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# Number of Nodes and Edges

These two metrics count all the nodes or edges, respectively, in the network.
Since it is not concerned with individual nodes, it is of global scope.
It has been proposed by Smith et al. (2009).

## Calculation

As a reminder the definition of the graph G with $$ G = (V,E), $$
where $V$ is the set of nodes and $E$ is the set of edges.
The number of vertices is calculated via the cardinality of the vertices set of the graph $G$:
$$ N_v(G) = |V|. $$

The number of edges is calculated via the cardinality of the edge set of the graph $G$:
$$ N_e(G) = |E|. $$

Note: On the page for the degree metric the network size has also been named $g$.
This is equal to the number of nodes $N_v$.

## Interpretation

The number of nodes and edges directly represent the size of the network.
While a high number of nodes equals a big userbase, a high count of edges represents high activity and interactions between users.
The number of edges overlaps with the Enterprise Social Network metric *Messages created* and the total degree of the network.
Viol et al. (2016) relate a high level of activity with engaging discussions and the sharing of ideas.
According to Steinfield et al. (2009) a high number of interactions and activity lead to bonding relationships and strong ties.
These strong ties are the source Bonding Social Capital.
Based on the Bonding Social Capital, it can be assumed that the network facilitates effective collaboration.
It enables the sharing ideas and solving of problems in a collaborative manner.

However, a low number of nodes and edges indicates a low level of engagement and a lack of communication.
To get reasonable analysis results, a minimum size of the network is required.