix. For compressing a data matrix, we suggest to extend so-called regular decomposition method for non-square matrices. We illustrate our method for several types of data matrices, in particular, distance matrices, and matrices obtained by augmenting a distance matrix by a column of node degrees, or by concatenating several distance matrices corresponding to layers of a multilayer network. We illustrate our method with synthetic power-law graphs and two real networks: an Internet autonomous systems graph and a world airline graph. We compare the outputs of different community recovery methods on these graphs and discuss how incorporating node degrees as a separate column to the data matrix leads our method to identify community structures well-aligned with tiered hierarchical structures commonly encountered in complex scale-free networks.

On the k-Anonymization of Time-Varying and Multi-Layer Social Graphs

The popularity of online social media platforms provides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user information. It has been shown that a naive anonymization of a network by removing the identity of the nodes is not sufficient to preserve users' privacy. In order to deal with malicious attacks, k-anonymity solutions have been proposed to partially obfuscate topological information that can be used to infer nodes' identity. In this paper, we study the problem of ensuring k-anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specifically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to generate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k-1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Generalized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs.

A Tensor-Based Markov Chain Model for Heterogeneous Information Network Collective Classification

Heterogeneous Information Network (HIN) collecitve classification studies the problem of predicting labels for one type of nodes in a HIN which contains multiple types of nodes multiple types of links among them. Previous studies have revealed that exploiting relative importance of links is quite useful to improve node classification performance as connected nodes tend to have similar labels. Most existing approaches exploit the relative importance of links either by directly counting the number of connections among nodes or by learning the weight of each type of link from labeled data only. However, these approaches either neglect the importance of types of links to the class labels or may lead to overfitting problem. We propose a <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</b> ensor-based <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Mark</b> ov chain (T-Mark) approach, which is able to automatically and simultaneously predict the labels for unlabeled nodes and give the relative importance of types of links that actually improve the classification accuracy. Specifically, we build two tensor equations by using the HIN and features of nodes from both labeled and unlabeled data. A Markov chain-based model is proposed and it is solved by an iterative process to obtain the stationary distributions. Theoretical analyses of the existence and uniqueness of such probability distributions are given. Extensive experimental results demonstrate that T-Mark is able to achieve superior performance in the comparison and obtain reasonable relative importance of links.

Heterogeneous Combat Network Link Prediction Based on Representation Learning

Integrated joint operations under the conditions of information make the battlefield environment increasingly complex and with great uncertainty. Link prediction for combat networks is of significant military values for improving the understanding of complicated battlefield situations, helping to identify key enemy targets, and optimizing combat plans. This article proposes a method called heterogeneous combat network link prediction based on representation learning (RLHCN) to predict multiple types of links in the combat networks. First, a heterogeneous combat network (HCN) model is built by abstracting diversified systems and information flows of the combat system of systems (CSoS) into multiple types of nodes and edges. Next, taking into the sparse feature of HCNs into consideration, we proposed a network representation learning-based link prediction method and a solution algorithm to predict links in HCNs. Then, a real-world combat network is taken as an example and extensive experiments are conducted to demonstrate the feasibility and effectiveness of the proposed method. The results show that RLHCN is superior to the baseline methods and can achieve good performance in predicting multiple types of links in HCN.

Percolation in multilayer complex networks with connectivity and interdependency topological structures

The concept of a multilayer network describes a typical class of networks that have multiple types of links, that represent the different natures of interactions among nodes. In this work, we investigate the cascading dynamics in double-layer networks with two topological layers composed of connectivity links and interdependency links. The failure of a node can disable the nodes that disconnect the viable nodes, but it can also cause some amount of damage to its interdependency neighbours. We find that the characteristics of the percolation transition can be categorized into three types: first-order, second-order and double phase transition, which depend on the interdependency strength among nodes and the density of interdependency links of the system. We develop a theoretical framework to predict the percolation transition points and the switching point of percolation types. We have also validated our model in a double-layer empirical network composed by an internet and a power grid, and found that the results reproduced by our model is in concordance with the observations of cascading failures occurred in the critical infrastructure systems. Our work not only gives a possible qualitative explanation for the unexpected large-scale damages or disruptive avalanches in real-world infrastructure systems, but it also provides enlightening significance for how the double-layer network can be designed to have a satisfying resilience level.

A methodology for multilayer networks analysis in the context of open and private data: biological application

Recently, an increasing body of work investigates networks with multiple types of links. Variants of such systems have been examined decades ago in disciplines such as sociology and engineering, but only recently have they been unified within the framework of multilayer networks. In parallel, many aspects of real systems are increasingly and routinely sensed, measured and described, resulting in many private, but also open data sets. In many domains publicly available repositories of open data sets constitute a great opportunity for domain experts to contextualise their privately generated data compared to publicly available data in their domain. We propose in this paper a methodology for multilayer network analysis in order to provide domain experts with measures and methods to understand, evaluate and complete their private data by comparing and/or combining them with open data when both are modelled as multilayer networks. We illustrate our methodology through a biological application where interactions between molecules are extracted from open databases and modelled by a multilayer network and where private data are collected experimentally. This methodology helps biologists to compare their private networks with the open data, to assess the connectivity between the molecules across layers and to compute the distribution of the identified molecules in the open network. In addition, the shortest paths which are biologically meaningful are also analysed and classified.

Implementation of an Interactive Environment With Multilevel Wireless Links for Distributed Botanical Garden in University Campus

In this contribution, an end to end system to enable user interaction with a distributed botanical university campus garden is designed, implemented and tested. The proposed system employs different wireless links to collect data related to different bio physiological parameters of both the vegetation mass and the surrounding environment. Detailed analysis of these multilevel communication links is performed by using deterministic volumetric wireless channel estimation and considering underground, near ground and over ground radio propagation conditions. An in-house developed technique enables accurate wireless channel characterization for complete campus scenario considering the multiple link types and all its composing elements. Node definition and network topology is thus obtained by wireless channel analysis of over ground, near ground and underground communication for both 868 MHz and 2.4 GHz Wireless Sensor Networks in an inhomogeneous vegetation environment. Connectivity to enable user interaction as well as for telemetry and tele-control purposes within the campus is achieved by combining ZigBee and LoRaWAN transceivers with the corresponding sensor/actuator platforms. Coverage studies have been performed in order to assess communication capabilities in the set of multiple underground/near ground/over ground links, by means of deterministic channel analysis for the complete university campus location. Measurement results in lab environment as well as full system deployment are presented, showing good agreement with deterministic simulations. Moreover, system level tests have been performed over a physical campus cloud, providing adequate quality of experience metrics. The proposed solution is a scalable system that provides real time trees status monitoring by a cloud-based platform, enabling user interaction within a distributed botanical garden environment in the university campus.

Newly Published Scientific Papers Recommendation in Heterogeneous Information Networks

Millions of new research papers are published each year, making it extremely difficult for researchers to find out what they really want. Existing paper recommendation algorithms cannot effectively address the recommendation of newly published papers due to lack of historical information(e.g., citation information; view log), the so-called cold start problem. Furthermore, in most of these studies, papers are considered in homogeneous or bipartite networks. However, in a real bibliographic network, there are multiple types of objects (e.g., researchers, papers, venues, topics) and multiple types of links among these objects. In this paper, we study the problem of new paper recommendation in the heterogeneous bibliographic network, and a new method called HIPRec, i.e., meta-graph based recommendation model, is proposed to solve this problem. First, the top-K most interesting meta-paths are selected based on the training data. Secondly, a greedy method is proposed to select the most significant meta-graphs generated by merging the meta-paths, which can describe more sophisticated semantics between researchers and papers than simple meta-paths. In the meantime, meta-path and meta-graph based topological features are systematically extracted from the network. Lastly, a supervised model is used to learn the best weights associated with different topological features in deciding the researcher-new paper recommendations. We present experiments on a real bibliographic network, the DBLP network, which show the effectiveness of our approach compared to state-of-the-art new paper recommendation methods.

NetCycle+: A Framework for Collective Evolution Inference in Dynamic Heterogeneous Networks

Collective inference has attracted considerable attention in the last decade, where the response variables within a group of instances are correlated and should be inferred collectively, instead of independently. Previous works on collective inference mainly focus on exploiting the autocorrelation among instances in a static network during the inference process. There are also approaches on time series prediction, which mainly exploit the autocorrelation within an instance at different time points during the inference process. However, in many real-world applications, the response variables of related instances can co-evolve over time and their evolutions are not following a static correlation across time, but are following an internal life cycle . In this paper, we study the problem of collective evolution inference , where the goal is to predict the values of the response variables for a group of related instances at the end of their life cycles. This problem is extremely important for various applications, e.g., predicting fund-raising results in crowd-funding and predicting gene-expression levels in bioinformatics. This problem is also highly challenging because different instances in the network can co-evolve over time and they can be at different stages of their life cycles and thus have different evolving patterns. Moreover, the instances in collective evolution inference problems are usually connected through heterogeneous information networks (HINs for short), which involve complex relationships among the instances interconnected by multiple types of links. We propose an approach, called NetCycle+ , by incorporating information from both the correlation among related instances and their life cycles. Furthermore, in order to study the deep dependencies between nodes in the network, we extend the graph convolution model into our algorithm. We compared our approach with existing methods of collective inference and time series analysis on two real-world networks. The results demonstrate that our proposed approach can improve the inference performance by considering the autocorrelation through networks and the life cycles of the instances.

Learning Heterogeneous Network Embedding From Text and Links

Finding methods to represent multiple types of nodes in heterogeneous networks is both challenging and rewarding, as there is much less work in this area compared with that of homogeneous networks. In this paper, we propose a novel approach to learn node embedding for heterogeneous networks through a joint learning framework of both network links and text associated with nodes. A novel attention mechanism is also used to make good use of text extended through links to obtain much larger network context. Link embedding is first learned through a random-walk-based method to process multiple types of links. Text embedding is separately learned at both sentence level and document level to capture salient semantic information more comprehensively. Then, both types of embeddings are jointly fed into a hierarchical neural network model to learn node representation through mutual enhancement. The attention mechanism follows linked edges to obtain context of adjacent nodes to extend context for node representation. The evaluation on a link prediction task in a heterogeneous network data set shows that our method outperforms the current state-of-the-art method by 2.5%–5.0% in AUC values with p-value less than 10−9, indicating very significant improvement.

A link prediction method for heterogeneous networks based on BP neural network

Most real-world systems, composed of different types of objects connected via many interconnections, can be abstracted as various complex heterogeneous networks. Link prediction for heterogeneous networks is of great significance for mining missing links and reconfiguring networks according to observed information, with considerable applications in, for example, friend and location recommendations and disease–gene candidate detection. In this paper, we put forward a novel integrated framework, called MPBP (Meta-Path feature-based BP neural network model), to predict multiple types of links for heterogeneous networks. More specifically, the concept of meta-path is introduced, followed by the extraction of meta-path features for heterogeneous networks. Next, based on the extracted meta-path features, a supervised link prediction model is built with a three-layer BP neural network. Then, the solution algorithm of the proposed link prediction model is put forward to obtain predicted results by iteratively training the network. Last, numerical experiments on the dataset of examples of a gene–disease network and a combat network are conducted to verify the effectiveness and feasibility of the proposed MPBP. It shows that the MPBP with very good performance is superior to the baseline methods.

Meta-path based heterogeneous combat network link prediction

The combat system-of-systems in high-tech informative warfare, composed of many interconnected combat systems of different types, can be regarded as a type of complex heterogeneous network. Link prediction for heterogeneous combat networks (HCNs) is of significant military value, as it facilitates reconfiguring combat networks to represent the complex real-world network topology as appropriate with observed information. This paper proposes a novel integrated methodology framework called HCNMP (HCN link prediction based on meta-path) to predict multiple types of links simultaneously for an HCN. More specifically, the concept of HCN meta-paths is introduced, through which the HCNMP can accumulate information by extracting different features of HCN links for all the six defined types. Next, an HCN link prediction model, based on meta-path features, is built to predict all types of links of the HCN simultaneously. Then, the solution algorithm for the HCN link prediction model is proposed, in which the prediction results are obtained by iteratively updating with the newly predicted results until the results in the HCN converge or reach a certain maximum iteration number. Finally, numerical experiments on the dataset of a real HCN are conducted to demonstrate the feasibility and effectiveness of the proposed HCNMP, in comparison with 30 baseline methods. The results show that the performance of the HCNMP is superior to those of the baseline methods.

Meta-Path Based Inductive Classification in Heterogeneous Information Networks

The goal of inductive classification approaches is to infer the correct mapping from test set to labels, while the goal of transductive inference is to predict the correct labels for the given unlabeled data. Hence, the increased unlabeled samples can’t be classified by transductive classification. In this paper, we focus on studying the inductive classification problems in heterogeneous networks, which involve multiple types of objects interconnected by multiple types of links. Moreover, the objects and the links are gradually increasing over time. To accommodate characteristics of heterogeneous networks, a meta-path-based heterogeneous inductive classification (Hic) was proposed. First, the different sub-networks were constructed according to the selected meta-path. Second, the characteristic paths of each sub-network were extracted via the specified minimum support, and were assigned appropriate weights. Then, Hic model based on characteristic path was built. Finally, the Hic scores of each classification label for each test sample was calculated via links between test samples and sub-networks. Experiments on the DBLP showed that the proposed method significantly improves the accuracy and stability over the existing state-of-the-art methods for classification in dynamic heterogeneous network.

Networks within networks: using multiple link types to examine network structure and identify key actors in a drug trafficking operation

Understanding criminal networks can aid in the identification of key players and important relationships within the network. We examined multiple, directed link types in a criminal network. Eight distinct link types were identified, each one related to the exchange of a particular resource (e.g. drugs, money). The analyses focused on the eight link-type network layers and a merged network representing links across all eight layers. We were able to determine the link type of around 31% of the links, and found that nearly 50% of the nodes were involved in more than one network layer. This suggests that many actors contribute in multiple, diverse ways to the operation of the network. Actors were found to specialise in the exchange of particular types of resources, and also to specialise in the strategic position they occupied in the transfer of particular resources.

Reliable Task Allocation with Load Balancing in Multiplex Networks

In multiplex networks, agents are connected by multiple types of links; a multiplex network can be split into more than one network layer that is composed of the same type of links and involved agents. Each network link type has a bias for communicating different types of resources; thus, the task’s access to the required resources in multiplex networks is strongly related to the network link types. However, traditional task allocation and load balancing methods only considered the situations of agents themselves and did not address the effects of network link types in multiplex networks. To solve this problem, this article considers both link types and agents, and substantially extends the existing work by highlighting the effect of network layers on task allocation and load balancing. Two multiplex network-adapted models of task allocation with load balancing are presented: network layer-oriented allocation and agent-oriented allocation. This article also addresses the unreliability in multiplex networks, which includes the unreliable links and agents, and implements a reliable task allocation based on a negotiation reputation and reward mechanism. Our findings show that both of our presented models can effectively and robustly satisfy the task allocation objectives in unreliable multiplex networks; the experiments prove that they can significantly reduce the time costs and improve the success rate of tasks for multiplex networks over the traditional simplex network-adapted task allocation model. Lastly, we find that our presented network layer-oriented allocation performs much better in terms of reliability and allocation time compared to our presented agent-oriented allocation, which further explains the importance of network layers in multiplex networks.

Regional and inter-regional effects in evolving climate networks

Abstract. Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges for interactions present among the nodes; the characteristic properties of the graph are subsequently studied and related to the system's behaviour. More detailed graph models may include edge weights, orientations or multiple types of links; potential time-dependency of edges is conveniently captured in so-called evolving networks. Recently, it has been shown that an evolving climate network can be used to disentangle different types of El Niño episodes described in the literature. The time evolution of several graph characteristics has been compared with the intervals of El Niño and La Niña episodes. In this study we identify the sources of the evolving network characteristics by considering a reduced-dimensionality description of the climate system using network nodes given by rotated principal component analysis. The time evolution of structures in local intra-component networks is studied and compared to evolving inter-component connectivity.

Epidemics in partially overlapped multiplex networks.

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted . We also theoretically determine the dependence of the epidemic threshold on the fraction of shared nodes in a system composed of two layers. We find that in the limit of the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.

Correlated multiplexity and connectivity of multiplex random networks

Nodes in a complex networked system often engage in more than one type of interactions among them; they form a multiplex network with multiple types of links. In real-world complex systems, a node's degree for one type of links and that for the other are not randomly distributed but correlated, which we term correlated multiplexity. In this paper, we study a simple model of multiplex random networks and demonstrate that the correlated multiplexity can drastically affect the properties of a giant component in the network. Specifically, when the degrees of a node for different interactions in a duplex Erdős–Rényi network are maximally correlated, the network contains the giant component for any nonzero link density. In contrast, when the degrees of a node are maximally anti-correlated, the emergence of the giant component is significantly delayed, yet the entire network becomes connected into a single component at a finite link density. We also discuss the mixing patterns and the cases with imperfect correlated multiplexity.

Across-Model Collective Ensemble Classification

Ensemble classification methods that independently construct component models (e.g., bagging) improve accuracy over single models by reducing the error due to variance. Some work has been done to extend ensemble techniques for classification in relational domains by taking relational data characteristics or multiple link types into account during model construction. However, since these approaches follow the conventional approach to ensemble learning, they improve performance by reducing the error due to variance in learning. We note however, that variance in inference can be an additional source of error in relational methods that use collective classification, since inferred values are propagated during inference. We propose a novel ensemble mechanism for collective classification that reduces both learning and inference variance, by incorporating prediction averaging into the collective inference process itself. We show that our proposed method significantly outperforms a straightforward relational ensemble baseline on both synthetic and real-world datasets.

Multiplex Multi-Core Pattern of Network Organizations: An Exploratory Study

Recent research on small-world theory has been expanded upon organizations behavior. However, most individual studies have taken a simplified view of individuals and relationships among members by focusing on a single type of links mainly within dyadic relationships. In reality, members of organizations are interacting with each other and often connected via many types of links within more complex relationships. To explore this complex interaction, this study models organization as network and proposes a multiplex approach that captures the complexity of relationships among members in organizations. This approach accounts for the multiple types of links among members and the multiple roles of members within network organizations. It is illustrated via a case study of a network organization. The case study demonstrates how this approach could capture the many types of relationship among members as well as the various roles that members play within the network organization. Such an approach can yield new insights on how to better manage network organizations.