Table 1 Network topological metrics and network properties used in microbial network stability studies, with references. The majority of the listed metrics can be calculated in the igraph package [72]. For calculating network robustness, we suggest the packages brainGraph [73] or NetSwan [https://cran.r-project.org/web/packages/NetSwan/index.html]

Average path length

The average shortest path (number of edges) between all pairs of nodes

[23, 26]

[39]

Betweenness centrality

Of a node, frequently occurring on the shortest path between all pairs of nodes

[23]

[20, 24, 74]

Connectivity

A measurement of how many connections are formed between nodes in a network

[18, 26]

[20, 25, 39, 58, 75]

Clustering coefficient/transitivity

The degree to which nodes in a network cluster together

[26, 39, 71, 76]

[20, 58]

Degree

The number of edges connected to a node

[76, 77]

[20, 58, 75]

Linkage density

The ratio of realized network edges to the total possible number of edges

[18, 24]

[58, 75]

Modularity

The partitioning within network communities into distinct and highly connected subcommunities

[18,19,20, 23,24,25, 39, 58, 77,78,79]

[75]

Network size

The total numbers of nodes in a network

[24, 39, 76]

Vulnerability

The maximum impact of a node’s removal on network efficiency

[39, 77]

Cohesion

A measurement of the abundance-weighted positive and negative correlations in a network, standardized by a null model. Or more simply, the ratio of negative to positive edges

[18, 19, 23, 24, 77, 79]

[20, 21, 26, 39, 48, 58, 75]

Complexity

Various definitions (see Table 2)

[18, 19, 21, 26, 39, 77]

[25, 58, 75]

Fragmentation

The number of disconnected subgraphs network divided by the total number of nodes, upon stepwise node removal

[22, 24]

Inter-kingdom associations

Networks involving interactions between microorganisms from different kingdoms (e.g., fungi with bacteria)

[13, 23]

[48]

Keystone taxa

A taxon with disproportionate importance on ecosystem function and stability in relation to its biomass. In networks, nodes with high betweenness centrality and degree or high connectivity within and among modules

[24, 39, 39, 76, 77, 79]

Robustness

Networks able to resist collapse upon targeted node removal

[13, 22, 23, 25, 39, 48, 58, 75,76,77]