Like other kinds of statistical procedures, network analysis provides graphical and numeric output. Network graphics are often referred to as “maps” because they show how the players in the network are linked together. Understanding how the numbers drive the graphics will help you to understand what is going on with your network. As you read the terms below, consider how you might use them to answer questions you have about your own network.
Partners are represented in network maps as a shape – usually circles or squares. These are often called “nodes.” Different partner types can be shown as different colors or shapes (i.e. lead agency in green, grantees in blue, etc.) They can be sized according to things like the number of other partners they’re connected to or their ability to link partners together. Nodes can represent individual people, or many individuals can be collapsed into a single organizational node.
Lines between partners indicate that they are connected in some way, and these connections can take a variety of forms.
Directed: These kinds of relationships are often depicted with an arrow indicating that something goes from one partner to another. This can include actual transfers, such as money or patient referrals. It can also indicate relationships that are not inherently reciprocal. An organization can nominate the work of the city mayor’s office as being highly important to their own work, but the mayor’s office may not even be aware of that particular organization.
Non-directed: These kinds of relationships are depicted with a regular line and are inherently reciprocal. If the YMCA says they are in contact with the Red Cross on a quarterly basis, then the Red Cross would likely say the same about their frequency of contact with the YMCA.
Valued: Sometimes the strength of a relationship can be rated on a scale, such as how often communication takes place or how strong a collaborative relationship is. If a network is small enough, displaying strong relationships with thicker lines can be informative.
Non-valued: (Also known as “binary” or “dichotomous”.) Other relationships are more cut-and-dry, and they are either present or absent. You’re either aware of another person or you’re not.
With large networks, it’s often the case that a valued relationship is dichotomized at a chosen cut-off point and displayed as if it were non-valued with uniform line thicknesses. Web-based interactive applications allow users to view the network at the value of their choosing.
Node-Level Descriptive Statistics
Network analysis can provide you with numbers describing each partner in the network. These numbers are often used to determine the size of the nodes in a network graph. A few of the most common ones are:
Degree or Degree Centrality is the number of connections a node has. For directed networks, in-degree is the number of incoming connections, e.g. the number of foundations an organization receives funding from. Out-degree is the number of outgoing connections, e.g., the number of organizations a foundation awards funding to. We can see how in- and out-degree would be very different for the same organization in relationships that are not reciprocal. Sizing by in-degree highlights nodes that play a large receiving role, while sizing by out-degree highlights nodes that play a large provider role.
For non-directed networks, sizing by degree highlights nodes that can reach many organizations directly.
Betweenness Centrality is, loosely speaking, the extent to which a node connects other nodes that are not otherwise connected.
High degree and high betweenness usually coincide, but not always. In the example below, the red node is only connected to two others so it has a very low degree, but every node on the the left that wants to exchange with any node on the right, and vice-versa, has to go through the red node, so it has very high betweenness. Nodes with high betweenness have a great deal of control over exchange in the network and may highlight bottlenecks, particularly if they have low degree or low capacity in other ways.
Brokerage is similar to betweenness in that nodes connect otherwise unconnected nodes, with the additional concept of taking the category of nodes into account. Several roles exist, depending on the configuration:
Consultants are of a different category than the nodes they connect, but the unconnected nodes are of the same category. Sizing by consultant role also highlights nodes that can bring together nodes from the same group, but a group that they themselves are not a part of.
Liaisons are of a different category than the nodes they connect, and the unconnected nodes are also from different categories. Sizing by liaison role highlights nodes that can bring together nodes from different groups that they themselves are also not a part of.
In directed relationships, Representatives take something from a node from the same category and bring it to a node from a different category, while Gatekeepers take something from a node from a different category and bring it to a node from the same category. In non-directed relationships, there is no difference between representatives and gatekeepers: they connect a node from their own category to a node from a different category. Sizing by representative or gatekeeper role highlights nodes that can bring together nodes from their own group and a different group.
Network-Level Descriptive Statistics
In addition to node-level numbers, network analysis can provide numbers that describe the network as a whole.
Average Degree is the average number of connections per node. Density is the percent of all possible links that actually exist. Both of these indicate the level of connectivity in the network.
Degree Centralization indicates the extent to which the network has one or a few nodes that have a large number of connections. Betweenness Centralization indicates the extent to which the network has one or a few nodes that keep the network connected. Both types of centralization are highest in a “star” type network, where one node is connected to all of the others, but all of the others are only connected to the central node. Centralization is lowest when the network is saturated: all of the nodes are connected to all of the other nodes.
To demonstrate the difference between degree and betweenness centralization, consider the first network below, which has both high degree (.545) and betweenness (.416) centralizations. The network has several “pendants,” or nodes that are connected to the network by only one link. The two blue nodes responsible for connecting them to the network have high betweenness because without them, the pendants would otherwise be “isolates” – completely disconnected from the network. These two nodes also happen to have the greatest number of connections in the network.
Conversely, the next network still has high degree centralization (.411) but low betweenness centralization (.178). Degree centralization is high because a few nodes are highly connected, with up to 47 connections. Betweenness centralization is low because the network is relatively cohesive; no one node is responsible for holding things together, and betweenness centrality tops out at .13 (on a 0-1 scale).
The “ideal” level of centralization depends on the context and what the partners are doing. Highly centralized networks can be very efficient, with a few central nodes able to reach others directly with little redundancy. They can also be sensitive to disconnection; if several nodes are dependent on a single hub and that hub experiences a failure, the dependent nodes will be disconnected from the rest of the network.
Modularity is the extent to which connections happen between the same kinds of nodes more often. Networks with high modularity have more connections between the same types of nodes and few cross-type connections, whereas networks with low modularity are less siloed.
Modularity is useful for tracking change in partnerships over time, particularly if one is interested in moving to a more (or less) diversified structure.