Network density

For any set of nodes in a network, there is a finite number of relationships possible. Each node can serve as the source or the target of a relationship with every other node. Consider a network consisting of the three nodes A, B, and C. The following table lists all possible directed relationships between the nodes.

Table 1. Possible directed relationships for three nodes
Source Target
A B
A C
B A
B C
C A
C B

Each node is the source of a relationship with the other two nodes. However, in practice, all possible relationships may not actually be present. Some nodes may not have any direct relationship with other nodes. In addition, some directed relationships may not be reciprocated.

The density statistic represents the proportion of possible relationships in the network that are actually present. The value ranges from 0 to 1, with the lower limit corresponding to networks with no relationships and the upper limit representing networks with all possible relationships. The closer the value is to 1, the more dense is the network and the more cohesive are the nodes in the network.

Information in dense networks can flow more easily than information in sparse networks. The "Sparse and dense networks" table displays two networks consisting of seven nodes. The sparse network includes only seven of the possible 42 relationships between the nodes, yielding a density of 0.17. The dense network, on the other hand, contains all possible relationships and has a density of 1.0.

Table 2. Sparse and dense networks
Sparse network Dense network
Seven node network with each node acting as a source for one relationship and also as a target for one relationship.
Seven node network with each node acting as a source and a target in relationships with all other nodes.

In the sparse network, for information to flow from node A to node G, it must pass through five other nodes. In contrast, in the dense network, the information can go directly from node A to node G.