Table 1 Definition of several social network metrics that are commonly used in SNA studies about environmental issues and what the metrics imply for environmental governance and management and the use of online hyperlink data

Node count

The number of nodes in a network, which indicates network size.

Knowing the number of actors for a given environmental problem is a basic and important variable to ensure policies and solutions fit the situation at hand (Ostrom 2009). Implications are contextual to the specific issue or problem.

Edge count

The number of relationships among nodes in the network.

The number and distribution of edges in a network forms the foundation of a network perspective for environmental governance and sustainability (Bodin and Crona 2009; Bodin 2017). See the following definitions for implications.

Components

Subgroups within a network that are weakly connected or disconnected from each other. The number and size of components indicates how fragmented a network is.

Information and resources can travel faster in highly connected networks and poorly or not at all among fragmented components; however, hyper-connectivity can stifle innovation or foster the spread of undesirable information (Bodin et al. 2006; Vargas et al. 2020).

Median in-degree

Median number of incoming edges for a given node. In-degree assumes that edges have a direction, e.g., node A sends information to node B, as opposed to node A and B just sharing information with an undefined direction. In a hyperlink network, in-degree of node A is the number of hyperlinks going from other web-pages (i.e., other nodes) to node A.

Highly connected organizations can be influential and act as information or resource hubs; though maintaining many relationships can be taxing if lacking adequate resources (Bodin and Crona 2009). When hyperlinks represent positive affiliations among organizations (Hayes and Scott 2018) they can be interpreted as described above; however, hyperlinks might also represent negative motivations (Park and Thelwall 2006) and thus, interpretation of in-degree values can be contextual. These metrics also indicate network connectivity.

Network density

The proportion of total possible edges that exists in the network. Density ranges from 0 to 1, where 1 means all possible edges are present and 0 means none are present.

Higher density facilitates transmission of knowledge and resources, but can stifle innovation if ideas become homogeneous (Janssen et al. 2006). Dense networks tend to support cooperation and trust building (Berardo and Scholz 2010).

Network centralization

How edges in a network are distributed. Centralization ranges from 0, where all edges are distributed equally among the nodes, to 1, where a single node holds the network together.

High centralization can be efficient in settings with high levels of trust and agreement (Berardo and Scholz 2010; McAllister et al. 2017), but can also lead to, or result from, power imbalance in the absence of trust and agreement (Ernstson et al 2008; Bodin and Crona 2009). Structurally, centralized networks can be fragmented if central nodes are lost (Janssen et al 2006).

Graph diameter

The greatest distance (i.e., number of edges) between any pair of nodes. (For a disconnected network, diameter is calculated for the largest component).

Diameter indicates the potential distance that information or material might have to travel to get from one side of a network to another. All other variables being equal (e.g., levels of trust, shared objectives, etc.), shorter distances facilitate the flow of information and materials (McAllister et al. 2017).

Reciprocity

The percentage of edges that are reciprocated among two nodes; e.g., node A has a hyperlink to node B and B has a hyperlink back to A.

Reciprocity often indicates a stronger relationship. In collaborative environmental governance settings, reciprocity can reinforce trust building and reduce the risk of defection in high-risk collaborative processes (Berardo and Scholz 2010).