Links In Complex Networks Research Articles

Beyond bond links in complex networks:Local bridges, global bridges and silk links

Many network researchers use intuitive or basic definitions when discussing the importance of strong and weak links and their roles. Others use an approach best described as “if not strong, then weak” to determine the strengths and weaknesses of individual links, thus deemphasizing hierarchical network structures that allow links to express different strength levels. Here we describe our proposal for a hierarchical edge type analysis (HETA) algorithm for determining link types at multiple network hierarchy levels based on the common neighbor concept plus statistical factors such as bond links, kth-layer local bridges, global bridges, and silk links—all generated during long-term network development and evolution processes. Two sets of networks were used to validate our proposed algorithm, one consisting of 16 networks employed in multiple past studies, and one consisting of two types of one-dimensional small-world networks expressing different random rewiring or shortcut addition probabilities. Two applications with potential for developmental contributions are demonstrated: a network fingerprint analysis framework, and a hierarchical network community partition method.

Link prediction based on linear dynamical response

Link prediction has attracted increasing research attention recently, which aims to predict missing links in complex networks. However, the existing link prediction methods are primarily based on network structures alone, which are incapable of capturing the dynamics defined on top of the fixed network structures. In this paper, we introduce a linear dynamical response-based similarity measure between nodes into link prediction task. To address the efficiency problem, we design a new iterative procedure to avoid the explicit computation of linear dynamical response (LDR) index. Empirically, we conduct extensive experiments on real networks from various fields. The results show that LDR index leads to promising predicting performance for link prediction.

Predicting Citation Count of Scientists as a Link Prediction Problem.

The studies dealing with the problem of predicting scientific impacts in the scientific world mostly focus on predicting citation count of papers (PCCP). However, in the literature, only a little bit of research has been conducted on estimating the future influence of scientists individually. Estimating the impact of scientists individually is a worthwhile task for the following scientific research and cooperatives. From this point of view, a new supervised link prediction method is proposed to predict the citation count of scientists (PCCS). Many PCCP studies employ document-based attributes, such as titles, abstracts, and keywords of papers; institutions of scientists; impact factors of publishers; etc. and they do not take advantage of any topological features of complex networks formed with citations among papers. However, citation networks include valuable features for PCCP and PCCS. Therefore, we formulate the problem of PCCS as a link prediction problem in directed, weighted, and temporal citation networks. The proposed approach predicts not only links but also its weights. Our supervised link prediction method is tested on two citation networks in Experiment 1. The results of Experiment 1 confirm that our method achieves promising performances when considering prediction links with its weights are addressed for the first time in terms of link prediction in directed, weighted, and temporal networks. In Experiment 2, the performance of the proposed link prediction metric and five well-known link prediction metrics are compared in terms of prediction new links in complex networks. The results of Experiment 2 demonstrate that the proposed link prediction metric outperforms all baseline link prediction metrics.

A local random walk model for complex networks based on discriminative feature combinations

Networks have become increasingly important to model many complex systems. This powerful representation has been employed in different tasks of artificial intelligence including machine learning, expert and intelligent systems. Link prediction, a branch of network pattern recognition, is the most fundamental and essential problem for complex network analysis. However, most existing link-prediction methods only consider a network’s topology structures, and in doing so, these methods miss the opportunity to use nodes’ attribute information. We present a combined approach here that uses nodes’ attribute information and topology structure to direct link prediction. First, we propose a discriminative feature combinations selection method. Specifically, we present a novel mathematics inference to detail discriminative feature combinations. Second, based on the selected feature combinations, we aggregate the network, and further compute each feature combination’s contributing degree to the link’s formation, called the strength of feature combination. Third, we apply discriminative feature combinations into a local random walk model; in particular, we compute and redistribute the random walk particle’s transfer probability in terms of each feature combination’s strength, which makes the transfer probability depend on feature combinations satisfied by each node’s edges. Finally, we predict links in complex networks based on the improved random walk model. Experimental results on real-life complex network datasets demonstrate that, compared to other baseline methods, using discriminative feature combinations and topology structures in tandem strengthens prediction performance remarkably.

Extended resource allocation index for link prediction of complex network

Recently, a number of similarity-based methods have been proposed to predict the missing links in complex network. Among these indices, the resource allocation index performs very well with lower time complexity. However, it ignores potential resources transferred by local paths between two endpoints. Motivated by the resource exchange taking places between endpoints, an extended resource allocation index is proposed. Empirical study on twelve real networks and three synthetic dynamic networks has shown that the index we proposed can achieve a good performance, compared with eight mainstream baselines.

Predicting missing links in complex networks based on common neighbors and distance.

The algorithms based on common neighbors metric to predict missing links in complex networks are very popular, but most of these algorithms do not account for missing links between nodes with no common neighbors. It is not accurate enough to reconstruct networks by using these methods in some cases especially when between nodes have less common neighbors. We proposed in this paper a new algorithm based on common neighbors and distance to improve accuracy of link prediction. Our proposed algorithm makes remarkable effect in predicting the missing links between nodes with no common neighbors and performs better than most existing currently used methods for a variety of real-world networks without increasing complexity.

Cascade of links in complex networks

Cascading failure is an important process which has been widely used to model catastrophic events such as blackouts and financial crisis in real systems. However, so far most of the studies in the literature focus on the cascading process on nodes, leaving the possibility of link cascade overlooked. In many real cases, the catastrophic events are actually formed by the successive disappearance of links. Examples exist in the financial systems where the firms and banks (i.e. nodes) still exist but many financial trades (i.e. links) are gone during the crisis, and the air transportation systems where the airports (i.e. nodes) are still functional but many airlines (i.e. links) stop operating during bad weather. In this letter, we develop a link cascade model in complex networks. With this model, we find that both artificial and real networks tend to collapse even if a few links are initially attacked. However, the link cascading process can be effectively terminated by setting a few strong nodes in the network which do not respond to any link reduction. Finally, a simulated annealing algorithm is used to optimize the location of these strong nodes, which significantly improves the robustness of the networks against the link cascade.

Prediction of missing links and reconstruction of complex networks

Predicting missing links in complex networks is of great significance from both theoretical and practical point of view, which not only helps us understand the evolution of real systems but also relates to many applications in social, biological and online systems. In this paper, we study the features of different simple link prediction methods, revealing that they may lead to the distortion of networks’ structural and dynamical properties. Moreover, we find that high prediction accuracy is not definitely corresponding to a high performance in preserving the network properties when using link prediction methods to reconstruct networks. Our work highlights the importance of considering the feedback effect of the link prediction methods on network properties when designing the algorithms.

English

English

“Conjectural” links in complex networks

This paper introduces the concept of Conjectural Link for Complex Networks, in particular, social networks. Conjectural Link we understand as an implicit link, not available in the network, but supposed to be present, based on the characteristics of its topology. It is possible, for example, when in the formal description of the network some connections are skipped due to errors, deliberately hidden or withdrawn (e.g. in the case of partial destruction of the network). Introduced a parameter that allows ranking the Conjectural Link. The more this parameter - the more likely that this connection should be present in the network. This paper presents a method of recovery of partially destroyed Complex Networks using Conjectural Links finding. Presented two methods of finding the node pairs that are not linked directly to one another, but have a great possibility of Conjectural Link communication among themselves: a method based on the determination of the resistance between two nodes, and method based on the computation of the lengths of routes between two nodes. Several examples of real networks are reviewed and performed a comparison to know network links prediction methods, not intended to find the missing links in already formed networks.

The Future of Weak Ties

The Future of Weak Ties

Weighting links based on edge centrality for community detection

Link weights have the equally important position as links in complex networks, and they are closely associated with each other for the emergence of communities. How to assign link weights to make a clear distinction between internal links of communities and external links connecting communities is of vital importance for community detection. Edge centralities provide a powerful approach for distinguishing internal links from external ones. Here, we first use edge centralities such as betweenness, information centrality and edge clustering coefficient to weight links of networks respectively to transform unweighted networks into weighted ones, and then a weighted function that both considers links and link weights is adopted on the weighted networks for community detection. We evaluate the performance of our approach on random networks as well as real-world networks. Better results are achieved on weighted networks with stronger weights of internal links of communities, and the results on unweighted networks outperform that of weighted networks with weaker weights of internal links of communities. The availability of our findings is also well-supported by the study of Granovetter that the weak links maintain the global integrity of the network while the strong links maintain the communities. Especially in the Karate club network, all the nodes are correctly classified when we weight links by edge betweenness. The results also give us a more comprehensive understanding on the correlation between links and link weights for community detection.

Correlations between Community Structure and Link Formation in Complex Networks

BackgroundLinks in complex networks commonly represent specific ties between pairs of nodes, such as protein-protein interactions in biological networks or friendships in social networks. However, understanding the mechanism of link formation in complex networks is a long standing challenge for network analysis and data mining.Methodology/Principal FindingsLinks in complex networks have a tendency to cluster locally and form so-called communities. This widely existed phenomenon reflects some underlying mechanism of link formation. To study the correlations between community structure and link formation, we present a general computational framework including a theory for network partitioning and link probability estimation. Our approach enables us to accurately identify missing links in partially observed networks in an efficient way. The links having high connection likelihoods in the communities reveal that links are formed preferentially to create cliques and accordingly promote the clustering level of the communities. The experimental results verify that such a mechanism can be well captured by our approach.Conclusions/SignificanceOur findings provide a new insight into understanding how links are created in the communities. The computational framework opens a wide range of possibilities to develop new approaches and applications, such as community detection and missing link prediction.

Complexity, Networks, and Non-Uniqueness

The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial—and often problematic—presumption that underlies the network approach to complex systems. Network scientists often talk of “the structure” of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I argue that this sort of naive realism about structure is not a coherent or plausible position, especially given the multiplicity of types of entities and relations that can feature as nodes and links in complex networks.

The organization of strong links in complex networks.

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods; we relate this to global robustness of the clustering to removal of the weakest links. Furthermore, we identify local learning rules that establish integrative networks and improve network traffic in response to past traffic failures. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

Removing spurious interactions in complex networks

Identifying and removing spurious links in complex networks is meaningful for many real applications and is crucial for improving the reliability of network data, which, in turn, can lead to a better understanding of the highly interconnected nature of various social, biological, and communication systems. In this paper, we study the features of different simple spurious link elimination methods, revealing that they may lead to the distortion of networks' structural and dynamical properties. Accordingly, we propose a hybrid method that combines similarity-based index and edge-betweenness centrality. We show that our method can effectively eliminate the spurious interactions while leaving the network connected and preserving the network's functionalities.

Robust classification of salient links in complex networks

Complex networks in natural, social and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods and concepts have been proposed to address this problem such as centrality statistics, motifs, community clusters and backbones, but such schemes typically rely on external and arbitrary parameters. It is unknown whether generic networks permit the classification of elements without external intervention. Here we show that link salience is a robust approach to classifying network elements based on a consensus estimate of all nodes. A wide range of empirical networks exhibit a natural, network-implicit classification of links into qualitatively distinct groups, and the salient skeletons have generic statistical properties. Salience also predicts essential features of contagion phenomena on networks, and points towards a better understanding of universal features in empirical networks that are masked by their complexity.

Wave Localization in Complex Networks with High Clustering

We show that strong clustering of links in complex networks, i.e., a high probability of triadic closure, can induce a localization-delocalization quantum phase transition (Anderson-like transition) of coherent excitations. For example, the propagation of light wave packets between two distant nodes of an optical network (composed of fibers and beam splitters) will be absent if the fraction of closed triangles exceeds a certain threshold. We suggest that such an experiment is feasible with current optics technology. We determine the corresponding phase diagram as a function of clustering coefficient and disorder for scale-free networks of different degree distributions P(k) approximately k;{-lambda}. Without disorder, we observe no phase transition for lambda<4, a quantum transition for lambda>4, and an additional distinct classical transition for lambda>4.5. Disorder reduces the critical clustering coefficient such that phase transitions occur for smaller lambda.

Geographical constraints to range-based attacks on links in complex networks

In this paper, we studied range-based attacks on links in geographically constrained scale-free networks and found that there is a continuous switching of roles of short- and long-range attacks on links when tuning the geographical constraint strength. Our results demonstrate that the geography has a significant impact on the network efficiency and security; thus one can adjust the geographical structure to optimize the robustness and the efficiency of the networks. We introduce a measurement of the impact of links on the efficiency of the network, and an effective attacking strategy is suggested.

Characterization of weighted complex networks.

To account for possible distinct functional roles played by different nodes and links in complex networks, we introduce and analyze a class of weighted scale-free networks. The weight of a node is assigned as a random number, based on which the weights of links are defined. We utilize the concept of betweenness to characterize the weighted networks and obtain the scaling laws governing the betweenness as functions both of the weight and of the degree. The scaling results may be useful for identifying influential nodes in terms of physical functions in complex networks.