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Fabbrini et al. Microbiome Res Rep 2023;2:25 https://dx.doi.org/10.20517/mrr.2023.25 Page 3 of 18

climate change scenario, it could contribute to our better life on earth.

NETWORK APPROACHES FOR MICROBIOME ANALYSIS
Considering all the aforementioned information, it becomes evident that understanding all microbiome
interactions, whether related to health, disease, global change, or other conditions, is of paramount
importance. A useful approach to better dissect these interactions and the high microbiome complexity in
terms of compositional variability, dynamic nature of both structure and function, and ability to self-
reproduce and self-organize is represented by network theory. In recent decades, various tools have been
developed for different types of networks and are used nowadays in several applications by biologists,
mathematicians, social scientists, and computer scientists exploring interactions between entities. For
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example, they have been applied in infectious disease research , social interaction analysis applied to
marketing and political science , analysis of neuroimaging data , information flow through the
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internet , and genomics data analysis . Recently, it has emerged that the microbiome also falls within the
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applicability of network theory because the architectural features of networks appear to be universal in any
complex system [4,28] . This universality has made it possible to use tools and theories developed in well-
studied non-biological systems to characterize the intricate relationships that define the high complexity of
microbial interactions, such as mutualism, synergism, commensalism, or parasitism . To date, several
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methods have been used in microbiome studies to construct ecological networks, ranging from simple
pairwise Pearson or Spearman correlation measures to more complex multiple regression and Gaussian
graphical models. The main differences between these methods are efficiency, accuracy, speed, and
computational requirements. To ensure a comprehensive understanding, it is important to first describe the
main components that make up a network before proceeding to explain these methods in detail.

Networks, also called graphs, are defined as a set of mathematical concepts for describing and examining
the relationships between system entities. Most biological systems can be described as networks where the
nodes can be, for example, metabolites in a metabolic network, genes or regulators in a gene regulatory
network, and microbial taxa in a microbiome network. The nodes represent the entities, and the edges are
plotted to visually depict the interactions that connect these entities. These interactions can be either
negative or positive, forming the graphical visualization of the relationships between the nodes. These
ecological interactions between one microorganism and another can be described by both the weight and
the sign of the interaction [Figure 1]. Based on the characteristics of the interactions, the networks are called
“weighted”, if it is possible to quantify and represent the strength of the interaction, and “signed” if both
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positive and negative values are represented . If the relationships are weighted, signed, and have a
direction, they can be defined in terms of a source and a target, so the network is classified as “directed”.
However, regarding microbiome analysis, generally, it is impossible to define the direction of the
interaction, so we generally talk about an “undirected” network.

Once the networks have been built, based on the data and the different methods, there are various
topological or ecological parameters useful for describing and analyzing the overall structure of the system.
For example, there are three main metrics used to define node characteristics [ Box 1]: 1) “degree”, defined
as the number of correlations of a node with the others; 2) “betweenness”, defined as the shortest path
between each pair of nodes in the network; and 3) “closeness”, calculated as the reciprocal of the sum of the
distances from a given node to all reachable nodes . Based on these parameters, it is possible to define
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other topological properties of a network such as “hub nodes”, “keystone nodes” and “network modules”, all
described in Box 1 as well and shown in Figure 2. Regarding network ecological parameters, several network
properties have been widely used to predict network stability in a lot of field studies investigating, for
example, plant-pollinator networks and food webs , and have recently been applied in microbiome
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