Revealing the predictability of intrinsic structure in complex networks

Effects of positive and negative social reinforcement on coupling of information and epidemic in multilayer networks

The spread of epidemics is often accompanied by the spread of epidemic-related information, and the two processes are interdependent and interactive. A social reinforcement effect frequently emerges during the transmission of both the epidemic and information. While prior studies have primarily examined the role of positive social reinforcement in this process, the influence of negative social reinforcement has largely been neglected. In this paper, we incorporate both positive and negative social reinforcement effects and establish a two-layer dynamical model to investigate the interactive coupling mechanism of information and epidemic transmission. The Heaviside step function is utilized to describe the influence mechanism of positive and negative social reinforcements in the actual transmission process. A microscopic Markov chain approach is used to describe the dynamic evolution process, and the epidemic outbreak threshold is derived. Extensive Monte Carlo numerical simulations demonstrate that while positive social reinforcement alters the outbreak threshold of both information and epidemic and promotes their spread, negative social reinforcement does not change the outbreak threshold but significantly impedes the transmission of both. In addition, publishing more accurate information through official channels, intensifying quarantine measures, promoting vaccines and treatments for outbreaks, and enhancing physical immunity can also help contain epidemics.

Link prediction of heterogeneous complex networks based on an improved embedding learning algorithm

Link prediction in heterogeneous networks is an active research topic in the field of complex network science. Recognizing the limitations of existing methods, which often overlook the varying contributions of different local structures within these networks, this study introduces a novel algorithm named SW-Metapath2vec. This algorithm enhances the embedding learning process by assigning weights to meta-path traces generated through random walks and translates the potential connections between nodes into the cosine similarity of embedded vectors. The study was conducted using multiple real-world and synthetic datasets to validate the proposed algorithm's performance. The results indicate that SW-Metapath2vec significantly outperforms benchmark algorithms. Notably, the algorithm maintains high predictive performance even when a substantial proportion of network nodes are removed, demonstrating its resilience and potential for practical application in analyzing large-scale heterogeneous networks. These findings contribute to the advancement of link prediction techniques and offer valuable insights and tools for related research areas.

The Ihara zeta function as a partition function for network structure characterisation

Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics. However, these two representations are usually regarded as separate tools for network analysis, without exploiting the potential synergies between them. In this paper, we establish a link between the Ihara Zeta function from algebraic graph theory and the partition function from statistical mechanics, and exploit this relationship to obtain a deeper structural characterisation of network structure. Specifically, the relationship allows us to explore the connection between the microscopic structure and the macroscopic characterisation of a network. We derive thermodynamic quantities describing the network, such as entropy, and show how these are related to the frequencies of prime cycles of various lengths. In particular, the n-th order partial derivative of the Ihara Zeta function can be used to compute the number of prime cycles in a network, which in turn is related to the partition function of Bose-Einstein statistics. The corresponding derived entropy allows us to explore a phase transition in the network structure with critical points at high and low-temperature limits. Numerical experiments and empirical data are presented to evaluate the qualitative and quantitative performance of the resulting structural network characterisations.

Deep-learning reconstruction of complex dynamical networks from incomplete data

Reconstructing complex networks and predicting the dynamics are particularly challenging in real-world applications because the available information and data are incomplete. We develop a unified collaborative deep-learning framework consisting of three modules: network inference, state estimation, and dynamical learning. The complete network structure is first inferred and the states of the unobserved nodes are estimated, based on which the dynamical learning module is activated to determine the dynamical evolution rules. An alternating parameter updating strategy is deployed to improve the inference and prediction accuracy. Our framework outperforms baseline methods for synthetic and empirical networks hosting a variety of dynamical processes. A reciprocity emerges between network inference and dynamical prediction: better inference of network structure improves the accuracy of dynamical prediction, and vice versa. We demonstrate the superior performance of our framework on an influenza dataset consisting of 37 US States and a PM2.5 dataset covering 184 cities in China.

The maximum capability of a topological feature in link prediction

Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound applications in biological, social, and other complex systems. Despite intensive utilization of the topological feature in this task, it is unclear to what extent a feature can be leveraged to infer missing links. Here, we aim to unveil the capability of a topological feature in link prediction by identifying its prediction performance upper bound. We introduce a theoretical framework that is compatible with different indexes to gauge the feature, different prediction approaches to utilize the feature, and different metrics to quantify the prediction performance. The maximum capability of a topological feature follows a simple yet theoretically validated expression, which only depends on the extent to which the feature is held in missing and nonexistent links. Because a family of indexes based on the same feature shares the same upper bound, the potential of all others can be estimated from one single index. Furthermore, a feature's capability is lifted in the supervised prediction, which can be mathematically quantified, allowing us to estimate the benefit of applying machine learning algorithms. The universality of the pattern uncovered is empirically verified by 550 structurally diverse networks. The findings have applications in feature and method selection, and shed light on network characteristics that make a topological feature effective in link prediction.

Machine learning prediction of academic collaboration networks

We investigate the different roles played by nodes' network and non-network attributes in explaining the formation of European university collaborations from 2011 to 2016, in three European Research Council (ERC) domains: Social Sciences and Humanities (SSH), Physical and Engineering Sciences (PE), Life Sciences (LS), as well as multidisciplinary collaborations. On link formation in collaboration networks, existing research has not yet compared and simultaneously examined both network and non-network attributes. Using four machine learning predictive algorithms (LASSO, Neural Network, Gradient Boosting, and Random Forest) our results show that, over various model specifications: (i) best model link formation accuracy is larger than 80%, (ii) among the non-network attributes, public funding plays an important role in PE and LS, (iii) network attributes count more than non-network attributes for the formation, sensibly increasing accuracy, (iv) feature-importance scores show a different ordering in the four domains, thus signalling different modes of knowledge production and transmission taking place within these different scientific communities.

A converging reputation ranking iteration method via the eigenvector

Ranking user reputation and object quality in online rating systems is of great significance for the construction of reputation systems. In this paper we put forward an iterative algorithm for ranking reputation and quality in terms of eigenvector, named EigenRank algorithm, where the user reputation and object quality interact and the user reputation converges to the eigenvector associated to the greatest eigenvalue of a certain matrix. In addition, we prove the convergence of EigenRank algorithm, and analyse the speed of convergence. Meanwhile, the experimental results for the synthetic networks show that the AUC values and Kendall’s τ of the EigenRank algorithm are greater than the ones from the IBeta method and Vote Aggregation method with different proportions of random/malicious ratings. The results for the empirical networks show that the EigenRank algorithm performs better in accuracy and robustness compared to the IBeta method and Vote Aggregation method in the random and malicious rating attack cases. This work provides an expectable ranking algorithm for the online user reputation identification.

Progresses and challenges in link prediction

Link prediction is a paradigmatic problem in network science, which aims at estimating the existence likelihoods of nonobserved links, based on known topology. After a brief introduction of the standard problem and evaluation metrics of link prediction, this review will summarize representative progresses about local similarity indices, link predictability, network embedding, matrix completion, ensemble learning, and some others, mainly extracted from related publications in the last decade. Finally, this review will outline some long-standing challenges for future studies.