Progress on network modeling and analysis of gut microecology: a review

ABSTRACT The gut microecological network is a complex microbial community within the human body that plays a key role in linking dietary nutrition and host physiology. To understand the complex relationships among microbes and their functions within this community, network analysis has emerged as a powerful tool. By representing the interactions between microbes and their associated omics data as a network, we can gain a comprehensive understanding of the ecological mechanisms that drive the human gut microbiota. In addition, the network-based approach provides a more intuitive analysis of the gut microbiota, simplifying the study of its complex dynamics and interdependencies. This review provides a comprehensive overview of the methods used to construct and analyze networks in the context of gut microecological background. We discuss various types of network modeling approaches, including co-occurrence networks, causal networks, dynamic networks, and multi-omics networks, and describe the analytical techniques used to identify important network properties. We also highlight the challenges and limitations of network modeling in this area, such as data scarcity and heterogeneity, and provide future research directions to overcome these limitations. By exploring these network-based methods, researchers can gain valuable insights into the intricate relationships and functional roles of microbial communities within the gut, ultimately advancing our understanding of the gut microbiota’s impact on human health.

occur on various timescales, ranging from daily to long-term shifts.For example, the composition of microbial communities may change abruptly to adapt to perturbations (14).Effectively scrutinizing the dynamics inherent in microecological data is paramount as it enables the capture of temporal patterns and unravels the underlying mechanisms of microbial community dynamics (15).Such analytical approaches enable researchers to track temporal changes in microbial diversity, identify key drivers of community dynamics, and assess ecosystem stability and resilience.

The compositional challenges related to sampling
Microbiome data are composite because of their inherent characteristics and measure ment methodology (16).Unlike traditional data types, data obtained from microbiome studies represent a fraction of the total gut microbial population.It is impractical to count and measure every microorganism in the gut directly.Researchers have employed various sequencing and profiling techniques to obtain representative samples (17).These proportional relationships provide vital insights into microbial interactions, community dynamics, and functional roles.Compositional data analysis should allow us to understand the relative abundance of certain taxa and how they relate to the overall microbial community (18).

Multiple origins: the derivation of heterogeneity
Another important characteristic of microecological data is inherent heterogeneity.Heterogeneity within microbiome data can stem from various origins, including sampling disparities, technical variations, and host discrepancies.The composition and abundance of microorganisms can vary owing to differences in sampling methods, sampling sites, or even temporal changes within an individual (19).Technical variabil ity arises from the diverse methods employed to generate microbiome data, such as sequencing platforms, DNA extraction techniques, and data analysis pipelines (20).Aspects such as host genetics, diet, lifestyle, and environmental exposure contribute to the between-individual deviations apparent in microbiome data (21).Overall, address ing the heterogeneity in microbiome data is essential for accurately interpreting and translating findings into clinical applications (22).

Sparsity of gut microecological data
The microbiome data displayed a distinctive attribute of high sparsity, marked by an abundance of zero values and numerous infrequent microbial species (23).Conse quently, the microbiome data exhibited a long-tailed distribution with a few dominant species and many rare species.Conventional statistical techniques designed for dense and customarily distributed data structures may be inadequate for managing sparse data sets (24).Therefore, appropriate treatment and analysis of such sparse data are imperative to ensure an accurate understanding of the assembly and physiology of gut communities.

TRADITIONAL MECHANISTIC MODELING AND MACHINE LEARNING METHODS
The gut microecological environment, shaped by dietary choices, human interactions, and environmental factors, constitutes an intricate microbial community that signifi cantly impacts the overall health of the human organism (Fig. 1a).Traditional methods for modeling gut microecological data can be categorized into two main methodolo gies to address these characteristics: mechanistic and statistical modeling.Given that each approach possesses its own set of strengths and limitations, the following section discusses each methodology separately.

Mechanistic modeling
Mechanistic modeling is a widely adopted approach in the study of gut microecology (25).By constructing biological mechanistic models encompassing elements such as microbial growth, metabolism, and nutrient availability, one can simulate and ana lyze the behavior of the microbial community over time (26) (Fig. 1b).Subsequently, integrating multiple genome-scale metabolic models (GEMs) from diverse bacteria into a simulated community enables researchers to analyze metabolic interactions using techniques such as flux balance analysis (FBA).Because traditional FBA lacks temporal information, dynamic modeling methodologies such as dynamic flux balance analysis and dynamic multi-species metabolic modeling (DMMM) are designed to account for temporal changes within bacterial communities (27) (Fig. 1c).It is worth mentioning that the DMMM may disregard the effects of metabolic shifts upon bacterial death and may lack direct integration of experimental data.An alternative, d-OptCom, introduces a temporal dimension by utilizing community metabolism rates to model individual growth.However, its computational demands present challenges.This limitation can be mitigated by leveraging optimization techniques that build upon previous solutions (28).For instance, leveraging biochemical knowledge and databases allows the generation of GEMs for organisms (26).Co-GEMs facilitate modeling conditionspecific microbial community metabolism by integrating metatranscriptomic data.
Additionally, incorporating an environmental component into the modeling framework accounts for the influence of metabolic gradients and physical location on metabolite availability (29).COMETS integrates metabolite diffusion with FBA to evaluate metabolic equilibration in spatial communities (30).AGORA (31) summarized the mechanism of action of metabolite precursor substances on new cell synthesis and was able to model the host-microbe co-metabolism mechanisms better.Bauer et al. (32,33) proposed the BacArena model to perform complex kinetic studies of metabolic interactions between microorganisms.In the microbial community COBRA model, Heirendt (34) constructed a paired community model of human gut flora using a dynamic assessment approach for small microbial communities.It is expanding rapidly with the development of various tools and approaches.

Machine learning
As opposed to mechanistic modeling, statistical machine learning adopts a data-driven methodology that emphasizes the analysis and interpretation of data without explic itly relying on predefined principles.This approach employs various techniques to uncover concealed patterns and relationships within the data, including regression, classification, clustering, and dimensionality reduction.By doing so, statistical machine learning facilitates predictions and informed decisions based on observed data (35).This adaptable approach is useful for managing intricate and high-dimensional microbiome data sets, enabling valuable knowledge discovery and smart decision-making (36).
Machine learning methods have three broad types: unsupervised, supervised, and reinforcement learning.Unsupervised modeling methods find utility in pattern clustering, dimension reduction, and association analysis (37).Furthermore, canonical correlation analysis, an unsupervised statistical approach, is valuable for microbiome data analysis (38) (Fig. 1e).Thus, unsupervised learning is pivotal in unraveling the complex relationships between the microbiome and its environmental determinants.Subsequently, it leverages the acquired knowledge to predict or classify unseen samples effectively.
Knights et al. (39) demonstrated the advantages of supervised classification methods for gut microbiome classification, including random forest, nearest shrunken centroids, elastic nets, and support vector machines.Their study showed that supervised classifica tion techniques can successfully identify subgroups of highly diverse microbial clusters associated with specific community types.In addition to classification, regression focuses on host trait prediction.Redundancy analysis is an inspection of the score matrix of the multilevel multiple linear regression between the return variable table and the descriptive variables (40).Machine learning methods are promising for analyzing and integrating diverse data from gut flora studies (Fig. 1e).However, these models do not directly suggest specific modulation strategies or interventions to alter phenotypes.
Unlike unsupervised and supervised learning, reinforcement learning (RL) offers a different sight of view (41).RL combines deep models with reinforcement learning, a learning process based on interactions with the environment, which enables more sophisticated decision-making processes (42).In microbiome research, deep RL has the potential to guide modulation strategies by optimizing interventions based on feedback and rewards (Fig. 1e).Recent developments include using deep reinforce ment learning to reward and penalize models based on improved performance, aiding biomarker identification and colony-driven node analysis (43,44).However, it is essential to recognize that RL approaches in microbiome research are still nascent and face challenges, such as the intricate modeling of microbiome-host interactions and the limited availability of large-scale experimental data to train deep RL models (45).

Limitations
The field of microbiome big data presents a unique set of challenges for understand ing complex interactions within microbial ecosystems.Mechanistic modeling, which focuses on describing the underlying physiological mechanisms, encounters difficulties in accurately capturing the intricate dynamics of microbial communities.This com plexity arises from the many microorganisms involved, their diverse metabolic activi ties, and their intricate interactions.Furthermore, a comprehensive understanding of the underlying physiological processes that drive these interactions remains elusive, impeding the precise development of mechanistic models.
Machine-learning approaches offer the ability to handle large-scale data sets and uncover patterns within the data.However, these studies often rely solely on data-driven methods and lack a deep understanding of the underlying microbial interactions.This limitation hampers the interpretation of learned patterns regarding biological mecha nisms and restricts their potential to offer insights into microbial ecosystems.

NETWORK MODELING BRIDGES THE GAP BETWEEN MECHANISTIC MODELING AND MACHINE LEARNING
Diverse microorganisms engage in various metabolic activities in the gut microenviron ment.Intricate relationships among these gut inhabitants encompass mutual bene fits, cohabitation, competition, and an intricate interplay between metabolites and microbial entities.Mechanism-based modeling approaches hinder the understanding of the intricate interactions within gut microecology.In this context, gut microecological communities inherently constitute a network, and the application of network analysis methods facilitates a more profound comprehension of inter-community dynamics and community characteristics.Machine learning approaches driven by data-based approaches lose the interpretability of biological information.Network modeling offers a cohesive framework for investigating the intrinsic properties of microbiome data and the structural properties of this complex community (46).Hence, network modeling approaches facilitate the exploration of microbial interactions, consolidation of various forms of data, and identification of key players, providing a valuable way to explore the complexity and dynamism of the gut microbiome (47)(48)(49).The network analysis method perfectly bridges the gap between mechanistic models and machine learning methods, thus presenting a new feasible solution for gut microecology analysis.
The following sections delve into four approaches to model the gut microbiome: co-occurrence, causal, dynamic, and multi-omics networks.By traversing these avenues, we intend to facilitate a holistic comprehension of the intricate interactions embedded within gut microecology (Fig. 2).

Co-occurrence network
Microorganisms usually exist in groups and influence their surroundings through synergistic interactions, thus shaping the structure and diversity of microbial communi ties (50).Co-occurrence networks are statistical association networks among microbial community taxa that offer insights into the structure of microbial communities (51).Cooccurrence network analysis has extensive applications in data mining and microbiome research (52).The networks were constructed assuming that specific microbial taxa cooccurred more often than anticipated, shedding light on potential ecological interac tions.
Correlation-based methods, such as SparCC (53), estimate associations by capturing sparsity among microorganisms, which focuses on correlation, while SPIEC-EASI (54) concentrates on conditional dependence and has requirements for the precision of the underlying data.These procedures assess the degree of similarity or dissimilarity in the abundance profiles of taxa across samples and excel at capturing linear relationships between variables (55).To capture nonlinearity, alternatives such as mutual information may be more suitable (56).The maximal information coefficient is the entropy of random variables based on mutual information, which measures the statistical magnitude of linear or non-linear connections across quantities for constructing non-linear networks to identify more correlated information (57,58).One notable approach, WGCNA-P+M, uniquely integrates linear and non-linear correlations, forging a novel pathway for constructing co-occurrence networks.This method leverages correlations to enhance the precision of WGCNA (weighted correlation network analysis) (59,60).
Statistical inference methods have also been used extensively to infer microbial associations while accommodating the compositional properties of given samples and addressing sparsity challenges.Prior to statistical modeling, log-ratio or centered log-ratio transformations are typically used to allow for more accurate relationship assessments while preserving the compositional texture of the domain data (61).Otherwise, increasing the amount of data can bring the relative abundance closer to the absolute abundance, thereby enhancing accurate limits (62).Additionally, sparsity problems can be reduced using covariance matrices, pseudo-counts, and de-redundant normalization (61,63).Some statistical techniques have been designed with regulariza tion tricks, such as CCLasso (64) and gCoda (65), and can also be applied to alleviate the sparsity issue (24).For instance, CCLasso refines the lasso algorithm by explicitly factoring in the correlation between the predictor and response based on the fundamental L1 penalty term (64,66).Thus, the robustness and interpretability of microbial associations can be improved by eliminating non-informative taxa.
Regarding individual networks, stability analyses gauge the extent of complex interaction fluctuations within the network (67).Meanwhile, module analysis aims to identify correlated node clusters (modules), shedding light on unique community traits among diverse modules.Techniques such as WGCNA enable the identification of these correlated clusters, the delineation of inter-module connections, and the quantification of module membership (60).Furthermore, an examination of pivotal nodes can uncover biomarkers with integrative significance across the entire network.
When examining multiple networks, identifying shared features becomes pivotal for improved classification and network diagnosis.Califf (68) extensively elucidated precise biomarker definitions and their applications in diagnosis, prediction, and safety assessment (69).Integrating disease and health networks enhances understanding of module transformations, enabling more personalized approaches to disease modulation.Tools such as NetCoMi provide the capacity to detect the differences between networks and identify taxa associated with these variations through joint analysis of disparate networks (70).Likewise, Kuntal et al. (71) introduced NetShift, employing a scoring method to identify driver nodes that quantify shifts and changes within microbial association networks spanning health and disease contexts.These innovative methods aid in disease diagnosis and prognosis by identifying microbial attributes linked to specific diseases.Furthermore, they contribute to predicting the risk of diverse diseases through the identification of crucial microbial interactions and pathways.

Causal network
Causal networks delineate the reciprocal causeandeffect connections between multiple microorganisms, where each node signifies a variable and directed arrows between nodes indicate the causeandeffect relationship or data generation process within microecology (72,73).These networks typify asymmetric associations based on the premise that alterations in one attribute directly or indirectly provoke changes in another, thus underscoring the causal bond between microorganisms.
Knowledge-driven methods shape causal relationships by incorporating expert domain knowledge, literature reviews, and research findings.For example, the knowl edge repositories of the GEMs (74) and Kyoto Encyclopedia of Genes and Genomes (75) serve as valuable resources for knowledge-driven approaches.These resources serve as a priori knowledge that drives the development of causal inference, thus helping us construct the desired causal network framework based on the inferred information.With integrated database resources, CROssBAR forms a knowledge graph of biological knowledge as known information and utilizes knowledge-driven causal networks to enable the causal analysis of multiple biological information (76).The construction of causal networks helps us trace the causes of microecological occurrence and develop ment, thus realizing the regulation of the gut microecological environment.
Data-driven methods involve constructing causal networks based on actual data and eliminating the reliance on prior domain knowledge.Commonly used techniques in data-driven methods are causal discovery algorithms such as probabilistic graphi cal models and causal inference methods.A DAG refers to a directed acyclic graph, a graphical model for causal inference that can represent direct and indirect causal relationships between variables (77).Bayesian networks use the DAG graph model, a widely used causal network generated according to the construction of nonparametric models, and rely on variance analysis of the best least-squares predictions using all information at some point in the past to predict possible outcomes (78).The causal inference approach enhances the readability of the network and reduces the heteroge neity of gut microecology data through causal associations.For example, Howey et al. (79) proposed a method using nearest neighbor estimation combined with a pseudo-Bayesian approach to improve the weighting of network edges, effectively bridging the heterogeneity of the data.These methods automatically learn causal relationships from data and generate models representing causal networks.
Theoretically speaking, the application of a causal network can be conceptually divided into three tiers: observation, intervention, and counterfactual analysis (80).In the initial tier, the causal network is employed to scrutinize the relationships between variables, relying solely on observed microecology data.For instance, causeandeffect analysis has been applied to empirical data to uncover traits such as microorganism stability and resistance to perturbation.In addition, studies indicate that in compar ison to healthy individuals, disease-associated microbiota exhibits diminished modu larity.This reduction in modularity might reflect a functional outcome of decreased microbial diversity in those affected by diseases (81).Advancing to the subsequent tier, the causal network is deployed to evaluate the impacts of deliberate inter ventions or alterations in microbiome variables.Grasping the essential causal links between microbiome components is crucial for comprehending disease mechanisms and formulating appropriate treatment strategies (82).Finally, in the counterfactual context, the causal network allows researchers to investigate hypothetical scenarios and evaluate the potential outcomes if variables were altered.Counterfactual reasoning is crucial for probing causal links and assessing possible repercussions, providing a framework to develop personalized disease treatment strategies (43).Most recently, the use of counterfactual reasoning serves as an aid to improve the accuracy of actual clinical diagnosis (83).

Dynamic network
A dynamic network model portrays the evolution of the network structure and connectivity relationships over time.Compared with static networks, dynamic networks consider the evolutionary process of nodes and edges in the network and have proven invaluable for studying network topology, information transfer, and dynamic properties across distinct timeframes (84).
The gut microbiota network is a dynamic and resilient system constantly affected by internal and external forces (85).When observed at the microscopic scale, notewor thy shifts can occur in the microbial community over months, weeks, and even days.This dynamic network is primarily driven by external factors and provides insights into the ecosystem-level distribution of microbial populations and nutrients (30).To model dynamic networks in the context of microbial ecosystems, two approaches can be used: mechanistic and data-driven methods.
Mechanistic modeling approaches for dynamic microbial communities often draw inspiration from established techniques used in population ecology, such as generalized Lotka (gLV) equations and other mathematical frameworks (86).These models incorpo rate factors, such as species growth rates, interspecies interactions, and environmental influences, to simulate the dynamics of microbial populations over time (87).Typically, plain correlation analysis using local similarity analysis or Markov loops is employed to analyze data spanning an entire duration of gut microecology (88).However, a more sophisticated approach involves deriving delayed networks from temporal correlation data, which enables a more effective dynamic network analysis.Using methods such as Granger-Lasso and dynamic time warping, an ensemble dynamic network can predict which taxa are more influential under different conditions (89).Although gLV model ing has proven useful in studying the stability of temporal bacterial communities, its applicability is limited when dealing with temporally sparse and non-uniform highdimensional microbiome time series data.
Data-driven tools such as probabilistic graphical models offer powerful capabilities for modeling dynamic processes and discovering causal interactions in microbiome data.Among them, hidden Markov models (HMMs), Kalman filters, and dynamic Bayesian networks (DBNs) are widely employed in microbiome research.For example, Umibato, an unsupervised learning-based inference for microbial interactions, combined HMMs with Gaussian process regression to estimate growth rates and interaction networks (90).HMMs are generally suitable for discrete latent status representation.Unlike the Kalman filter, which is primarily designed for continuous state estimation, and HMMs, which are suited for discrete latent status representation, the DBN can handle both continuous and discrete variables, making it more flexible and versatile.For example, the DBN was developed to capture causal relationships among microbial taxa, clinical states, and population-related factors (91).Integrating data-driven, dynamic network-based techniques with other methodologies can enhance the complementarity of sparsity and emotional attributes, resulting in a better fit for gut microecological data.
Dynamic networks serve as a powerful tool for comprehending interaction pat terns among diverse microorganisms.Local similarity analysis (LSA) ( 92) is a popular method aimed at studying the temporal changes in microbial community composition by inferring significant associations between operational taxonomic units (OTUs) and between OTUs and their hosts.Building upon LSA, Faust and colleagues (10) introduced a time-varying network construction technique to infer temporal changes in microbial interactions.This framework can be further integrated with dynamic Bayesian networks to establish a time-varying DBN approach.Analyzing the dynamic network of the microbiome offers the potential to predict changes like the microbial network.Pet tersen et al. (93) explored the significant difference between K-selection (via continuous feeding) and R-selection (via pulsed feeding) utilizing dynamic data network modularity analysis and proposed that clustering may be a similar ecological niche preference among the involved bacteria.The impact of different intervention strategies on the pattern and the role of the microbiome can be assessed using micro-ecological dynamic network analysis.Li et al. (94) employed longitudinal multitemporal data to identify the disease transition process in Alzheimer's disease mice.This analysis facilitated the identification of an optimal intervention window for disease management (95).

Multi-omics network
The construction of multi-omics networks offers a multifaceted approach to delve into gut microecology, and exploring the correlations between diverse histologies will further enrich our research (96).Multiomics data on microbiomes include acquiring multiple types of high-dimensional biological taxa from microbiome samples and their environ ments and hosts, such as 16S rRNA, metagenomics, metatranscriptomics, and metabolo mics.
Aggregating data from disparate sources into a federated framework guided by correlation information provides a panoramic perspective on crucial units.By forming associations between multiple histologies into heterogeneous networks, this process allows us to extract richer and more integrated feature representations, thus improving the feature representation.Tadaka et al. (97) created jMorp, a database with much more data, by correlating and analyzing multi-omics data between genomes, metabolomes, and proteomes.In addition to static network fusion, dynamic network fusion methods have also been introduced.For example, integrating multi-omics time-series microbiome data to construct dynamic Bayesian networks is common in multi-omics networks (98).DBNs are adept tools for amalgamating multiomics information to dynamically monitor the ever-evolving gut microecological environments through Markov cycles.This approach enables the discernment of causal associations in time-series data by explicitly capturing specific relationships and overarching trends within the data (99).Integrating multiple omics into network representations can help maximize microbial community classification and functional interpretation, providing valuable insights for practical applications (100).Multi-omics networks offer diverse utilities, facilitating the indepth investigation of disease mechanisms and biomarker discovery.Additionally, they serve as powerful tools for predicting drug-target associations and aid in developing therapeutic drugs.Furthermore, a joint analysis of multiple omics levels enables uncovering the complex regulatory mechanisms within an organism.
Correlating multi-omics data with disease information yields enhanced precision in disease prediction and the discovery of biomarkers.Mikaeloff et al. (101) performed multi-omics analysis on HIV-infected patients with different clinical characteristics, revealing metabolic risk profiles among those under treatment.The construction of multi-omics networks offers a pathway to predicting drug responses, preempting side effects, refining drug design, and devising personalized treatment strategies.The integration of multi-omics data for collective analysis enhances our understanding of gut microecology's health status.Ruiz-Perez et al. ( 102) created a pipeline, PALM, for longitudinal multi-omics data analysis.PALM employs DBN to construct a unified model, addressing sampling rate disparities and enhancing regulatory mechanism interpretabil ity.As multi-omics data and machine learning intertwine more intricately, biological researchers access improved data processing and analysis tools, facilitating holistic insights and discoveries (Table 1).

ANALYSIS OF NETWORK IN MICROECOLOGY
We reviewed diverse network types and their distinctive methodologies and applications in the previous section.Each network variant serves a distinct purpose and is tailored to address specific challenges in different domains.However, analyzing these networks from a network perspective is equally important.An array of network analysis metrics, encompassing degree centrality, clustering coefficients, and betweenness centrality, were used to discern microbial community structures, pivotal nodes, and modular insights (107).Integrating various networks for microbiota network analysis can advance our understanding of diseases and help identify targeted improvements in treatment based on host and microbiota composition (108) (Table 2).

Structure of the network: topology classification
Topological analysis of the gut microbiota entails exploring the spatial distribution and interaction relationships among gut microbes.This process reveals the spatial organization of gut microbial communities by analyzing microbial diversity, commun ity composition, and interactions via high-throughput sequencing techniques (109).Network topology is assumed to be pivotal for influencing network resilience, with random and scale-free networks being the most representative topologies.In network theory, it has been widely postulated that many complex biomedical networks exhibit a scale-free topology.In such networks, most nodes have a modest number of edges, while a small subset of nodes have numerous connections.This scale-free organiza tion facilitates the robustness of microbial ecosystems in the face of disruptions (110).Specifically, modules are defined as highly connected groups of nodes relatively isolated from others.Network degree centrality (DC) serves as a metric for gauging the promi nence of nodes within a network and is quantified by the number of direct connections to other nodes.The higher the node degree, the higher its centrality in the network.This indicates that it is directly connected to more nodes and extensively influences the spread and interaction of information throughout the network.Overall, network topology analysis is a potent avenue for investigating interactions among microbial strains, unraveling ecological dynamics among diverse microbial communities, and unveiling patterns of symbiosis and competition (111).

Community closeness: modularity specificity
The network clustering coefficient measures the degree to which the adjacent nodes are mutually interconnected.This coefficient holds pivotal significance in comprehending the dynamics of the gut microbiome and is associated with various aspects of gut health, including inflammation, immunity, and metabolic disorders.A lower clustering coefficient signified less tightly bound connections within the microbial community, potentially indicating an ecological imbalance or other gut-related health concerns.Conversely, a higher clustering coefficient indicated that the microbial community connections were more tightly linked, possibly related to a healthy gut state.
In the realm of network topology and modular analysis, Baldassano discovered distinctions in microbiota structure between individuals with IBD and healthy counter parts (112).Meanwhile, Srivastava et al. (113) introduced EviMass to validate hypotheses arising from microbiome research, facilitating interactive querying of microbial-microbial and disease-microbial associations within a processed backend database.For example, Xiao et al. (103) introduced NetMoss, a method that evaluates shifts within microbial network modules to pinpoint robust biomarkers associated with multiple diseases.MicNet calculates diverse modular properties, encompassing network density, aver age degree, degree standard deviation, positive-negative relationship ratio, clustering coefficient, and modularity (114).This modularization analysis aids in comprehending network systems within a broader metabolic health context.

Finding the key players in the network: key-nodes analysis
Network centrality measures the extent to which a node mediates the movement of information or resources between its peers in a network.Betweenness centrality (BC) measures the extent to which a particular node serves as a "bridge" between other nodes in the network.For each node in the network, the betweenness centrality is the aggregate of the instances in which that node appears on the closest path among the

Degree
The degree represents the number of connections of nodes, while the degree of an undirected graph only has the concept of degree, and the degree of a directed graph consists of two components: in degree and out degree.

Construction Adjacency matrix
The adjacency matrix is a matrix diagram that characterizes the nodes and edges in an image, in which two nodes with edges are labeled as 1, otherwise as 0.

Closeness centrality
CC i = n − 1 ∑ i ≠ j dij Closeness centrality uses the total distance of the target node from other nodes to express the centrality of that node.

Betweenness centrality
Betweenness centrality is equal to the quotient of the shortest path through the node and the shortest path from the node to the other nodes, indicating the degree of betweenness of the node as a bridge.
other nodes in the network.Closeness centrality (CC) uses the total distance of the target node from other nodes to express the centrality of that node.These metrics help to identify key nodes that significantly affect the network structure, and node importance can be calculated using a sparse matrix's eigenvectors or a layer-by-layer cycle subtrac ted from the number of common circles to find the core nodes.Key nodes have typically been considered biomarkers in microecology due to the importance of network centrality.In analyzing gut microbiota networks, key bacterial species can be used as biomarkers to identify various gut diseases and facilitate the treatment and maintenance of disease and health states.Long-term dietary regulation can help alleviate diseases and promote health education (68), and analysis of the gut microbiota can be used as part of personalized treatment strategies in the future (115).Fecal microbiota transplantation using healthy donor fecal microbiota can alter the composition of the human microbiota in diseases and can be used to alleviate and treat serious diseases.

CHALLENGES OF MICROBIOME NETWORK
Clustering and analyzing the extensive volume of gut microbial data open the door for deeper gut microbiome exploration.Employing constructed networks to stream line microbiological investigations can enhance our understanding of the microbiome and refine our approach to deciphering intricate phenomena within gut microecology (116).In the subsequent discussion, we offer a detailed examination of microecological network challenges, addressing three key facets: data sources, network construction, and performance evaluation.

Challenges in network integration and batch effect removal
Addressing microbiome data heterogeneity is a paramount challenge in constructing microecological networks and microbiome analyses and presents a formidable test for statistical methodologies governing network inference.Despite the pronounced uniqueness of the gut microecological network structure within each sample, network integration analysis can provide insights that can help find targets and driver nodes of consistent robustness (103).As the volume of network data grows, it enhances our ability to grasp network control and unearth shared regulatory patterns amidst individual variability (117).However, network integration analysis also introduces batch effects that can potentially obscure correlations within the network.Consequently, it is imperative to conduct batch-removal operations before network construction.An essential considera tion during this process is retaining pertinent information about sample distinctions while executing effective batch-removal strategies, thereby maintaining the intrinsic characteristics of each sample (118).

The challenge of spurious correlations and causal inference
In a contemporary exploration of gut microecological networks, correlation is the preferred choice for network construction by many scholars.However, correlation is neither necessary nor sufficient for establishing causal relationships.Therefore, the inference of causality from correlations entails inherent risks, particularly in the context of non-linear and pervasively dynamic biological systems.In contrast to other correlated analyses, the causal theory holds promise for constructing dynamic models of microbial ecosystems and identifying pivotal species (119,120).
Moreover, the application of causal networks in gut microecology has some limitations.Constructing these networks encounters challenges in representation due to the intricate interactions within the gut microecology.A notable example is the potential expansion of the network owing to the customization of gut microorganisms.In tandem with this, the challenge of causal inference arises, stemming from the absence of a comprehensive theory for analyzing crucial and driving nodes within gut microeco logical data.Consequently, network inference algorithms may not consistently pinpoint nodes accurately, leaving uncertainty regarding the network's representativeness of the ecosystem and the credibility of the conclusions drawn from the network analy sis.Furthermore, this intricate web of mutual causality deviates from the conceptual prerequisites of a directed acyclic graph, which is the core tenet of a causal network model.

The challenge in mechanistic modeling and data-driven integration
Most state-of-the-art data-driven methods suffer from a lack of biological inter pretability, often resembling "black boxes."This opacity imitates our ability to gain insights into potential biomedical applications from a biological perspective.Moreover, mapping intricate node associations within a network to the realworld dynamics of microbes is complicated.Network topology offers only limited characterization of gut microbes, and the network's transformation patterns and driving nodes are challenging to study in a manner that perfectly aligns with actual scenarios.In contrast, mechanism or knowledge-driven models have perfect interpretability, and because of a series of constraints, we can better start from a micro-level perspective.One promising approach involves amalgamating the strengths of data-driven performance using knowledge-driven interpretations (76,121).For example, with the current literature reports, a network of gut microbes and metabolites is generated, and the network information is analyzed (122).This fusion enables a more holistic exploration of the enigmas within gut microecology, uniting the macro-and microdomains.Through this integrated lens, we better understood the methods that propel individuals from disease toward health.

Challenges in network controllability and drive feasibility
Realizing network controllability in a complex gut microecological network structure and the joint analysis of dietary networks can help us implement better dietary guidelines and disease interventions for disease populations.The sparse non-uniform network that appears in many real complex systems is the most difficult to control, and the gut microecological data network is a sparse scale-free network that simple driving nodes cannot control (123).The concept of driving species diverges from that of keystones and key species.Although employing kinetic and intervention models can simplify investigations, an idealized operational context introduces formidable challenges to model robustness.Identifying the driving species subsets within the gut microecological network could significantly bolster the efficacy of dietary interventions aimed at gut health improvement (124).Mining key nodes in sparse scale-free networks is time-con suming and difficult, and the increase in nodes directly doubles the analysis time (125).Consequently, reducing the driving node set while ensuring network controllability is a pressing challenge in analyzing gut microecological networks.

The challenge of performance evaluation
Due to the scarcity of extensive biological comparative data, the assessment of gut microecological networks is still primarily simulated using computers.There are significant questions regarding the accuracy of the data source and the completeness of the interactions.As a result, the predicted interactions were either incorrect or not observed.A priori knowledge is valuable for assessing the network tool performance, although it does not definitively ascertain the accuracy of network inference tools (126).Most of the data currently used are experimental; therefore, the problem of the need for accurate and stable multi-omics data must be addressed.In addition, the feasibility of using kinetic synthetic data sets has been demonstrated; however, there are challenges in synthetic data sets, such as the generalizability of microbial kinetics for different states, the difficulty of obtaining steady-state samples, and whether the size of the training samples can be guaranteed.Therefore, researchers urgently need a network performance evaluation index to characterize actual accuracy better.

DISCUSSION
The gut microecological environment, shaped by dietary choices, human interactions, and environmental factors, constitutes an intricate microbial community that signif icantly impacts the overall health of the human organism.Extensive exploration of gut microecological data has led to a surge in research, yielding an increasing array of solutions for both intrinsic and extrinsic data characterization.In the quest for health, individuals commonly resort to microecological regulation, often utilizing dietary modifications as the most accessible and amendable factor.Advanced network analysis methods serve as a bridge between traditional mechanistic modeling and machine learning approaches, integrating biological interpretability with the sophisti cated processing power needed for complex data.The analysis approach facilitates a more in-depth examination of network structure and community characteris tics while emphasizing key players facilitates the study of crucial markers.This conver gence presents a novel analytical solution for comprehending intestinal microecology and establishes a theoretical foundation for personalized dietary adjustments.
Admittedly, we acknowledge that network analysis methods have inherent limita tions.Co-occurrence networks introduce compositional biases by using paired data.Correlation metrics cannot distinguish between direct and indirect associations and produce erroneous predictions of the relationships between microbial taxa.Construct ing causal networks relies on assuming explicit causal associations among microflora.Constructing dynamic networks proves valuable in identifying the equilibrium state of a colony and studying the adaptability of microbiota to external microbial challenges.Nevertheless, limitations emerge when interactions are weak or when spatial/temporal resolution falls short of capturing ecological dynamics.Multi-omics networks provide a comprehensive analysis of gut microecology, yet the unresolved question pertains to whether data or epigenomics contribute more to the integration of multidimensional data.Multi-omics networks can introduce interstratum biases and batch effects, which pose computational difficulties.
Therefore, researchers can develop and assess interactivity-driven network dynamic tests and apply them to microbial network inferences, which will prompt the creation of novel computational tools and mathematical models.A rigorous comparison of various batch-removal techniques within network inference tools is pivotal for identify ing effective blends for robust network construction.As the field advances, tackling these complexities will be vital for unlocking the full potential of microbial network analyses.Data-driven and knowledge-driven network analysis-based approaches are about to usher in a new era of gut microecology.Co-occurrence networks constructed by correlation analysis methods ought to take nonlinearities into account more frequently.Knowledge graphs as causal inference methods for a priori knowledge should also take a bigger share in network analysis.The third step of the causal ladder calls for us to develop more personalized counterfactual inference schemes.The development of dynamic networks will be contingent on the generation of longitudinal cohorts, and more research teams are needed to fill this data gap.Incomplete multi-omics data should prompt further development in multi-omics, and studies integrating nucleotide variant fragments could enhance the network analysis of gut microecology to better consider individual differences.

FIG 1
FIG 1 Overview of traditional mechanistic modeling and machine learning approaches for gut microecology data.(a) Dietary intakes, social interpersonal, and environmental factors furnish a minimum source of nutrients and bacterial strains for gut microecology.(b) Within the limits of basal kinetics, strains can maximize their species ranges in the gut environment.(c) Mechanistic modeling uses dynamic flux balance analysis to calculate the amount of basal metabolism required by the organism as a means of simulating normal metabolic activity in the body.(d) Machine learning by collecting assorted data regarding the microecology of the gut.(e) Tackling challenging gut issues across intractable problems using three approaches to machine learning: unsupervised learning, supervised learning, and reinforcement learning.

FIG 2
FIG2 An overview of the methodologies for the construction and application of the four main types of networks discussed in this paper.Methods of construction and application of the identical types of networks are in clockwise order.

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networks are the norm for intestinal microecological networks, i.e., the nodes obey a power-law distribution, most of them have few edges, and only a few intestinal microorganisms are closely associated with other strains of bacteria.ModularityModularity is the degree to which nodes in a network come together to form clusters that can characterize the community properties of gut microbes.TopologyTopology refers to the way the edges are connected and can help us find the key nodes in the network in the intestinal Degree centrality indicates the degree of normalization of the number of neighboring nodes of a node, where N degree refers to the number of neighboring nodes and n indicates the number of nodes.

TABLE 1
Overview of the microbial association network approach (Continued on next page)

TABLE 1
Overview of the microbial association network approach (Continued)

TABLE 2
Summary of concepts and formulas used smallest building blocks of the graph, and each node in the flora network is a gut microbe.EdgeEdges are relationships between nodes, and edges in a colony network indicate associations between microorganisms.