Node Degree Distribution Research Articles

Hiding secret messages in large-scale graphs

Digital steganography is an information hiding technique that conceals secret messages within cover data. While image and audio data have traditionally been the primary focus, graph datasets have recently gained attention for steganographic purposes. To explore the feasibility and characteristics of graph datasets in steganography, we develop two algorithms, BIND and BYNIS, for real-world and synthetic graphs. BIND encodes two bits of a message into node degrees, whereas BYNIS synthesizes the edges of a stego graph from a message. We introduce the concepts of the payload unit ‘bpe (bits per edge)’ and ‘ELBPC (estimated lower bound of the payload capacity)’ to analyze the payload capacity of BIND. Through Monte Carlo experiments on random and real-world graphs, we demonstrate that BIND is sensitive to edge type imbalance, particularly in smaller graphs, as shown by experiments on the Open Graph Benchmark and Netzschleuder datasets. In contrast, BYNIS is not limited by edge type imbalance, as it synthesizes the graph structure. In the graph synthesis experiments, BYNIS could generate graphs with either a power-law or binomial distribution of node degrees, depending on the edge addition policy. To overcome BIND’s limitations on smaller graphs, we also develop AdaBIND, which supplements the necessary edges with synthetic edges for BIND. Additionally, we explore the collaboration between BIND and BYNIS, leveraging BYNIS’s graph synthesis capability to complement BIND’s encoding process and ensure robust performance.

Feature analysis of 5G traffic data based on visibility graph

IntroductionAs 5G networks become widespread and their application scenarios expand, massive amounts of traffic data are continuously generated. Properly analyzing this data is crucial for enhancing 5G services.MethodsThis paper uses the visibility graph method to convert 5G traffic data into a visibility graph network, conducting a feature analysis of the 5G traffic data. Using the AfreecaTV dataset as the research object, this paper constructs visibility networks at different scales and observes the evolution of degree distribution with varying data volumes. The paper employs the Hurst index to evaluate the 5G traffic network and uses community detection to study the networks converted from 5G traffic data of different applications.ResultsExperimental results reveal significant differences in node degree distribution and topological structures of 5G traffic data across different application scenarios, such as star structures and multiple subnetwork structures. It is found that the node degree distribution of 5G traffic networks exhibits heterogeneity, reflecting the uneven growth of node degrees during network expansion. The Hurst index analysis discovers that the 5G traffic network retains the long-term dependence and trends of the original data. Through community detection, it is observed that networks converted from 5G traffic data of different applications exhibit diverse community structures, such as high centrality nodes, star-like community structures, modularity, and multilayer characteristics.DiscussionThese findings indicate that 5G traffic networks in different application scenarios exhibit complex and diverse characteristics. The heterogeneity of node degree distribution and differences in topological structures reflect the imbalance in node connection methods during network expansion. The results of the Hurst index show that the 5G traffic network inherits the long-term dependence of the original data, providing a basis for analyzing the dynamic characteristics of the network. The diverse community structures reveal the inherent modularity and hierarchy of the network, which helps to understand the performance and optimization directions of 5G networks in different applications.

A hierarchical GNN across semantic and topological domains for predicting circRNA-microRNA interactions

Identifying circRNA-microRNA interactions (CMI) is a significant biomedical issue in recent years. This problem provides insights into using circRNA as biomarkers, developing cancer therapies and producing cancer vaccines. Using computational methods for identification is a more time-efficient and cost-effective approach. In computational methods, using graphs to represent and explore the CMI is a mainstream approach. However, existing relevant methods do not achieve optimal results by utilizing both the semantic information extracted from sequences and the topological information extracted from graph structures. To address this issue, we propose HGLMALLM, a graph contrastive learning method that learns node representation crossing both the semantic domain generated via motif-aware pre-trained LLMs and the topological domain extracted from hierarchical graph structures. Our method effectively addresses the issue in existing Message Passing Neural Network (MPNN) method that edge components losing heterogeneity after multiple iterations. Moreover, this method utilizes the heterogeneity of graph which is extended from the traditional bipartite graph to heterogeneous through the semantic domain. Two commonly used datasets were partitioned based on the distribution of node degrees. Then, we benchmarked our method against existing methods. In the independent testing set evaluation, it achieved a 3 % and 1 % improvement on two datasets. Our method demonstrated the best stability in ten-fold cross-validation on the training set. A test conducted on the peripheral components reveals robust performance of our model. A dataset collected from real scenarios was used to demonstrate the strong predictive ability of our method for identifying unidentified CMI.

Properties of the connected components in projections of random bipartite networks: effects of clique size fluctuations

Projection is a helpful description for treating bipartite networks as (monopartite) networks with pairwise interactions. Projections induce correlation spontaneously, avoiding negative degree correlation, even if bipartite networks are entirely random. In this study, we examined the structure of projections of random bipartite networks characterized by the degree distribution of individual and group nodes through the generating function method. We decomposed a projection into two subgraphs, the giant component, and finite components and analyzed their degree correlation. We demonstrate that positive degree correlations in projections originating from the clique size fluctuation remain after the decomposition at the set of finite components, although the values of their clustering coefficient are still finite. The giant component can exhibit either positive or negative degree correlations based on the structure of the projection. However, they are positively correlated in most cases. In addition, we found that a projection removed the giant component coincides with one in the subcritical phase, i.e., the discrete duality relation, when the degree distributions for group and individual are of Poisson.

Cascading failure model and resilience-based sequential recovery strategy for complex networks

Complex networks, which exhibit high connectivity, self-organization, small-world properties, and heterogeneity, are susceptible to the rapid spread of local failures, often resulting in cascading effects throughout the entire system. The paper introduces a cascading failure model based on biased random walks that incorporate betweenness centrality and the power-law distribution of node degrees. This model is used to investigate cascade failures triggered by extreme fluctuations in load that follow a Poisson distribution. Furthermore, we propose a resilience-based sequential recovery strategy that accounts for varying node recovery time and resource limitations, setting an upper limit on the number of nodes that can be in recovery simultaneously. The network’s robustness improves, and the variation in the power-law exponent during cascading failures and recovery decreases when the betweenness bias parameter is set to 1 instead of -1. The capacity parameter has the most significant and direct effect on improving the network’s robustness. Reducing node recovery time can improve the network’s initial invulnerability; however, its impact on final residual resilience remains limited. The power-law exponent of the initial network significantly affects residual resilience during the recovery process, with higher exponents leading to improved network performance. An appropriate increase in the number of nodes that can be in recovery simultaneously can enhance the overall recovery performance of the network. Extensive comparative simulations reveal substantial advantages of our proposed recovery strategy in enhancing network recovery.

Building a network with assortative mixing starting from preference functions, with application to the spread of epidemics

Compartmental models of disease spread have been well studied on networks built according to the Configuration Model, i.e., where the degree distribution of individual nodes is specified, but where connections are made randomly. Dynamics of spread on such “first order” networks were shown to be profoundly different compared to epidemics under the traditional mass action assumption. Assortativity, i.e., the preferential mixing of nodes according to degree, is a second order property that is thought to impact epidemic trajectory. We first show how assortative mixing can come about from individual preferences to connect with others of lower or higher degree, and propose an algorithm for constructing such a network. We then investigate via simulation how this network structure favors or inhibits diffusion processes, such as the spread of an infectious disease.

Enhancing predictive models for illicit activities in the Bitcoin transaction network using advanced graph analytical techniques

The Elliptic dataset compiles a comprehensive history of Bitcoin transactions, integrating both anti-money laundering (AML) tags and distinct graph network features. Given the nature of the Bitcoin transaction networka complex, weakly interconnected structureleveraging graph analysis techniques for its study holds immense potential, especially in the realm of detecting illicit activities like hacking, drug trades, gambling, and more. A detailed examination of the Elliptic dataset, encompassing transaction amounts, frequencies, source and destination addresses, sheds light on the inherent structure and peculiarities of the Bitcoin transaction ecosystem. By conceptualizing this transactional landscape as a graph, a slew of analytical attributes emerge: node degree distribution, community architecture, centrality measures, and so forth. Such attributes pave the way for the creation of predictive models that can pinpoint and prognosticate potential unlawful trade actions. Several computational models have been employed on the Elliptic dataset, such as Logistic Regression (LR), Random Forest (RF), Multilayer Perceptrons (MLP), and Graph Convolutional Networks (GCN). The authors of this particular study delve into augmentations of the GCN model, juxtaposing the efficacy of the original GCN model against their enhanced algorithm within the context of the Elliptic dataset.

Brain-inspired modular echo state network for EEG-based emotion recognition.

Previous studies have successfully applied a lightweight recurrent neural network (RNN) called Echo State Network (ESN) for EEG-based emotion recognition. These studies use intrinsic plasticity (IP) and synaptic plasticity (SP) to tune the hidden reservoir layer of ESN, yet they require extra training procedures and are often computationally complex. Recent neuroscientific research reveals that the brain is modular, consisting of internally dense and externally sparse subnetworks. Furthermore, it has been proved that this modular topology facilitates information processing efficiency in both biological and artificial neural networks (ANNs). Motivated by these findings, we propose Modular Echo State Network (M-ESN), where the hidden layer of ESN is directly initialized to a more efficient modular structure. In this paper, we first describe our novel implementation method, which enables us to find the optimal module numbers, local and global connectivity. Then, the M-ESN is benchmarked on the DEAP dataset. Lastly, we explain why network modularity improves model performance. We demonstrate that modular organization leads to a more diverse distribution of node degrees, which increases network heterogeneity and subsequently improves classification accuracy. On the emotion arousal, valence, and stress/calm classification tasks, our M-ESN outperforms regular ESN by 5.44, 5.90, and 5.42%, respectively, while this difference when comparing with adaptation rules tuned ESNs are 0.77, 5.49, and 0.95%. Notably, our results are obtained using M-ESN with a much smaller reservoir size and simpler training process.

Node-degree aware edge sampling mitigates inflated classification performance in biomedical random walk-based graph representation learning.

Graph representation learning is a family of related approaches that learn low-dimensional vector representations of nodes and other graph elements called embeddings. Embeddings approximate characteristics of the graph and can be used for a variety of machine-learning tasks such as novel edge prediction. For many biomedical applications, partial knowledge exists about positive edges that represent relationships between pairs of entities, but little to no knowledge is available about negative edges that represent the explicit lack of a relationship between two nodes. For this reason, classification procedures are forced to assume that the vast majority of unlabeled edges are negative. Existing approaches to sampling negative edges for training and evaluating classifiers do so by uniformly sampling pairs of nodes. We show here that this sampling strategy typically leads to sets of positive and negative examples with imbalanced node degree distributions. Using representative heterogeneous biomedical knowledge graph and random walk-based graph machine learning, we show that this strategy substantially impacts classification performance. If users of graph machine-learning models apply the models to prioritize examples that are drawn from approximately the same distribution as the positive examples are, then performance of models as estimated in the validation phase may be artificially inflated. We present a degree-aware node sampling approach that mitigates this effect and is simple to implement. Our code and data are publicly available at https://github.com/monarch-initiative/negativeExampleSelection.

Analyzing the diffusion of feminist discourses on Chinese social media: A case study of the 2022 Tangshan restaurant attack.

Network platforms have ushered in a novel propagation model for feminist discourses. The emergence of oriental feminism in society has led to gender-based public opinions surrounding public events becoming a trending topic on Chinese social media. This study uses the 2022 Tangshan restaurant attack as a case study, an incident that sparked widespread discussions across China in 2022. The research gathered 366,602 network communication nodes within a week and examined the communication networks of three types of content nodes (information, opinion, and appeasement) using the complex network modeling method. The findings revealed that all three types of information communication networks exhibit an apparent scale-free characteristic, and the "key minority" of nodes significantly affects information communication. Information-type and appeasement-type Weibo display notable similarities in the quantity and degree distribution of nodes within the communication networks and in the information decay rate. Moreover, authoritative information issuers have become the primary catalyst for information propagation. Conversely, opinion-type Weibo has the widest communication network diameter and features a high degree of participation, multilevel propagation, and a slow decay rate. This indicates that the interaction between opinion leaders and netizens has enhanced the depth and breadth of information diffusion for opinion-type Weibo.

Discovering different acupoint combinations of manual or electro-acupuncture to treat chemotherapy-induced nausea and vomiting based on the complex networks analysis.

The aim of this research was to find the acupoint combinations of manual and electro-acupuncture to treat chemotherapy-induced nausea and vomiting via the complex networks analysis. We conducted searches using PubMed, ScienceDirect, MEDLINE, Ovid, spring, Wiley, EMBASE, the Chinese biomedicine database, VIP information network, and China National Knowledge Infrastructure from the establishment of the databases to the August, 2023. Information about titles, journals, interventions, and main acupoints was extracted using the self-established "acupoint for prevention CINV data base" powered by EpiData. According to the level of literature evidence and sample size, the clinical trials and weights of the outcome indicators including nausea/vomiting efficiency were combined. After identifying articles, literature processing and complex network analysis were conducted. The degree distribution of each node, the probability distribution of node degree, the node clustering coefficient, and the distance matrix are calculated by software. Of the 4001 screened publications, 489 were eligible after careful selection. Our result showed the acupoints ST36 and PC6 were the most common combination acupoints in both electro and manual acupuncture. In terms of efficiency, ST36, PC6, and CV12 are significantly effective acupoints for manual acupuncture, and the PC6 and ST36 are effective acupoint for electro-acupuncture. We found that the near-far collocation method has been commonly used for different types of acupuncture treatment in CINV. Zhongwan, Shangwan, and Liangmen have been mainly used as local acupoints, while Neiguan, Hegu, Quchi, Zusanli, Gongsun, TaiChong, and Neiguan have been mainly used as distal acupoints. From the effect analysis, acupuncture treatment of nausea manual acupuncture effect is better; acupuncture treatment of vomiting or electro-acupuncture effect is better.

The Evolution of the Global Liquefied Natural Gas (LNG) Seaborne Trade Network: A Complex Network Analysis

In the global push to cut carbon emissions, liquefied natural gas (LNG) is increasingly valued as a clean and efficient energy source. Maritime transport is crucial for LNG trade. This study utilizes AIS data and complex network analysis to discover:(1) Overall, maritime LNG trade has consistently grown, showing regional concentration of supply and demand. Despite uneven node degree distribution, the network remains stable. (2) Regionally, trade is becoming more diverse, with multiple subgroups indicating strengthening multilateral trade relationships. Port cooperation is expected to densify, diversify, and embrace multilateralism. (3) Individually, there’s significant growth in LNG transshipment ports, especially in Asia and Europe, with Asian ports playing a crucial role alongside emerging ports in Western countries and the United States.

Estimating the connectional brain template based on multi-view networks with bi-channel graph neural network

Multi-view networks constructed from multiple brain functional or structural measures (e.g., fractional anisotropy, fiber number, and fiber length, etc.) describe brain connectivity from different views. The connectional brain template (CBT) of multi-view networks from a given population provides a standard graph template incorporating complementary information for analyzing intergroup differences. However, preserving the complex topology of multi-view networks and building the CBT end-to-end remains challenging. Hence, we proposed a bi-channel convolution framework, including a local connection channel (LCC) with edge-conditioned convolution layers and a global network channel (GNC) with graph convolution network, to estimate the CBT in an end-to-end manner. The LCC captured the local connection topology across individual networks, and the GNC learned the global network topology through the high-order population network built by the similarity between the node strength distributions of individual networks for each view. Additionally, we improved topological similarity constraint in the loss function by minimizing the KL divergence of the node strength and degree distributions between the CBT and multi-view networks. Compared with four existing methods, our CBT exhibited optimal centrality, topological structure retention ability and differentiation between the younger and older age groups. Using the harmonic bases of the CBT, we found that the total harmonic energy of cortical thickness presented significant differences among different age groups. Our method provided a standard common template for examining the structural connection changes in the spatial domain and the anatomical features alterations in the harmonic domain, thus distinguishing the different population groups.

Properties of a Random Bipartite Geometric Associator Graph Inspired by Vehicular Networks.

We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines, such as vehicles on a network of roads and sensors deployed along trails in a forest. Inspired by vehicular networks in which vehicles connect with their nearest wireless base stations (BSs), we consider a random bipartite associator graph in which each point of the PLP-PPP is associated with the nearest point of an independent PPP through an edge. This graph is equivalent to the partitioning of PLP-PPP by a Poisson Voronoi tessellation (PVT) formed by an independent PPP. We first characterize the exact distribution of the number of points of PLP-PPP falling inside the ball centered at an arbitrary location in R2 as well as the typical point of PLP-PPP. Using these distributions, we derive cumulative distribution functions (CDFs) and probability density functions (PDFs) of kth contact distance (CD) and the nearest neighbor distance (NND) of PLP-PPP. As intermediate results, we present the empirical distribution of the perimeter and approximate distribution of the length of the typical chord of the zero-cell of this PVT. Using these results, we present two close approximations of the distribution of node degree of the random bipartite associator graph. In a vehicular network setting, this result characterizes the number of vehicles connected to each BS, which models its load. Since each BS has to distribute its limited resources across all the vehicles connected to it, a good statistical understanding of load is important for an efficient system design. Several applications of these new results to different wireless network settings are also discussed.

The development of digital model of college Civics teaching combined with information diffusion model

Abstract In this paper, the information sphere radiation model describes the diffusion process of information in cyberspace. In real space, the information ring radiation model represents how information diffuses through interpersonal transmission in social circles. Secondly, the degree distribution of nodes in the network is described by the spatial topology’s degree distribution function and how information diffusion in the network is constructed. Finally, the model’s effectiveness is verified through the simulation of the total number of nodes function Q(t) for the diffusion of information in Civic and Political Science teaching. The mean diffusion degree is around 1.2 according to the results when teachers and students are the main interactors. In the case of student-content interaction and hybrid interaction, the mean value of diffusion is around 2.3. In the exercise session, however, the student-student diffusion degree reached 3. Through the information diffusion model, this paper facilitates the development of a digital model for college Civics teaching.

A local rewiring strategy for accelerating information propagation under complex propagation mechanism

Controlling the spread of information or rumors in complex networks has always been a subject of extensive attention and research. Generally speaking, taking the most influential node in the network as the propagation spreader or cutting off the most important link in the propagation process can maximize the promotion or suppression of information transmission. Therefore, many scholars have put forward many measurement methods to identify specific nodes and links in the network, and their theories are becoming more and more mature. However, in the face of large-scale networks, most of these methods are exposed to high computational complexity, low accuracy, and only applicable to specific networks. Some scholars try to enhance (inhibit) the dissemination of information by adding or deleting links, but the structural characteristics of the original network will be changed to a large extent, which also means that some basic functions related to the network have been changed. In this work, we propose a rewiring strategy to accelerate information propagation under complex propagation mechanism, which increases the number of redundant links by rewiring the second-order neighborhood of the initial propagation node. At the same time, the rewiring strategy preserves the degree distribution of nodes and modularization feature of the original network to a large extent. We apply our strategy to simulate the complex propagation of the information propagation (IST(I)) model on different networks. The simulation results show that the rewired network can accelerate the propagation of information more effectively, and the number of spreaders in the network increases significantly, and the propagation rate of information is enhanced significantly. In addition, this paper also proposed for the first time an index that quantifies both the transmission ability and infectivity of the information at the micro level, namely the number of regenerated infections which was optimally estimated by statistical inference. We also compare the changes of various topological characteristics of the network before and after the rewiring. We find that the structural characteristics related to the propagation dynamics of the network after the rewiring are significantly enhanced.

Some empirical and theoretical attributes of random multi-hooking networks

Multi-hooking networks are a broad class of random hooking networks introduced in [H. Mahmoud, Local and global degree profiles of randomly grown self-similar hooking networks under uniform and preferential attachment, Adv. Appl. Math. 111 (2019), p. 101930.] wherein multiple copies of a seed are hooked at each step, and the number of copies follows a predetermined building sequence of numbers. For motivation, we provide two examples: one from chemistry and one from electrical engineering. We explore the empirical and theoretical local degree distribution of a specific node during its temporal evolution. We ask what will happen to the degree of a specific node at step n that first appeared in the network at step j. We conducted an experimental study to identify some cases with Gaussian asymptotic distributions, which we then proved. Additionally, we investigate the distance in the network through the lens of the average Wiener index for which we obtain a theoretical result for any building sequence and explore its empirical distribution for certain classes of building sequences that have systematic growth.

An analysis of the spatio-temporal behavior of COVID-19 patients using activity trajectory data

During the global pandemic, COVID-19 patients' activity trajectories and actions emerge as revelatory conduits elucidating their spatiotemporal behavior and transmission dynamics. This study analyzes COVID-19 patients' behavior in Nanjing and Yangzhou, China, by using patient activity trajectory data in conjunction with complex network theory. The main findings are as follows: (1) The evaluation of the activity network structure of patients revealed that “residential areas” and “vegetable markets” had the highest betweenness centrality, indicating that these are the primary nodes of COVID-19 transmission. (2) The power-law distribution of the degree distribution of nodes for different facility types revealed that residential areas, vegetable markets, and shopping malls had the most scale-free characteristics, indicating that a large number of patients visited these three facility types at a few access points. (3) Community detection showed that patient visitation sites in Nanjing and Yangzhou were divided into five or six communities, with the largest community containing the outbreak origin and several residential areas surrounding it. (4) Patients had fewer activities across administrative regions but more activities across the life circle when the pandemic broke out in the suburbs, and more activities across administrative regions but fewer activities across the life circle when the pandemic broke out in the central city. Based on these findings, this paper makes recommendations for future pandemic preparedness in an effort to achieve effective pandemic control and reduce the damage caused by pandemics. Overall, this study provides insights into understanding the transmission patterns of COVID-19 and may inform future pandemic control strategies.

Multifractality and scale-free network topology in a noise-perturbed laminar jet

We present experimental evidence of multifractality and scale-free network topology in a noise-perturbed laminar jet operated in a globally stable regime, prior to the critical point of a supercritical Hopf bifurcation and prior to the saddle-node point of a subcritical Hopf bifurcation. For both types of bifurcation, we find that (i) the degree of multifractality peaks at intermediate noise intensities, (ii) the conditions for peak multifractality produce a complex network whose node degree distribution obeys an inverse power-law scaling with an exponent of $2 < \gamma < 3$ , indicating scale-free topology and (iii) the Hurst exponent and the global clustering coefficient can serve as early warning indicators of global instability under specific operating and forcing conditions. By characterising the noise-induced dynamics of a canonical shear flow, we demonstrate that the multifractal and scale-free network dynamics commonly observed in turbulent flows can also be observed in laminar flows under certain stochastic forcing conditions.

Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications.

Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works have shown that considering relationships between input data samples has a positive regularizing effect on the downstream task in healthcare applications. These relationships are naturally modeled by a (possibly unknown) graph structure between input samples. In this work, we propose Graph-in-Graph (GiG), a neural network architecture for protein classification and brain imaging applications that exploits the graph representation of the input data samples and their latent relation. We assume an initially unknown latent-graph structure between graph-valued input data and propose to learn a parametric model for message passing within and across input graph samples, end-to-end along with the latent structure connecting the input graphs. Further, we introduce a Node Degree Distribution Loss (NDDL) that regularizes the predicted latent relationships structure. This regularization can significantly improve the downstream task. Moreover, the obtained latent graph can represent patient population models or networks of molecule clusters, providing a level of interpretability and knowledge discovery in the input domain, which is of particular value in healthcare.