High-degree Nodes Research Articles

Analysis of HIV transmission characteristics and intervention effects in Guangxi based on molecular networks

Objective: This study evaluates changes in HIV transmission and the effectiveness of interventions after two rounds of the Guangxi AIDS Conquering Project (GACP) in Guangxi, China. Methods: Samples and epidemiological data from newly diagnosed people living with HIV (PLWH) between 2014-2020 were analyzed. Molecular networks were constructed using nested PCR amplification and sequencing of the pol region, and multivariable logistic regression identified factors associated with clustering and high-degree nodes. Results: A total of 4,227 valid sequences (73.12% inclusion rate) were analyzed. Demographic changes included an increasing proportion of individuals aged ≥50 years (49.66%), with lower education (50.51%), peasants (76.82%), and heterosexual transmission (90.29%). The overall clustering rate was 86.89%, with higher clustering among individuals aged ≥50 (92.57%), those with primary school or below (89.09%), peasants (88.11%), and CRF08_BC infections (91.48%). Annual declines in cluster growth rate and clustering rates were observed, particularly among individuals aged <30, college graduates, men who have sex with men (MSM), and people who inject drugs (PWID). Key transmission hotspots were identified in Lingshan, particularly among older, less-educated individuals, and peasants. Factors associated with clustering included being male (aOR: 1.27), aged ≥50 (aOR: 3.84), and infected with CRF08_BC (aOR: 2.12). From 2017 to 2020, the risk of clustering and high-degree nodes was lower compared to 2014–2016, suggesting the effectiveness of interventions. Conclusion: Interventions in Guangxi effectively reduced HIV transmission among younger, high-degree populations. However, older, less-educated individuals remain at high risk, necessitating targeted strategies to address their specific needs and achieve better HIV control.

Twitter User Geolocation Based on Location Feature Enhancement

User location discovery from social media is crucial for location-based services like emergency awareness and event monitoring. Existing approaches generally integrate user-generated text features and social relationships, but insufficiently explore location-specific features and geographically proximate relationships, leading to suboptimal accuracy. In this paper, we propose a Twitter user geolocation method based on location feature enhancement, to better capture the location characteristics in users’ tweets and social relationships. Specifically, a user tweet representation algorithm based on location feature separation (TwLS) is designed. By leveraging words’ location-aware weight matrix and pre-trained embeddings, TwLS calculates a tweet representation for each user in every location, explicitly indicating the relevance between users and various locations. Additionally, we develop the local celebrity discovery method (LocCel) to construct social networks by identifying and preserving geographically concentrated high-degree nodes while filtering noise. Thereby LocCel enhances local relationships and strengthens location-proximate connections within the user social network. Experiments on two real-world datasets show that our method outperforms seven baselines, improving user geolocation accuracy by 3.1% ∼ 8.1% and 1.8% ∼ 8.8%, while reducing median error by 22.2% ∼ 52.8% and 19.4% ∼ 50.7%, respectively.

Analysis of type 2 diabetes mellitus-related genes by constructing the pathway-based weighted network.

Complex network is an effective approach to studying complex diseases, and provides another perspective for understanding their pathological mechanisms by illustrating the interactions between various factors of diseases. Type 2 diabetes mellitus (T2DM) is a complex polygenic metabolic disease involving genetic and environmental factors. By combining the complex network approach with biological data, this study constructs a pathway-based weighted network model of T2DM-related genes to explore the interrelationships between genes, here a weight is assigned to each edge in terms of the number of the same pathways in which the two nodes (genes) connected to the edge are involved. The edge weights can reflect differences in the strength of connections (interactions) between nodes (genes), which intuitively reflect the extent of biological correlations between genes and contribute to the importance of the nodes. Analysis of statistical and topological characteristics shows that the edge weights are correlated to the network topology, and the edge weight distribution decays as a power-law. The disparity of the weights indicates that the edge weight distribution for the nodes with the same degree is of approximately equal weights; and most edges with the higher weights tend to connect with the higher degree nodes. To determine the key hub genes of the weighted network, an integrated ranking index is used to comprehensively reflect the contribution of the three indices (strength, degree and number of pathways) of nodes; by taking the threshold of integrated ranking index greater than 0.56, 12 key hub genes are identified: MAPK1, PIK3CD, PIK3CA, PIK3R1, AKT2, AKT1, KRAS, TNF, MAPK8, PRKCA, IL6 and MTOR. These genes should play an important role in the occurrence and development of T2DM, and can be regarded as potential therapeutic targets for further biological and medical research on their functions in T2DM. It can be expected that combining complex network approach with other data analysis techniques can provide more clues for exploring the pathogenesis and treatment of T2DM and other complex diseases in the future.

Video tracking of single cells to identify clustering behavior

Cancer cell clustering is a critical factor in metastasis, with cells often believed to migrate in groups as they establish themselves in new environments. This study presents preliminary findings from an in vitro experiment, suggesting that co-culturing cells provides an effective method for observing this phenomenon, even though the cells are grown as monolayers. We introduce a novel single-cell tracking approach based on graph theory to identify clusters in PC3 cells cultivated in both monoculture and co-culture with PC12 cells, using 66-h time-lapse recordings. The initial step consists of defining “linked” pairs of PC3 cells, laying the foundation for the application of graph theory. We propose two alternative definitions for cell pairings. The first method, Method 1, defines cells as “linked” at a given time t if they are close together within a defined time period before and after t. A second potential alternative method, Method 2, pairs cells if there is an overlap between the convex hulls of their respective tracks during this time period. Pairing cells enables the application of graph theory for subsequent analysis. This framework represents a cell as a vertex (node) and a relation between two cells as an edge. An interconnected set of high-degree nodes (nodes with many connections or edges) forms a subgraph, or backbone, that defines a patch (cluster) of cells. All nodes connected to this backbone are part of the subgraph. The backbone of high-degree nodes functions as a partition (or cut) of the initial graph. Two consecutive clusters in the video are considered to share the same identity if the following cluster contains at least p = 75 % of the cells from the preceding cluster, and the mean positions of their cells are within △r = 75μm. PC3 cells grown in co-culture appear to form persistent clusters exceeding 10 cells after 40–50 h incubation following seeding. In contrast, PC3 cells cultured alone (mono-culture) did not exhibit this behavior. This approach is experimental and requires further validation with a broader dataset.

Can Random Friends Seed More Buzz and Adoption? Leveraging the Friendship Paradox

A critical element of word of mouth (WOM) or buzz marketing is to identify seeds, often central actors with high degree in the social network. Seed identification typically requires data on the relevant network structure, which is often unavailable. We examine the impact of WOM seeding strategies motivated by the friendship paradox, which can obtain more central nodes without knowing network structure. Higher degree nodes may be less effective as seeds if these nodes communicate less with neighbors or are less persuasive when they communicate; therefore, whether friendship paradox–motivated seeding strategies increase or reduce WOM and adoption remains an empirical question. We develop and estimate a model of WOM and adoption using data on microfinance adoption across village social networks in India. Counterfactuals show that the proposed strategies with limited seeds are about 13%–30% more effective in increasing adoption relative to random seeding. These strategies are also on average 5%–11% more effective than the firm’s leader seeding strategy. We also find these strategies are relatively more effective when we have fewer seeds. This paper was accepted by Juanjuan Zhang, marketing. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.4991 .

Insights into the Therapeutic Potential of Active Ingredients of Citri Reticulatae Pericarpium in Combatting Sarcopenia: An In Silico Approach.

Sarcopenia is a systemic medical disorder characterized by a gradual decline in muscular strength, function, and skeletal muscle mass. Currently, there is no medication specifically approved for the treatment of this condition. Therefore, the identification of new pharmacological targets may offer opportunities for the development of novel therapeutic strategies. The current in silico study investigated the active ingredients and the mode of action of Citri Reticulatae Pericarpium (CRP) in addressing sarcopenia. The active ingredients of CRP and the potential targets of CRP and sarcopenia were determined using various databases. The STRING platform was utilized to construct a protein-protein interaction network, and the key intersecting targets were enriched through the Kyoto Encyclopedia of Genes and Genomes (KEGG) and Gene Ontology (GO) analyses. Molecular docking was used to determine the binding interactions of the active ingredients with the hub targets. The binding affinities obtained from molecular docking were subsequently validated through molecular dynamics simulation analyses. Five active ingredients and 45 key intersecting targets between CRP and sarcopenia were identified. AKT1, IL6, TP53, MMP9, ESR1, NFKB1, MTOR, IGF1R, ALB, and NFE2L2 were identified as the hub targets with the highest degree node in the protein-protein interaction network. The results indicated that the targets were mainly enriched in PIK3-AKT, HIF-1, and longevity-regulating pathways. The active ingredients showed a greater interaction affinity with the hub targets, as indicated by the results of molecular docking and molecular dynamics simulations. Our findings suggest that the active ingredients of Citri Reticulatae Pericarpium, particularly Sitosterol and Hesperetin, have the potential to improve sarcopenia by interacting with AKT1 and MTOR proteins through the PI3K-AKT signaling pathway.

Zero-cost upgrade to a multi-fiber network with partial lane-change capabilities

Growing capacity requirements are leading to the deployment of multiple fibers in each optical network link. Even though deploying state-of-the-art multi-fiber network architectures with stacked and independent fiber layers simplifies network design and control, spectrum can be used more efficiently if the optical-network nodes allow fiber layers to be interconnected, i.e., if the so-called lane change is enabled. Unfortunately, lane change in high-degree optical nodes requires wavelength selective switches (WSSs) with a high number of ports, which is prohibitively costly or even unfeasible with current WSS technology. Instead, lane change in low-degree optical nodes can be enabled at no extra cost, using WSS ports that are otherwise left empty. In this study, we describe our proposal for a multi-fiber network with partial lane-change capabilities and perform a simulative study to identify the advantages of this architecture, as well as discuss the emerging resource allocation challenges associated with it. We demonstrate that, by enabling lane change in degree-2 nodes, we can increase network throughput by 3% and restore 5%–8% more traffic in the case of single- and double-link failures at no additional equipment cost.

Analysis of changes in river connectivity during the urbanization process: a case study of the southeastern plain of Yinzhou, China.

Affected by human activities, the naturally occurring river network in the southeastern plain of Yinzhou has gradually evolved into a natural-artificial composite water system, and changes in river connectivity due to changes in river network systems have caused water security problems, including urban flooding. To clarify the river connectivity change and its relationship with the urbanization process, this paper discusses an evaluation method for river connectivity based on complex networks and cellular automata (CA) from the perspective of complex systems, quantitatively analyzes the spatial-temporal characteristics of the structural and functional river connectivity in the study area during the 1990s-2020s, and reveals the impact of river nodes and chains on the connectivity level under the disturbance of natural or human factors. The results contained the following revelations: ① River connectivity showed a decreasing trend in the initial and rapid development stages of urbanization from the 1990s to the 2010s and a limited increasing trend in the optimization and upgrading stages from the 2010s to the 2020s. ② River network degradation and ongoing connectivity decline are found in the northeastern part of the study area. The highest river connectivity exists in Dongqianhukaifaqu. ③ The number of river nodes and chains should be maintained at approximately 80% for normal river connectivity. The nodes of high degree in the inflow area are listed in the key protection areas. ④ Changes in river connectivity are significantly correlated with the urbanization process. Changes in the functional connectivity level affect the magnitude of a flood. This study provides a theoretical basis for river network connectivity improvement and flood prevention in plain areas.

Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network

Abstract We study the dynamics of the generalized Lotka–Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, g c . In the competitive regime g c serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct.

Analysis and experimental validation of genes and their transcription factor prediction in contused rat spinal cord at the intermediate phase.

The intermediate phase of spinal cord injury (SCI) serves as an important target site for therapeutic mediation of SCI. However, there is a lack of insight into the mechanism of the intermediate phase of SCI. The present study aimed to investigate the molecular mechanism and the feasible treatment targets in the intermediate phase of SCI. We downloaded GSE2599 from GEO and identified 416 significant differentially expressed genes (DEGs), including 206 downregulated and 210 upregulated DEGs. Further enrichment analysis of DEGs revealed that many important biological processes and signal pathways were triggered in the injured spinal cord. Furthermore, a protein-protein interaction (PPI) network was constructed and the top 10 high-degree hub nodes were identified. Furthermore, 27 predicted transcription factors (TFs) and 136 predicted motifs were identified. We then selected insulin-like growth factor 1 (IGF1) and its predicted transcription factor, transcription factor A, mitochondrial (TFAM) for further investigation. We speculated and preliminarily confirmed that TFAM may regulate gene transcription of IGF1 and effected alterations in the function recovery of rats after SCI. These findings together provide novel information that may improve our understanding of the pathophysiological processes during the intermediate phase of SCI.

Local dominance unveils clusters in networks

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data.

Sparse dynamic discretization discovery via arc-dependent time discretizations

While many time-dependent network design problems can be formulated as time-indexed formulations with strong relaxations, the size of these formulations depends on the discretization of the time horizon and can become prohibitively large. The recently-developed dynamic discretization discovery (DDD) method allows many time-dependent problems to become more tractable by iteratively solving instances of the problem on smaller networks where each node has its own discrete set of departure times. However, in the current implementation of DDD, all arcs departing a common node share the same set of departure times. This causes DDD to be ineffective for solving problems where all near-optimal solutions require many distinct departure times at the majority of the high-degree nodes in the network. Region-based networks are one such structure that often leads to many high-degree nodes, and their increasing popularity underscores the importance of tailoring solution methods for these networks.To improve methods for solving problems that require many departure times at nodes, we develop a DDD framework where the set of departure times is determined on the arc level rather than the node level. We apply this arc-based DDD method to a temporal variant of the service network design problem (SND). We show that an arc-based approach is particularly advantageous when instances arise from region-based networks, and when candidate paths are fixed in the base graph for each commodity. Moreover, our algorithm builds upon the existing DDD framework and achieves these improvements with only benign modifications to the original implementation.

Link-limited bypass rewiring for enhancing the robustness of complex networks

Real-world networks often encounter disruptions that can have profound societal impacts. Therefore, enhancing network robustness against random failures and targeted attacks is crucial. Bypass rewiring, in which adjacent nodes are immediately reconnected following node removal, has been proposed as a promising method for enhancing network robustness. However, this method typically requires numerous bypass links and incurs significant costs. In this paper, we propose link-limited bypass rewiring, in which bypass links are reconnected stochastically. Additionally, we investigate the relationship between the number of bypass links and robustness improvement. Our findings, which are based on analytical and numerical results, reveal a tradeoff relationship between the number of added bypass links and robustness enhancement. Notably, preferentially reconnecting high-degree nodes was found to be effective for improving robustness. These insights can inform the design of resilient systems in real-world networks, offering strategies for enhancing robustness against node removal.

Elucidating the semantics-topology trade-off for knowledge inference-based pharmacological discovery.

Leveraging AI for synthesizing the deluge of biomedical knowledge has great potential for pharmacological discovery with applications including developing new therapeutics for untreated diseases and repurposing drugs as emergent pandemic treatments. Creating knowledge graph representations of interacting drugs, diseases, genes, and proteins enables discovery via embedding-based ML approaches and link prediction. Previously, it has been shown that these predictive methods are susceptible to biases from network structure, namely that they are driven not by discovering nuanced biological understanding of mechanisms, but based on high-degree hub nodes. In this work, we study the confounding effect of network topology on biological relation semantics by creating an experimental pipeline of knowledge graph semantic and topological perturbations. We show that the drop in drug repurposing performance from ablating meaningful semantics increases by 21% and 38% when mitigating topological bias in two networks. We demonstrate that new methods for representing knowledge and inferring new knowledge must be developed for making use of biomedical semantics for pharmacological innovation, and we suggest fruitful avenues for their development.

Representative and Back-In-Time Sampling from Real-world Hypergraphs

Graphs are widely used for representing pairwise interactions in complex systems. Since such real-world graphs are large and often evergrowing, sampling subgraphs is useful for various purposes, including simulation, visualization, stream processing, representation learning, and crawling. However, many complex systems consist of group interactions (e.g., collaborations of researchers and discussions on online Q&A platforms) and thus are represented more naturally and accurately by hypergraphs than by ordinary graphs. Motivated by the prevalence of large-scale hypergraphs, we study the problem of sampling from real-world hypergraphs, aiming at answering (Q1) how can we measure the goodness of sub-hypergraphs, and (Q2) how can we efficiently find a “good” sub-hypergraph. Regarding Q1, we distinguish between two goals: (a) representative sampling , which aims at capturing the characteristics of the input hypergraph, and (b) back-in-time sampling , which aims at closely approximating a past snapshot of the input time-evolving hypergraph. To evaluate the similarity of the sampled sub-hypergraph to the target (i.e., the input hypergraph or its past snapshot), we consider 10 graph-level, hyperedge-level, and node-level statistics. Regarding Q2, we first conduct a thorough analysis of various intuitive approaches using 11 real-world hypergraphs. Then, based on this analysis, we propose MiDaS and MiDaS-B , designed for representative sampling and back-in-time sampling, respectively. Regarding representative sampling, we demonstrate through extensive experiments that MiDaS , which employs a sampling bias toward high-degree nodes in hyperedge selection, is (a) Representative : finding overall the most representative samples among 15 considered approaches, (b) Fast : several orders of magnitude faster than the strongest competitors, and (c) Automatic : automatically tuning the degree of sampling bias. Regarding back-in-time sampling, we demonstrate that MiDaS-B inherits the strengths of MiDaS despite an additional challenge—the unavailability of the target (i.e., past snapshot). It effectively handles this challenge by focusing on replicating universal evolutionary patterns, rather than directly replicating the target.

NetFense: Adversarial Defenses against Privacy Attacks on Neural Networks for Graph Data

Recent advances in protecting node privacy on graph data and attacking graph neural networks (GNNs) gain much attention. The eye does not bring these two essential tasks together yet. Imagine an adversary can utilize the powerful GNNs to inferusers’ private labels in a social network. How can we adversarial defend against such privacy attacks while maintaining the utility of perturbed graphs? In this work, we propose a novel research task, adversarial defenses against GNN-based privacy attacks, and present a graph perturbation-based approach, NetFense, to achieve the goal. NetFense can simultaneously keep graph data unnoticed ability (i.e., having limited changes on the graph structure), maintain the prediction confidence of targeted label classification (i.e., preserving data utility), and reduce the prediction confidence of private label classification (i.e., protecting the privacy of nodes). Experiments conducted on ingle- and multiple-target perturbations using three real graph data exhibit that the perturbed graphs by NetFense can effectively maintain data utility (i.e., model unnoticed ability) on targeted label classification and significantly decrease the prediction confidence of private label classification (i.e., privacy protection). Extensive studies also bring several insights, such as the flexibility of NetFense, preserving local neighbourhoods in data unnoticed ability, and better privacy protection for high-degree nodes.

Identification of different myofiber types in pigs muscles and construction of regulatory networks

BackgroundSkeletal muscle is composed of muscle fibers with different physiological characteristics, which plays an important role in regulating skeletal muscle metabolism, movement and body homeostasis. The type of skeletal muscle fiber directly affects meat quality. However, the transcriptome and gene interactions between different types of muscle fibers are not well understood.ResultsIn this paper, we selected 180-days-old Large White pigs and found that longissimus dorsi (LD) muscle was dominated by fast-fermenting myofibrils and soleus (SOL) muscle was dominated by slow-oxidizing myofibrils by frozen sections and related mRNA and protein assays. Here, we selected LD muscle and SOL muscle for transcriptomic sequencing, and identified 312 differentially expressed mRNA (DEmRs), 30 differentially expressed miRNA (DEmiRs), 183 differentially expressed lncRNA (DElRs), and 3417 differentially expressed circRNA (DEcRs). The ceRNA network included ssc-miR-378, ssc-miR-378b-3p, ssc-miR-24-3p, XR_308817, XR_308823, SMIM8, MAVS and FOS as multiple core nodes that play important roles in muscle development. Moreover, we found that different members of the miR-10 family expressed differently in oxidized and glycolytic muscle fibers, among which miR-10a-5p was highly expressed in glycolytic muscle fibers (LD) and could target MYBPH gene mRNA. Therefore, we speculate that miR-10a-5p may be involved in the transformation of muscle fiber types by targeting the MYHBP gene. In addition, PPI analysis of differentially expressed mRNA genes showed that ACTC1, ACTG2 and ACTN2 gene had the highest node degree, suggesting that this gene may play a key role in the regulatory network of muscle fiber type determination.ConclusionsWe can conclude that these genes play a key role in regulating muscle fiber type transformation. Our study provides transcriptomic profiles and ceRNA interaction networks for different muscle fiber types in pigs, providing reference for the transformation of pig muscle fiber types and the improvement of meat quality.

The impact of input node placement in the controllability of structural brain networks

Network controllability refers to the ability to steer the state of a network towards a target state by driving certain nodes, known as input nodes. This concept can be applied to brain networks for studying brain function and its relation to the structure, which has numerous practical applications. Brain network controllability involves using external signals such as electrical stimulation to drive specific brain regions and navigate the neurophysiological activity level of the brain around the state space. Although controllability is mainly theoretical, the energy required for control is critical in real-world implementations. With a focus on the structural brain networks, this study explores the impact of white matter fiber architecture on the control energy in brain networks using the theory of how input node placement affects the LCC (the longest distance between inputs and other network nodes). Initially, we use a single input node as it is theoretically possible to control brain networks with just one input. We show that highly connected brain regions that lead to lower LCCs are more energy-efficient as a single input node. However, there may still be a need for a significant amount of control energy with one input, and achieving controllability with less energy could be of interest. We identify the minimum number of input nodes required to control brain networks with smaller LCCs, demonstrating that reducing the LCC can significantly decrease the control energy in brain networks. Our results show that relying solely on highly connected nodes is not effective in controlling brain networks with lower energy by using multiple inputs because of densely interconnected brain network hubs. Instead, a combination of low and high-degree nodes is necessary.

Granting leaders priority exit options promotes and jeopardizes cooperation in social dilemmas

Cooperation in human interactions often involves voluntary participation rather than obligatory requirements. This paper investigates the impact of voluntary exit strategies on cooperation within scale-free networks, employing spatial prisoner’s dilemma games as the framework. We analyze three distinct exit strategies: leader priority exit, fringe priority exit, and random exit, across varying dilemma strengths. Our findings reveal that in scenarios of weak dilemma strength, leader priority exit significantly diminishes cooperation, particularly when only a small subset of players is granted exit rights. In contrast, under strong dilemma strength conditions, both leader priority and random exits serve to unexpectedly bolster cooperation. This enhancement is primarily facilitated by high-degree nodes opting out, thereby enabling low-degree nodes to establish stable cooperation. Furthermore, our study underscores the pivotal role of network structure. In assortative networks, random exit emerges as the most effective strategy in promoting cooperation. On the other hand, disassortative networks exhibit a substantial increase in cooperation levels when employing leader priority exit. These results highlight the intricate interplay between exit strategies, dilemma strength, and network topology, offering critical insights for promoting cooperation in varied social contexts.

Tourist Flows and Multi-Destination Trips: A Network Analysis

ABSTRACT Conventional approaches to modeling multi-destination trips are either based on trade-offs between one single destination and multiple destinations or on a sequence of destinations in a linear manner. These approaches are inadequate to capture the manifestation of multi-destination trips as a network at the aggregate level. Hence, built upon network analytical frameworks, this study adopted a directed network to model multi-destination trips. Using a visitor profile survey of Hong Kong, we found that the networks of multi-destination trips for both leisure and business travelers have several interesting properties, such as high densities, high clustering coefficients, and short diameters. High-degree nodes represent either destinations or origins in the leisure network, but they have a dual role as both destinations and origins in the business network. Network sparsity has a significant impact on the topology of the leisure network, but the impact is negligible on the business network.