K-core Decomposition Research Articles

A learning-based influence maximization framework for complex networks via K-core hierarchies and reinforcement learning

Influence maximization (IM) is a critical aspect of complex network analysis, as it holds considerable commercial value across various domains such as recommendation systems and viral marketing. Its objective is to identify a set of seed nodes that can initiate the most extensive cascade of influence within the network. However, IM encounters significant challenges due to its NP-hard nature of accurately identifying the optimal seed nodes and estimating the spread of influence. Although recent learning-based IM methods have shown promising results, there are still challenges related to scalability, efficiency, and avoiding influence overlap that need to be addressed. This paper proposes CoreQ, a novel reinforcement learning-based framework that leverages K-core hierarchies to address IM challenges and make advised decisions to learn the optimal policy to select seed nodes. CoreQ significantly enhances IM by reducing computational costs and effectively addressing the influence overlap problem, making it a scalable and efficient solution. CoreQ first utilizes K-core decomposition to analyze the network structure and extract hierarchical features that guide the process of seed node identification. Then, it employs a novel maximum likelihood-based approach to identify a sufficient number of candidate seed nodes from K-core hierarchies. Finally, it leverages Q-learning’s decision-making capabilities to optimize a policy for learning the most effective seed selection strategy. The experimental results demonstrate that CoreQ not only outperforms state-of-the-art IM methods in terms of influence spread under the weighted independent cascade model but also surpasses other competing learning-based IM methods in terms of time efficiency.

Quantifying Women’s Marginalisation in Ibero-American Film Culture During the First Half of the Twentieth Century: A Network-Science Proposal

The research presented here uses the tools of social network analysis to empirically show a socio-cultural phenomenon already addressed by the social sciences and history: the historical marginalisation of women in the field of cinema. The novelty of our approach lies in the use of a large amount of heterogeneous historical data. On the one hand, we built a network of interactions between people involved in the film field in Ibero-America during the first half of the twentieth century. On the other hand, we propose a k-core decomposition and a multi-layered analysis, as a quantitative way to study the position of women within the cultural melieu. After conducting our analysis, we concluded that women were mostly situated in the outer k-shells of the empirical network, and their distribution was not uniform across the k-shells. From a qualitative perspective, these results can be interpreted as the consequence of the lack of evidence of the participation of women in the public sphere.

Efficient filter pruning: Reducing model complexity through redundancy graph decomposition

Filter pruning has emerged as a crucial technique facilitating the efficient deployment of Convolutional Neural Networks (CNNs) on edge devices. The resultant lightweight models often present a challenging trade-off between performance and compression rate. Moreover, the excessive granularity of filter selection, coupled with intricate fine-tuning procedures, hampers the practical applicability of numerous pruning methodologies. To tackle these limitations, our paper introduces a novel pruning approach that initially constructs an undirected graph, effectively capturing convolutional layer redundancy by quantifying the similarity among output feature maps. Subsequently, our method iteratively eliminates highly redundant and low-value filters, employing both k-core decomposition and importance ranking criteria. In practical implementation, we adopt a one-shot pruning strategy, thereby minimizing the requirement for extensive fine-tuning. Comprehensive comparative experiments demonstrate the efficacy of our proposed approach in achieving remarkable improvements in model compression without compromising performance. For instance, with CIFAR-10, our method achieves state-of-the-art results on DenseNet-40 with a mere 70 fine-tuning epochs, while effectively removing 49.39% of FLOPs, resulting in a mere 0.01% accuracy loss. Furthermore, in the context of ImageNet, our approach excels by removing 48.81% of FLOPs and 23.71% of parameters from ResNet-50, exhibiting only 1.47% and 0.83% decline in Top-1 and Top-5 Accuracy respectively. The code is publicly available at https://github.com/lijiang99/redundancy-graph-decomposition.

Anomalous process detection for Internet of Things based on K-Core

In recent years, Internet of Things security incidents occur frequently, which is often accompanied by malicious events. Therefore, anomaly detection is an important part of Internet of Things security defense. In this paper, we create a process whitelist based on the K-Core decomposition method for detecting anomalous processes in IoT devices. The method first constructs an IoT process network according to the relationships between processes and IoT devices. Subsequently, it creates a whitelist and detect anomalous processes. Our work innovatively transforms process data into a network framework, employing K-Core analysis to identify core processes that signify high popularity. Then, a threshold-based filtering mechanism is applied to formulate the process whitelist. Experimental results show that the unsupervised method proposed in this paper can accurately detect anomalous processes on real-world datasets. Therefore, we believe our algorithm can be widely applied to anomaly process detection, ultimately enhancing the overall security of the IoT.

Evolution of the global terrorist organizational cooperation network.

Terrorism has shown a trend of organizational cooperation in a large number of terrorist attacks around the world, posting a great challenge to counter-terrorism efforts. To investigate the trend and pattern of global terrorist organizational cooperations and to propose effective measures for effectively enforcing and restricting terrorist attacks, based on the Global Terrorism Database and the UN sanctions list of terrorist groups, this study constructs a cooperative evolutionary network of terrorist organizations from 119,803 terrorist attacks that occurred globally between 2001 and 2018. The evolution of worldwide terrorist cooperation is evaluated in terms of network characteristics, including key nodes, cohesion, and motifs. The network keeps expanding, with a large number of new nodes emerging each year. On average, there are 13 additional organizations entering in the collaboration network each year, with a yearly survival rate of about 34.66%, and the rank of node importance iterate and update frequently. Through k-core decomposition, for which the breakdown of the network has increased from three to five partitions, we find that the core of the terrorist organization's cooperation network changes much less frequently than the edges. The dominating modal structure of the network is the "star" motif (90%), and "triadic closed" motif (9%). We conclude that, over time, the cooperative network of terrorist groups has gradually evolved into a cluster of star-shaped networks, with various organizations serving as the centers of the networks and showing core-periphery structure in their individual communities. The core organizations are highly connected and stable, whereas the periphery organizations are loosely connected and highly variable.

Identifying influential nodes through an improved k-shell iteration factor model

Measuring the importance of nodes is a rapidly developing field in network science, with centrality measures playing a critical role in various applications, including epidemic control, influence maximization, and network integration. The commonly used coreness calculated by the k-core decomposition process for identifying influential spreaders has limitations, which fail to consider the topological position of nodes and lead to low node discrimination. To address these issues, we propose a novel approach called the structural iteration factor ranking method to identify the influential nodes in complex networks, which considers the remaining structural properties when implementing the k-core decomposition. Our method considers both local and global hierarchy information and selects the neighbor information attribute to avoid problems with overlapping neighbor information propagation caused by the significant clustering coefficient of networks. We consider ground-truth influence ranking based on the Susceptible–Infected–Recovered model, on which the performance of the proposed ranking method is verified. Our proposed method outperforms previous methods in calculating monotonicity, similarity, and accuracy. It provides a more comprehensive evaluation of nodes and enables more in-depth identification of critical nodes. These findings imply that considering the remaining structural properties when implementing the k-core decomposition dominates the spreading strength of nodes and catches more details for ranking the node influence in complex networks.

Identifying Key Factors of Hazardous Materials Transportation Accidents Based on Higher-Order and Multilayer Networks.

This paper focuses on the application of higher-order and multilayer networks in identifying critical causes and relationships contributing to hazardous materials transportation accidents. There were 792 accidents of hazardous materials transportation that occurred on the road from 2017 to 2021 which have been investigated. By considering time sequence and dependency of causes, the hazardous materials transportation accidents causation network (HMTACN) was described using the higher-order model. To investigate the structure of HMTACN such as the importance of causes and links, HMTACN was divided into three layers using the weighted k-core decomposition: the core layer, the bridge layer and the peripheral layer. Then causes and links were analyzed in detail. It was found that the core layer was tightly connected and supported most of the causal flows of HMTACN. The results showed that causes should be given hierarchical attention. This study provides an innovative method to analyze complicated accidents, which can be used in identifying major causes and links. And this paper brings new ideas about safety network study and extends the applications of complex network theory.

Formula omitted]-core decomposition of hypergraphs

In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential subgroups in hypergraphs, named (k,q)-core decomposition. The (k,q)-core is defined as the maximal subgraph in which each vertex has at least k hypergraph degrees and each hyperedge contains at least q vertices. The method contains a repeated pruning process until reaching the (k,q)-core, which shares similarities with a widely used k-core decomposition technique in a graph. Second, we analyze the pruning dynamics and the percolation transition with theoretical and numerical methods in random hypergraphs. We set up evolution equations for the pruning process, and self-consistency equations for the percolation properties. Based on our theory, we find that the pruning process generates a hybrid percolation transition for either k≥3orq≥3. The critical exponents obtained theoretically are confirmed with finite-size scaling analysis. Next, when k=q=2, we obtain a unconventional degree-dependent critical relaxation dynamics analytically and numerically. Finally, we apply the (k,q)-core decomposition to a real coauthorship dataset and recognize the leading groups at an early stage.

An analysis on the spatiotemporal behavior of inbound tourists in Jiaodong Peninsula based on Flickr geotagged photos

Exploring the spatiotemporal behavior characteristics of inbound tourists is of great practical significance to the management and planning of attractions. Based on Flickr geotagged photos and metadata, the research analyzes the spatiotemporal behavior characteristics of inbound tourists in Jiaodong Peninsula from the perspective of tourist flow network. We decompose the time series characteristics of tourists with STL decomposition algorithm, and predict the inbound tourism trend through the time series model. We propose the Hot Status Index (HSI) based on network centrality, extract and analyze the distribution pattern of inbound tourism hotspots with the structural hole method. The k-core decomposition algorithm is introduced to analyze the hierarchical characteristics of the tourist flow network. And Fast Unfolding algorithm is adopted to analyze the characteristics of community aggregation under different scales, dividing the scenic area into four communities. The results show that the time series model can accurately estimate the trend of the number of tourists. And there is a “competition” effect among attractions in Jiaodong Peninsula. The attractions show a hierarchy effect, of which the core layer has obvious small-world characteristics, with a clustering coefficient of 0.768. The inter-city tourist flow in Jiaodong Peninsula reveals a closed “multi-triangle” distribution pattern, mainly in the marginal coastal cities. Qingdao old town presents community stability, and other urban communities have a scale effect, mainly comprising two tourism circles.

Multi-objective Optimization Overlapping Community Detection Algorithm based on Subgraph Structure

Community detection in complex networks has increasingly become an important topic in the network, but in most community detection methods, a single node only belongs to one community. In fact, there is often overlap among real-world online communities. In this paper, an overlapping community detection algorithm based on subgraph structure and multi-optimization method is designed. In this algorithm, the maximum clique mined by k-core decomposition is used as the clique node, thus the overlap characteristic is transformed into the inherent characteristic of the new graph. After that, a population initialization method based on k-core decomposition is designed, and the discrete framework of multi-objective particle swarm optimization algorithm is used to optimize the two objectives on the basis of maximal clique graph to solve the problem of overlapping community detection. In the real-world network, this algorithm is compared with similar community detection algorithms. The comparison of the evaluation indexe shows that the community detection effect of this algorithm is similar to that of similar algorithms, and has a good application prospect.

Research on Deep Integration of the “Belt and Road” Aviation Network Based on Community Structure from the Perspective of China

Air transport has broad development potential along the “ Belt and Road” by owing to its fast, direct, and comfortable advantages, and the community structure is an important factor determining the efficiency and service functions of the aviation network. The community detection and community structure analysis of the “Belt and Road” aviation network would help to understand the internal relationship of the “Belt and Road” aviation network spatial structure and better integrated and optimized the network. Based on the data of international routes between 522 airports along the “Belt and Road” in 2019, this paper establishes an aviation network model and calculates the degree, average path, clustering coefficient, and centrality index of the “Belt and Road” aviation network. Through Louvain community detection method, 522 airports in the aviation network were divided into four communities, and the structural characteristics and geographical distribution characteristics of the community network were analyzed. The key node identification model in the community is constructed, the hierarchy of each community network is analyzed using the k-core decomposition method, the core node set of the community network is found, the core boundary node set of four aviation community networks is identified, the core node set and core boundary nodes are analyzed repeatedly, and the key node set of the whole network is obtained. Finally, from the perspective of China, a deep integration scheme between Chinese airports, their communities, and other key node sets was proposed. The research found that there are four associations in the “Belt and Road” aviation network: West Asia and North Africa, Russia, Central and Eastern Europe, and China and Southeast Asia. Chinese and Southeast Asian societies rank third among the four societies in terms of scale. They not only have the largest number of key nodes but also the lowest repetition rate of the key nodes. The international airline links in the “Belt and Road” aviation network are more complex. A total of 118 key nodes were identified, of which 83.1% were in the top 20% of overall network centrality.

NOVEL ACCESSIBILITY METRICS BASED ON HIERARCHICAL DECOMPOSITION OF TRANSPORT NETWORKS

Scientific analysis of public transport systems at the urban, regional, and national levels is vital in this contemporary, highly connected world. Quantifying the accessibility of nodes (locations) in a transport network is considered a holistic measure of transportation and land use and an important research area. In recent years, complex networks have been employed for modeling and analyzing the topology of transport systems and services networks. However, the design of network hierarchy-based accessibility measures has not been fully explored in transport research. Thus, we propose a set of three novel accessibility metrics based on the k-core decomposition of the transport network. Core-based accessibility metrics leverage the network topology by eliciting the hierarchy while accommodating variations like travel cost, travel time, distance, and frequency of service as edge weights. The proposed metrics quantify the accessibility of nodes at different geographical scales, ranging from local to global. We use these metrics to compute the accessibility of geographical locations connected by air transport services in India. Finally, we show that the measures are responsive to changes in the topology of the transport network by analyzing the changes in accessibility for the domestic air services network for both pre-covid and post-covid times.

Finding spatial and temporal features of delay propagation via multi-layer networks

Air traffic system is a typical complex network with dynamic delay propagation between airports. However, difficulties in measuring delay propagation strength and constructing rational networks make investigating the features of delay propagation based on real data from the perspective of complex network is rarely seen. In this paper, using two largest real-world flights dataset of China and the USA over a period of two months in 2018 (from Jul. to Aug.), we construct the delay propagation networks among airports by calculating causality relationship between delay time series of airports. We identify the multilayer structures of networks by k-core decomposition and reveal that a core layer with a few of tightly connected airports dominants delay propagation in the whole systems. Through the analysis on motifs, bidirectional edges are found to be the culprit to expand the scope of delay propagation from airport pairs to local structures. At the system level, we analyze the properties of communities and found that airports geographically close to each other are likely to be classified into a delay propagation community, while the delay propagation between communities is mainly affected by the air traffic flow between them. Moreover, through the comparisons of structures for the delay propagation networks on different days, we reveal the temporal dependence of delay propagation that the more serious the delay propagation in one day, the more similar it will be to that in the next day. Finally, the usefulness of features found is assessed through applying them to predict the delay propagation in the future.

INFORMATION TECHNOLOGY FOR STATISTICAL CLUSTER ANALYSIS OF INFORMATION IN COMPLEX NETWORKS

Information technology has been developed, which is used to collect, process and save large volumes of data from the web space. With the help of technology, the statistical characteristics of various segments of the web space and their cluster structure are studied. Two methods are used to find the optimal number of clusters and cluster centers: the well-known k-core decomposition algorithm and a new method developed by the authors. The new algorithm is based on the distribution of eigenvalues of the stochastic matrix, which describes the process of Markov transitions in the system. The clustering process is carried out using the Power iteration clustering algorithm.
 With the help of written software (crawler), information is collected on a given segment of the web space. For the studied area, there are statistical characteristics, namely: node degree, clustering coefficient, node probability distributions by input and output connections. Oriented and unoriented graphs of web pages of the studied zones are constructed. By combining the calculated dependencies for the input and output subnets, we can obtain the statistical characteristics of the undirected graphs of the web pages of the web space zones that we are investigating.
 For cluster analysis, the optimal number of clusters and cluster centers can be found in 2 ways: by the well-known k-core decomposition algorithm and by using a new method developed by the author. The new algorithm is based on the distribution of eigenvalues of the stochastic matrix, which describes the process of Markov transitions in the system. Using the Rower iteration clustering algorithm, the cluster structure of various segments of the web space is studied.
 The advantage of the developed information technology is that with its help one can work with large sets of data collected on the Internet, study their structure and statistical characteristics, and perform the clustering process. To implement the clustering process and find the optimal number of clusters and centroids a new algorithm is suggested. The results of the algorithm indicate high accuracy in determining the optimal number of clusters.

Analytical results of the k-core pruning process on multiplex networks

Multiplex networks are generally considered as networks that have the same set of vertices but different types of edges. Multiplex networks are especially useful when describing systems with several kinds of interactions. In this paper, we study the analytical solution of the k-core pruning process on multiplex networks. k-Core decomposition is a widely used method to find the dense core of the network. Previously, the Non-Backtracking Expansion Branch (NBEB) has been found to be able to easily derive the exact analytical results in the k-core pruning process. Here, we further extend this method to solve the k-core pruning process on multiplex networks by designing a variation of the method called the Multicolor Non-Backtracking Expansion Branch (MNEB). Our results show that, given any uncorrelated multiplex network, the Multicolor Non-Backtracking Expansion Branch can offer the exact solution for each intermediate state of the pruning process.

Analytical solution to the [formula omitted]-core pruning process

k-core decomposition is a widely-used method in ranking nodes or extracting important information of complex networks. It is a pruning process in which we recursively remove the vertices with degree less than k to obtain the core of a complex network. The simplicity and effectiveness of this approach has led to a variety of applications in many scientific fields, including bioinformatics, neurosciences, computer sciences, economics, and network sciences. However, the analytical theory of the k-core pruning process is still lacking. Here we find that in every pruning step of any given network, the Non-Backtracking Expansion Branch (NBEB) is directly related to the remaining k-core. Using this NBEB method, we obtain the analytical results of the k-core pruning process and its detailed critical behaviour.

Maximization influence in dynamic social networks and graphs

Social influence and influence diffusion have been extensively studied in social networks. However, most existing works on influence diffusion focus on static networks. In this paper, we study the problem of maximizing influence diffusion in dynamic social networks, i.e. networks that change over time. We propose the following algorithms under the Linear Threshold (LT) and Independent Cascade (IC) models: (a) the DM algorithm which is an extension of MATI algorithm and solves the Influence Maximization (IM) problem in dynamic networks, (b) the DM-C algorithm which is a latter version of DM and solves the IM problem using k-core decomposition and the core number information, (c) the DM-T algorithm which is another version of DM, that uses K-truss decomposition and the truss number information in order to solve the IM problem. Experimental results show that our proposed algorithms increase diffusion performance by 2 times compared with several state of the art algorithms and achieve comparable results in diffusion with the Greedy algorithm. Also, the proposed algorithms are 8.5 times faster in computational time compared with previous methods.

Effects of iron-based substrate on coupling of nitrification, aerobic denitrification and Fe(II) autotrophic denitrification in tidal flow constructed wetlands

The aerobic properties of nitrification and the anaerobic properties of denitrification in constructed wetlands are difficult to reconcile. In this study, two constructed wetlands were constructed with pyrite and steel slag in combination with zeolite, and their respective nitrification and denitrification capacities were evaluated under different tidal strategies. The steel slag wetland achieved 70.89 % and 46.04 % removal rates of NH4+-N and total nitrogen (TN), and the carbon consumption of denitrification was 1.51 mg BOD/mgN, which was better than pyrite wetland. Microbial analysis showed that Fe(II) autotrophic denitrification and aerobic denitrification occurred in both wetlands, and they were coupled with nitrification to achieve simultaneous removal of NH4+-N and TN. Microbial co-occurrence network and k-core decomposition analysis indicated that the core genus of steel slag wetlands was nitrifying bacteria. This study provides new insights into the application of tidal flow wetlands to treat rural sewage.

Porphyromonas gingivalis resistance and virulence: An integrated functional network analysis

BackgroundThe gram-negative bacteria Porphyromonas gingivalis (PG) is the most prevalent cause of periodontal diseases and multidrug-resistant (MDR) infections. Periodontitis and MDR infections are severe due to PG's ability to efflux antimicrobial and virulence factors. This gives rise to colonisation, biofilm development, evasion, and modulation of the host defence system. Despite extensive studies on the MDR efflux pump in other pathogens, little is known about the efflux pump and its association with the virulence factor in PG. Prolonged infection of PG leads to complete loss of teeth and other systemic diseases. This necessitates the development of new therapeutic interventions to prevent and control MDR. ObjectiveThe study aims to identify the most indispensable proteins that regulate both resistance and virulence in PG, which could therefore be used as a target to fight against the MDR threat to antibiotics. MethodsWe have adopted a hierarchical network-based approach to construct a protein interaction network. Firstly, individual networks of four major efflux pump proteins and two virulence regulatory proteins were constructed, followed by integrating them into one. The relationship between proteins was investigated using a combination of centrality scores, k-core network decomposition, and functional annotation, to computationally identify the indispensable proteins. ResultsOur study identified four topologically significant genes, PG_0538, PG_0539, PG_0285, and PG_1797, as potential pharmacological targets. PG_0539 and PG_1797 were identified to have significant associations between the efflux pump and virulence genes. This type of underpinning research may help in narrowing the drug spectrum used for treating periodontal diseases, and may also be exploited to look into antibiotic resistance and pathogenicity in bacteria other than PG.

Investigating Fake and Reliable News Sources Using Complex Networks Analysis

The rise of disinformation in the last years has shed light on the presence of bad actors that produce and spread misleading content every day. Therefore, looking at the characteristics of these actors has become crucial for gaining better knowledge of the phenomenon of disinformation to fight it. This study seeks to understand how these actors, meant here as unreliable news websites, differ from reliable ones. With this aim, we investigated some well-known fake and reliable news sources and their relationships, using a network growth model based on the overlap of their audience. Then, we peered into the news sites’ sub-networks and their structure, finding that unreliable news sources’ sub-networks are overall disassortative and have a low–medium clustering coefficient, indicative of a higher fragmentation. The k-core decomposition allowed us to find the coreness value for each node in the network, identifying the most connectedness site communities and revealing the structural organization of the network, where the unreliable websites tend to populate the inner shells. By analyzing WHOIS information, it also emerged that unreliable websites generally have a newer registration date and shorter-term registrations compared to reliable websites. The results on the political leaning of the news sources show extremist news sources of any political leaning are generally mostly responsible for producing and spreading disinformation.