Number Of Common Neighbors Research Articles

Reconstruction of random geometric graphs: Breaking the [formula omitted] distortion barrier

Embedding graphs in a geographical or latent space, i.e. inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We consider the classic model of random geometric graphs where n points are scattered uniformly in a square of area n, and two points have an edge between them if and only if their Euclidean distance is less than r. The reconstruction problem then consists of inferring the vertex positions, up to the symmetries of the square, given only the adjacency matrix of the resulting graph. We give an algorithm that, if r=nα for any 0<α<1/2, with high probability reconstructs the vertex positions with a maximum error of O(nβ) where β=1/2−(4/3)α, until α≥3/8 where β=0 and the error becomes O(logn). This improves over earlier results, which were unable to reconstruct with error less than r. Our method estimates Euclidean distances using a hybrid of graph distances and short-range estimates based on the number of common neighbors. We extend our results to the surface of the sphere in R3 and to hypercubes in any constant fixed dimension.

Harnessing the Power of Ego Network Layers for Link Prediction in Online Social Networks

Being able to recommend links between users in online social networks is important for users to connect with like-minded individuals as well as for the platforms themselves and third parties leveraging social media information to grow their business. Predictions are typically based on unsupervised or supervised learning, often leveraging simple yet effective graph topological information, such as the number of common neighbors. However, we argue that richer information about personal social structure of individuals might lead to better predictions. In this article, we propose to leverage well-established social cognitive theories to improve link prediction performance. According to these theories, individuals arrange their social relationships along, on average, five concentric circles of decreasing intimacy. We postulate that relationships in different circles have different importance in predicting new links. To validate this claim, we focus on popular feature extraction prediction algorithms (both unsupervised and supervised) and we extend them to include social circles’ awareness. We validate the prediction performance of these circle-aware algorithms against several benchmarks (including their baseline versions as well as node-embedding- and graph neural network (GNN)-based link prediction), leveraging two Twitter datasets comprising a community of video gamers and generic users. We show that social awareness generally provides significant improvements in prediction performance, beating also state-of-the-art solutions such as node2vec and learning from Subgraphs, Embeddings and Attributes for Link prediction (SEAL), and without increasing the computational complexity. Finally, we show that social awareness can be used in place of using a classifier (which may be costly or impractical) for targeting a specific category of users.

How to Realize Efficient and Scalable Graph Embeddings via an Entropy-Driven Mechanism

Graph embedding is becoming widely adopted as an efficient way to learn graph representations required to solve graph analytics problems. However, most existing graph embedding methods, owing to computation-efficiency challenges for large-scale graphs, generally employ a one-size-fits-all strategy to extract information, resulting in a large amount of redundant or inaccurate representations. In this work, we propose HuGE+, an efficient and scalable graph embedding method enabled by an entropy-driven mechanism. Specifically, HuGE+ leverages hybrid-property heuristic random walk to capture node features, which considers both information content of nodes and the number of common neighbors in each walking step. More importantly, to guarantee information effectiveness of sampling, HuGE+ adopts two heuristic methods to decide the random walk length and the number of walks per node, respectively. Extensive experiments on real-world graphs demonstrate that HuGE+ achieves both efficiency and performance advantages over recent popular graph embedding approaches. For three downstream graph tasks, our approach not only offers >10% average gains, but also exhibits 23×–127× speedup over existing sampling-based methods. In addition, HuGE+ significantly reduces memory footprint by an average of 68.9%, facilitating training for billion-node-scale graph embeddings.

CSS: A new combined spreading score measurement for identifying multiple influential spreaders in complex networks

Identifying multiple influential spreaders is a significant procedure to understand, control or accelerate the dynamics of information diffusion process in complex networks effectively. For a given network [Formula: see text] and an integer [Formula: see text], we need to find a set of [Formula: see text] vertices as “seeds” which carry the information originally, and then through a certain diffusion model, the information can be spread as widely as possible. Note that these seeds cannot be too close to each other, otherwise information is easy to be congested. In this paper, we make an attempt to identify multiple spreaders by considering the “marginal benefit” [Formula: see text] of a vertex [Formula: see text] when it is added to an existing seed set [Formula: see text]. Here [Formula: see text] is defined as a function of [Formula: see text]’s influential ability and the common influence range between vertex [Formula: see text] and [Formula: see text]. In particular, we use the degree to measure the vertex’s influential ability and use the number of common neighbors between vertex [Formula: see text] and [Formula: see text] to measure their common influence range. In order to verify this new algorithm’s validity, we apply it on several social networks and the new method performs better than others. This new method is simple to implement and has lower time complexity, thus is expected to have promising applications in the future.

Influence of clustering coefficient on network embedding in link prediction

Multiple network embedding algorithms have been proposed to perform the prediction of missing or future links in complex networks. However, we lack the understanding of how network topology affects their performance, or which algorithms are more likely to perform better given the topological properties of the network. In this paper, we investigate how the clustering coefficient of a network, i.e., the probability that the neighbours of a node are also connected, affects network embedding algorithms’ performance in link prediction, in terms of the AUC (area under the ROC curve). We evaluate classic embedding algorithms, i.e., Matrix Factorisation, Laplacian Eigenmaps and node2vec, in both synthetic networks and (rewired) real-world networks with variable clustering coefficient. Specifically, a rewiring algorithm is applied to each real-world network to change the clustering coefficient while keeping key network properties. We find that a higher clustering coefficient tends to lead to a higher AUC in link prediction, except for Matrix Factorisation, which is not sensitive to the change of clustering coefficient. To understand such influence of the clustering coefficient, we (1) explore the relation between the link rating (probability that a node pair is the missing link) derived from the aforementioned algorithms and the number of common neighbours of the node pair, and (2) evaluate these embedding algorithms’ ability to reconstruct the original training (sub)network. All the network embedding algorithms that we tested tend to assign higher likelihood of connection to node pairs that share an intermediate or high number of common neighbours, independently of the clustering coefficient of the training network. Then, the predicted networks will have more triangles, thus a higher clustering coefficient. As the clustering coefficient increases, all the algorithms but Matrix Factorisation could also better reconstruct the training network. These two observations may partially explain why increasing the clustering coefficient improves the prediction performance.

VSIM: Distributed local structural vertex similarity calculation on big graphs

In many graph analytical applications, the local structural vertex similarity calculation is an essential prerequisite for advanced graph mining. The similarity calculation finds out all the similar vertex pairs whose local structural similarity scores (like the number of common neighbors, and the Jaccard index of adjacency sets) are above a given threshold. The real-world applications use a wide range of similarity thresholds. However, the existing distributed methods for the problem only optimize for either high thresholds (> 0.7) or low thresholds (< 0.1). To overcome the drawback, we propose a new distributed vertex similarity calculation framework VSIM that is efficient under a broad range of thresholds. VSIM processes static undirected graphs with local structural similarity scores that measure the similarity between vertices based on the first-order topology information. VSIM generates a similarity calculation task for every vertex in the graph and conducts all the tasks in parallel on a distributed computing platform along with a distributed key-value store. Each task finds vertices similar to a given center vertex with two task execution modes. The two modes optimize for high and low thresholds, respectively. Each task picks the suitable mode adaptively according to cost estimation models. We also propose an efficient implementation for VSIM on Apache Spark, with three optimization techniques to reduce communication costs and balance workloads on power-law graphs. The experimental evaluation shows that VSIM outperforms the state-of-the-art distributed methods by up to 67x speedup. VSIM can achieve near-linear node scalability in low-threshold and small cache scenarios.

Trust Prediction Based on Extreme Learning Machine and Asymmetric Tri-Training

Currently, more and more people communicate and trade through online social networks, so it is necessary to predict the trust between users. In order to predict the trust between users through a social network requires some other factors, such as user similarity, topic relevance, and the number of common neighbors should be considered. Some scholars use BP neural network based on the asymmetric tri-training model to train one social network and use transfer learning to predict the social relationship of another social network. However, this method has high computational complexity and slow operation speed. To solve the problem, the three classifiers are expanded into four classifiers on the basis of asymmetric tri-training, and the extreme learning machine classifier is used to replace the BP neural network classifier. The specific steps are: we first obtain the common features between different networks, use source data samples to train the first three classifiers, save the model, and train target samples to generate pseudo labels; then we use standard pseudo label samples to train the fourth classifier and use it to predict the social relations of the target network. Finally, compare with the existing evaluation methods, we proposed an algorithm on six online social networks. The experimental results show that the model in this paper is superior to other evaluation methods in recall and stability.

Similarity-based link prediction in social networks using latent relationships between the users

Social network analysis has recently attracted lots of attention among researchers due to its wide applicability in capturing social interactions. Link prediction, related to the likelihood of having a link between two nodes of the network that are not connected, is a key problem in social network analysis. Many methods have been proposed to solve the problem. Among these methods, similarity-based methods exhibit good efficiency by considering the network structure and using as a fundamental criterion the number of common neighbours between two nodes to establish structural similarity. High structural similarity may suggest that a link between two nodes is likely to appear. However, as shown in the paper, the number of common neighbours may not be always sufficient to provide comprehensive information about structural similarity between a pair of nodes. To address this, a neighbourhood vector is first specified for each node. Then, a novel measure is proposed to determine the similarity of each pair of nodes based on the number of common neighbours and correlation between the neighbourhood vectors of the nodes Experimental results, on a range of different real-world networks, suggest that the proposed method results in higher accuracy than other state-of-the-art similarity-based methods for link prediction.

Experimental analyses on 2-hop-based and 3-hop-based link prediction algorithms

Link prediction is a significant and challenging task in network science. The majority of known methods are similarity-based, which assign similarity indices for node pairs and assume that two nodes of larger similarity have higher probability to be connected by a link. Due to their simplicity, interpretability and high efficiency, similarity-based methods, in particular those based only on local information, have found successful applications on disparate fields. An intuitive consensus is that two nodes sharing common neighbors are likely to have a link, while some recent evidences indicate that the number of 3-hop paths more accurately predicts missing links than the number of common neighbors. In this paper, we implement extensive experimental comparisons between 2-hop-based and 3-hop-based similarity indices on 137 real networks. Overall speaking, the class of Cannistraci–Hebb indices performs the best among all considered candidates. In addition, 3-hop-based indices outperform 2-hop-based indices on ROC-AUC, and 3-hop-based indices and 2-hop-based indices are competitive on precision. Further statistical results show that 3-hop-based indices are more suitable for disassortative networks with lower densities and lower average clustering coefficients.

Network effects govern the evolution of maritime trade

Maritime transport accounts for over 80% of the world trade volume and is the backbone of the global economy. Global supply chains create a complex network of trade flows. The structure of this network impacts not only the socioeconomic development of the concerned regions but also their ecosystems. The movements of ships are a considerable source of CO2 emissions and contribute to climate change. In the wake of the announced development of Arctic shipping, the need to understand the behavior of the maritime trade network and to predict future trade flows becomes pressing. We use a unique database of daily movements of the world fleet over the period 1977-2008 and apply machine learning techniques on network data to develop models for predicting the opening of new shipping lines and for forecasting trade volume on links. We find that the evolution of this system is governed by a simple rule from network science, relying on the number of common neighbors between pairs of ports. This finding is consistent over all three decades of temporal data. We further confirm it with a natural experiment, involving traffic redirection from the port of Kobe after the 1995 earthquake. Our forecasting method enables researchers and industry to easily model effects of potential future scenarios at the level of ports, regions, and the world. Our results also indicate that maritime trade flows follow a form of random walk on the underlying network structure of sea connections, highlighting its pivotal role in the development of maritime trade.

Probabilistic diagnosis of clustered faults for hypercube-based multiprocessor system

As the sizes of multiprocessor systems grow, chances of processors becoming faulty increase, making it an important issue to diagnose faulty nodes in the system. Different models have been proposed and studied. One proposed by Huang et al. employed a probabilistic fault model to determine the status of a cluster of nodes in rectangular grid structures [8]. Later, Tang et al. extended the diagnosis algorithm to more general, regular topologies, in which any pair of adjacent nodes has no common neighbors [25]. In a recent work by Lu et al., the algorithm was further extended to regular topologies where any pair of adjacent nodes has a certain number of common neighbors [18]. In this paper, we extend the threshold to apply the probabilistic diagnosis algorithm for hypercube-based multiprocessor system, and carry out an analysis on the algorithm's effectiveness. The analysis shows a very high rate of correct diagnosis, both for an individual node and for nodes as a whole. Although the analysis is done for a particular regular network (the hypercube), the outcome can serve as a useful reference, and can shed light on the effectiveness of the probabilistic diagnosis for a large group of triangle-free multiprocessor systems.

Link prediction via linear optimization

Link prediction is an elemental challenge in network science, which has already found applications in guiding laboratorial experiments, digging out drug targets, recommending online friends, probing network evolution mechanisms, and so on. With a simple assumption that the likelihood of the existence of a link between two nodes can be unfolded by a linear summation of neighboring nodes’ contributions, we obtain the analytical solution of the optimal likelihood matrix, which shows remarkably better performance in predicting missing links than the state-of-the-art algorithms for not only simple networks, but also weighted and directed networks. To our surprise, even some degenerated local similarity indices from the solution outperform well-known local indices, which largely refines our knowledge, for example, the number of 3-hop paths between two nodes more accurately predicts missing links than the number of 2-hop paths (i.e., the number of common neighbors), while in previous methods, longer paths are always considered to be less important than shorter paths.

Community detection using boundary nodes in complex networks

We propose a new local community detection algorithm that finds communities by identifying borderlines between them using boundary nodes. Our method performs label propagation for community detection, where nodes decide their labels based on the largest “benefit score” exhibited by their immediate neighbors as an attractor to their communities. We try different metrics and find that using the number of common neighbors as benefit scores leads to better decisions for community structure. The proposed algorithm has a local approach and focuses only on boundary nodes during iterations of label propagation, which eliminates unnecessary steps and shortens the overall execution time. It preserves small communities as well as big ones and can outperform other algorithms in terms of the quality of the identified communities, especially when the community structure is subtle. The algorithm has a distributed nature and can be used on large networks in a parallel fashion.

Balancing the popularity bias of object similarities for personalised recommendation

Network-based similarity measures have found wide applications in recommendation algorithms and made significant contributions for uncovering users’ potential interests. However, existing measures are generally biased in terms of popularity, that the popular objects tend to have more common neighbours with others and thus are considered more similar to others. Such popularity bias of similarity quantification will result in the biased recommendations, with either poor accuracy or poor diversity. Based on the bipartite network modelling of the user-object interactions, this paper firstly calculates the expected number of common neighbours of two objects with given popularities in random networks. A Balanced Common Neighbour similarity index is accordingly developed by removing the random-driven common neighbours, estimated as the expected number, from the total number. Recommendation experiments in three data sets show that balancing the popularity bias in a certain degree can significantly improve the recommendations’ accuracy and diversity simultaneously.

On K 1,3-free strictly Deza graphs

A graph on v vertices is called a Deza graph with parameters (v, k, b, a) if it is k-regular and the number of common neighbors of two distinct vertices takes on one of two values. We describe strictly Deza graphs that do not contain K 1,3 among their induced subgraphs and are unions of closed neighborhoods of two nonadjacent vertices. The latter condition means that there are two nonadjacent vertices such that any other vertex is adjacent to at least one of the them.

Framework to identify protein complexes based on similarity preclustering

Proteins interact with each other to form protein complexes, and cell functionality depends on both protein interactions and these complexes. Based on the assumption that protein complexes are highly connected and correspond to the dense regions in Protein-protein Interaction Networks (PINs), many methods have been proposed to identify the dense regions in PINs. Because protein complexes may be formed by proteins with similar properties, such as topological and functional properties, in this paper, we propose a protein complex identification framework (KCluster). In KCluster, a PIN is divided into K subnetworks using a K-means algorithm, and each subnetwork comprises proteins of similar degrees. We adopt a strategy based on the expected number of common neighbors to detect the protein complexes in each subnetwork. Moreover, we identify the protein complexes spanning two subnetworks by combining closely linked protein complexes from different subnetworks. Finally, we refine the predicted protein complexes using protein subcellular localization information. We apply KCluster and nine existing methods to identify protein complexes from a highly reliable yeast PIN. The results show that KCluster achieves higher Sn and Sp values and f-measures than other nine methods. Furthermore, the number of perfect matches predicted by KCluster is significantly higher than that of other nine methods.

The role of direct links for link prediction in evolving networks

Link prediction is the problem of predicting the existence and location of unknown links from uncertain structural information of a network. Most existing accuracy measures do not consider the role of time evolution within the network. Moreover, almost all existing methods use indirect links to infer and evaluate the validity of links. We introduce time as a parameter for link prediction accuracy measures, and we modify the structure of the link prediction algorithms to exploit information of the known direct links for link prediction. We find that the direct link algorithm performs better than the indirect link algorithm for a range of time varying networks. We show that the network structure plays a more important role than weights for links prediction. In addition, our analysis finds that the number of common neighbours also plays an important role for the so-called weak-ties phenomenon.

Prediction of protein-protein interaction network using a multi-objective optimization approach.

Protein-Protein Interactions (PPIs) are very important as they coordinate almost all cellular processes. This paper attempts to formulate PPI prediction problem in a multi-objective optimization framework. The scoring functions for the trial solution deal with simultaneous maximization of functional similarity, strength of the domain interaction profiles, and the number of common neighbors of the proteins predicted to be interacting. The above optimization problem is solved using the proposed Firefly Algorithm with Nondominated Sorting. Experiments undertaken reveal that the proposed PPI prediction technique outperforms existing methods, including gene ontology-based Relative Specific Similarity, multi-domain-based Domain Cohesion Coupling method, domain-based Random Decision Forest method, Bagging with REP Tree, and evolutionary/swarm algorithm-based approaches, with respect to sensitivity, specificity, and F1 score.

Sinkhole Attack Detection Scheme using Neighbors’ Information for LEAP based Wireless Sensor Networks

Intrinsic resource constraints and vulnerability to a variety of malicious attacks hinders the widespread deployment of wireless sensor networks (WSNs). One of the malicious attacks is the so-called sinkhole attack where one or more compromised nodes, pretending to be closer to the base station, disseminates a false advertisement. The event reporting nodes start forwarding their reports to these compromised nodes. These compromised nodes can take control of the network traffic, eavesdrop on real communication, and forge reports that are then forwarded to the base-station. In the localized encryption and authentication protocol (LEAP) key management protocol, compromised nodes can expose the keys to the adversary. Therefore, it is crucial to detect and evict compromised nodes instead of using a key sharing approach. In this paper, a fuzzy logic system-based method to detect the compromised nodes and to prevent sinkhole attacks is proposed. Proposed method use neighbor information (i.e., number of common neighbors and their parent node information) to detect compromised nodes. Experimental results demonstrate the validity of the proposed approach in that it provides maintained safeguards and reduces communication cost.

Link prediction with node clustering coefficient

Predicting missing links in incomplete complex networks efficiently and accurately is still a challenging problem. The recently proposed Cannistrai–Alanis–Ravai (CAR) index shows the power of local link/triangle information in improving link-prediction accuracy. Inspired by the idea of employing local link/triangle information, we propose a new similarity index with more local structure information. In our method, local link/triangle structure information can be conveyed by clustering coefficient of common-neighbors directly. The reason why clustering coefficient has good effectiveness in estimating the contribution of a common-neighbor is that it employs links existing between neighbors of a common-neighbor and these links have the same structural position with the candidate link to this common-neighbor. In our experiments, three estimators: precision, AUP and AUC are used to evaluate the accuracy of link prediction algorithms. Experimental results on ten tested networks drawn from various fields show that our new index is more effective in predicting missing links than CAR index, especially for networks with low correlation between number of common-neighbors and number of links between common-neighbors.