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# Graph Density

Graph density describes how closely knit the network is connected.
The number of edges in the graph are compared to the maximum possible number of edges in the graph.
Therefore it is of global scope.
This metric was proposed by Smith et al. (2009) and the calculation is based on Wasserman et al. (1994).

## Calculation

Let $g = |V|$ be the network size or the number of nodes in the graph.
With loops being excluded this leads to the maximum number of possible undirected edges:
$$ e_{max} = g*(g-1)/2. $$

For a network with directed edges the value needs to be doubled as there can be two edges between a pair of nodes:
$$ e_{max} = g*(g-1). $$

The density is the ratio of the number of existing edges to the number of possible edges:
$$ dens = \frac{|E|}{e_{max}} = \frac{|E|}{g*(g-1)}. $$

The value ranges from 0, which is an empty graph to 1, which is a complete graph with all possible edges present.

## Interpretation

The graph density describes how closely knit the relationships in the network are.
It is directly related to Coleman's (1988) closure theory.
A cohesive group has a common ground and understanding (Burt, 2001) and is able to effectively collaborate.
The dense network facilitates strong ties between the actors in the network and establishes Bonding Social Capital.
Provided by the Social Capital and the strongly tied relationships is a sustained solidarity and trust within the group (Coleman, 1990).
This enables long-term project success and commitment to the organisation (Singh et al., 2011; Scott, 2012).
A low density shows a lack of cohesion in the network, and in therefore a lack of Bonding Social Capital.
The users are not interacting on a regular basis in the network.