Modeling the Local and Global Evolution Pattern of Community Structures for Dynamic Networks Analysis

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Modeling the dynamics of online social networks over time not only helps us understand the evolution of structures and user behaviors, but also improves the performance of other analysis tasks, such as link prediction and community detection. Nowadays, users engage in multiple networks and form a social network by considering common users as the bridge. State-of-the-art network-dynamics analysis is performed in isolation for individual networks, but users' interactions in one can influence their behaviors in other networks, and in an individual network, different types of user interactions also affect each other. Without considering the influences across networks, one may not be able to model the dynamics in a given correctly due to the lack of information. In this paper, we study the problem of modeling the dynamics of composite networks, where the evolution processes of different networks are jointly considered. However, due to the difference in properties, simply merging multiple networks into a single one is not ideal because individual evolution patterns may be ignored and differences may bring negative impacts. The proposed solution is a nonparametric Bayesian model, which models each user's common latent features to extract the cross-network influences, and use network-specific factors to describe different networks' evolution patterns. Empirical studies on large-scale dynamic composite social networks demonstrate that the proposed approach improves the performance of link prediction over several state-of-the-art baselines and unfolds the evolution accurately.

In network neuroscience, temporal network models have gained popularity. In these models, network properties have been related to cognition and behavior. Here, we demonstrate that calculating nodal properties that are dependent on temporal community structure (such as the participation coefficient [PC]) in time‐varying contexts can potentially lead to misleading results. Specifically, with regards to the participation coefficient, increases in integration can be inferred when the opposite is occurring. Further, we present a temporal extension to the PC measure (temporal PC) that circumnavigates this problem by jointly considering all community partitions assigned to a node through time. The proposed method allows us to track a node's integration through time while adjusting for the possible changes in the community structure of the overall network.

As dynamic systems, social networks exhibit continuous topological changes over time, and are typically modeled as temporal networks. In order to understand their dynamic characteristics, it is essential to investigate temporal community detection (TCD), which poses significant challenges compared to static network analysis. These challenges arise from the need to simultaneously detect community structures and track their evolutionary behaviors. To address these issues, we propose TCDA-NE, a novel TCD algorithm that combines evolutionary clustering with convex non-negative matrix factorization (Convex-NMF). Our method innovatively integrates community structure into network embedding, preserving both microscopic details and community-level information in node representations while effectively capturing the evolutionary dynamics of networks. A distinctive feature of TCDA-NE is its utilization of a common-neighbor similarity matrix, which significantly enhances the algorithm’s ability to identify meaningful community structures in temporal networks. By establishing coherent relationships between node representations and community structures, we optimize both the Convex-NMF-based representation learning model and the evolutionary clustering-based TCD model within a unified framework. We derive the updating rules and provide rigorous theoretical proofs for the algorithm’s validity and convergence. Extensive experiments on synthetic and real-world social networks, including email and phone call networks, demonstrate the superior performance of our model in community detection and tracking temporal network evolution. Notably, TCDA-NE achieves a maximum improvement of up to 0.1 in the normalized mutual information (NMI) index compared to state-of-the-art methods, highlighting its effectiveness in temporal community detection.

In real-world complex networks, understanding the dynamics of their evolution has been of great interest to the scientific community. Predicting non-existent but probable links is an essential task of social network analysis as the addition or removal of the links over time leads to the network evolution. In a network, links can be categorized as intra-community links if both end nodes of the link belong to the same community, otherwise inter-community links. The existing link-prediction methods have mainly focused on achieving high accuracy for intra-community link prediction. In this work, we propose a network embedding method, called NodeSim, which captures both similarities between the nodes and the community structure while learning the low-dimensional representation of the network. The embedding is learned using the proposed NodeSim random walk, which efficiently explores the diverse neighborhood while keeping the more similar nodes closer in the context of the node. We verify the efficacy of the proposed embedding method over state-of-the-art methods using diverse link prediction. We propose a machine learning model for link prediction that considers both the nodes’ embedding and their community information to predict the link between two given nodes. Extensive experimental results on several real-world networks demonstrate the effectiveness of the proposed method for both inter and intra-community link prediction.

The link prediction problem is a time-evolving model in network science that has simultaneously abetted myriad applications and experienced extensive methodological improvement. Inferring the possibility of emerging links in dynamic social networks, also known as the dynamic link prediction task, is complex and challenging. In contrast to the link prediction in cross-sectional networks, dynamic link prediction methods need to cater to the actor-level temporal changes and associated evolutionary information regarding their micro- (i.e., link formation/deletion) and mesoscale (i.e., community formation) network structure. With the advent of abundant community detection algorithms, the research community has examined community-aware link prediction strategies in static networks. However, the same task in dynamic networks where, apart from the actors and links among them, their community pattern is also dynamic, is yet to be explored. Evolutionary community-aware information, including the associated link structure and temporal neighborhood changes, can effectively be mined to build dynamic similarity metrics for dynamic link prediction. This study aims to develop and integrate such dynamic features with machine learning algorithms for link prediction tasks in dynamic social networks. It also compares the performances of these features against well-known similarity metrics (i.e., ResourceAllocation) for static networks and a time series-based link prediction strategy in dynamic networks. These proposed features achieved high-performance scores, representing them as prospective candidates for both dynamic link prediction tasks and modeling the network growth.

Community structure is an important feature of complex networks. These community structures have the fractal characteristics, that is, there is a self similarity of statistical sense between the complex networks and their local. There have been more and more recent researches on communities’ discovery in complex network. However, most existing approaches require the complete information of entire network, which is impractical for some networks, e.g. the dynamical network and the network that is too large to get the whole information. Therefore, the study of community discovery in complex networks has rather important theoretical and practical value. Through the analysis and study of the complex network evolution models with renormalization and the community change of the complex network evolution, using the tool of adjusting scales as the renormalization process, a multi-scale network community detection algorithm based on fractal feature evolution was proposed. The purpose is to solve community discovery problems in dynamic complex networks, and the effectiveness of the proposed method is verified by real data sets. By comparing result of this paper with the previous methods on some real world networks, and experimental results verify the feasibility and accuracy.

Inductive link prediction on temporal networks through causal inference

Link prediction of time-evolving network based on node ranking

Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream applications such as link prediction and anomaly detection, it is essential for such networks to be transferred into a low dimensional space. Recently, network embedding, a technique that converts a large graph into a low-dimensional representation, has become increasingly popular due to its strength in preserving the structure of a network. Efficient dynamic network embedding, however, has not yet been fully explored. In this paper, we present a dynamic network embedding method that integrates the history of nodes over time into the current state of nodes. The key contribution of our work is 1) generating dynamic network embedding by combining both dynamic and static node information 2) tracking history of neighbors of nodes using LSTM 3) significantly decreasing the time and memory by training an autoencoder LSTM model using temporal walks rather than adjacency matrices of graphs which are the common practice. We evaluate our method in multiple applications such as anomaly detection, link prediction and node classification in datasets from various domains.

Lack of temporal structure in the short term HIV-1 evolution within asymptomatic naïve patients

Dynamic network link prediction is a hot research problem in complex networks. Network representation learning can effectively learn the similarity of nodes and can be used for link prediction. Existing dynamic network representation learning methods mainly discrete window dynamic networks and then model them on static network snapshot graphs, which is difficult to effectively deal with dynamic networks with fine-grained temporal characteristics. In this paper, we propose a link prediction model that can learn complex temporal properties in dynamic networks. The model uses continuous time event sequences to represent dynamic networks, learns continuous temporal information and structural evolution features in the networks, and proposes a temporal attention-based information transfer mechanism to model the diffusion and aggregation of information in the networks. Finally, it transforms link prediction into a classification problem. The experiments are conducted on four real dynamic network datasets and simulated networks, using ap and auc as evaluation metrics. The experimental results of real networks demonstrate that the model can effectively learn the continuity of network evolution and obtain an effective node representation, thus improving the link prediction effect. The experimental results of the simulated network show that the effect of link prediction is related to the network model, but the model in this paper can still obtain better prediction results.

With the ubiquity of complex networks in domains as diverse as social network analysis, recommender systems and epidemiology, improvements in link predictions have a potential for far-reaching impact. In machine learning, a well-known approach to improve classification performance is to combine several methods in an ensemble. It is also well established that, diversity or complementarity of the classifiers to be combined, is a prerequisite for a potential performance improvement of the formed ensemble. In this work, we combine link prediction heuristics (e.g. Common Neighbour, Adamic-Adar etc.), with static graph neural networks, discrete dynamic graph neural networks, and continuous dynamic graph neural networks. We analyze the importance of each of the methods and how complementary they are with respect to each other. We also use greedy searches to select better subsets of methods to combine and train the ensemble in a roll-forward manner to make it adapt to changes in the dynamic network over time. In the conducted experiments on a number of challenging link prediction tasks, the ensemble from the greedy search and the roll-forward ensemble shows on average a 55% and 61% improvement respectively, over the best single method.

Link prediction aims to find the missing link in current networks or estimate the likelihood the link will appear in the future. In many real-world scenarios, networks can be massive and drastically evolving. Many recent works concentrated on how to solve the procession of massive data, which cares less about the effects of the temporal information. In some dynamic networks, the edge that appears a long time ago will have fewer effects on the appearance of edges in the future. The accuracy of link prediction in dynamic networks can be further improved by adding temporal information in prediction measures. In this paper, we mainly explore the effects of the link temporal information in the graph stream link prediction. We design a graph stream-based framework to solve link prediction problems in dynamic networks which can provide a convenient platform to implement different link prediction methods for dynamic networks, and evaluate these methods on a fair basis. Then, we proposed the Time Decay-based Link Prediction (TDLP) method to improve the efficient of link prediction problem in the dynamic networks. TDLP extends the neighborhood-based measure with time decay functions in graph stream scenarios which can handle temporal information and massive data. Experiment results demonstrate that the accuracy of link prediction for dynamic networks can be efficiently improved in our TDLP method.

Background Autism spectrum disorder (ASD) is characterized by aberrant functional brain connectivity and deficits in network dynamics. Transcranial direct current stimulation (tDCS) has emerged as a promising intervention with potential therapeutic effects; however, its effects on both static and dynamic functional brain network organization remained insufficiently understood. Methods A total of 42 children with ASD aged 4–6 years were enrolled and randomly assigned to either active tDCS or sham stimulation groups. Resting-state electroencephalography (EEG) data were acquired before and after the intervention. Low-order functional connectivity (LOFC) and high-order functional connectivity (HOFC) networks were constructed, followed by graph-theoretical analyses to assess clustering coefficient, characteristic path length, global efficiency, and local efficiency. Furthermore, state entropy was employed to evaluate dynamic network transitions between integrated and segregated states. Results Active tDCS was associated with increased LOFC strength in the delta, alpha, and beta bands, and more widespread increases in HOFC across all examined frequency bands. Changes in network topology were primarily observed in HOFC, with reductions in characteristic path length and increases in global and local efficiency, particularly in the delta and theta bands. Dynamic network analysis indicated that tDCS modulated state entropy at specific time scales in both LOFC and HOFC networks. These findings suggest shifts in functional coordination and temporal variability among the recorded regions. Behavioral measures exhibited a trend toward improvement in the active group; however, these changes were not the focus of the present analysis, and their relationship to neural modulation remains to be clarified in future work. Conclusions tDCS modulated functional interaction patterns and dynamic state characteristics among the recorded brain regions in children with ASD. These results provide preliminary neurophysiological evidence regarding the influence of tDCS on both static and dynamic network organization and highlight potential network-based markers to guide future individualized neuromodulation research. Further studies with larger samples and longitudinal follow-ups are needed to clarify the functional and clinical significance of these network-level changes.