Hubs and bridge nodes in an association network: meaning and application

You have mapped the association network around a choice and see dozens of associations with lines between them. Which of them deserve the most attention in your communication? Often it is not the most striking associations, but the nodes that hold a central or connecting position in the network.

In Neurofactor's working definition, a hub is a node with many connections and high total connection strength, which therefore colours the meaning of much of the association network. A bridge node is an association that appears in, or connects to, several clusters or themes, so it can touch different themes at once.

Both terms describe a position in the network, not how often an association is mentioned or how positive it is. They are working concepts using network-science calculations: the outcome depends on how you build the network.

In an association network, associations are the nodes and the links between them are connections. Other articles cover properties of a single association: how firmly it is tied to the choice (association strength) and how quickly it comes to mind (salience). Groups of related associations are called association clusters.

This article covers something else: the position an association holds in the network. An inconspicuous association can still connect many others. The distinction between primary and secondary associations describes layers in the network; hubs and bridge nodes describe positions. The two classifications do not automatically coincide.

In network science, a hub is a node with exceptionally many connections. Neurofactor uses a stricter working definition: a hub has both many connections and a high total connection strength. In network terms, these are degree (the number of connections) and strength (the sum of their weights).

Why both? Opsahl, Agneessens and Skvoretz call strength a blunt measure: it counts a node's total involvement, not how many other nodes it is connected to. They therefore propose measures that combine the number and weight of connections (Opsahl et al., 2010). An association with one very strong connection therefore differs from one that is reasonably strongly connected to many others; only the second is what we call a hub.

That a hub 'colours' the rest of the network is a working hypothesis, not a measured effect: because many associations connect to the hub, its meaning is often present when they come up.

In Neurofactor's working definition, a bridge node is an association that appears in, or connects to, several clusters or themes. A bridge node need not be a hub: it can have few connections, as long as they lead to different clusters.

A related approach comes from psychological network analysis: Jones, Ma and McNally developed bridge centrality measures to identify symptoms that connect two disorders (Jones et al., 2021). They distinguish four bridge measures; two are directly useful as a frame of reference:

• Bridge strength: the sum of the (absolute) weights of all connections between a node and nodes outside its own group.
• Bridge betweenness: how often a node lies on the shortest path between two nodes from different groups.

These measures require you to define the groups first. A bridge node therefore only exists relative to a cluster structure; a different structure may produce different bridge nodes.

You identify hubs and bridge nodes with centrality measures. In 1978, Freeman formalised three classic measures (Freeman, 1978; as summarised by Opsahl et al., 2010):

• Degree: the number of connections or neighbours of a node.
• Closeness: how close a node is to all other nodes along the shortest paths.
• Betweenness: on how many shortest paths between other nodes a node lies.

These measures were developed for social networks. Bringmann and colleagues show that their assumptions, such as a flow along shortest paths, do not automatically hold in psychological networks. They conclude that betweenness and closeness in particular are poorly suited there as measures of importance, and that you must make explicit what 'central' means (Bringmann et al., 2019).

In an association network, too, it is not self-evident that meaning travels along the shortest path. Use degree and strength as the basis for hubs and treat betweenness-type measures as a supplementary signal.

Barabási and Albert described how, in many large networks, the number of connections per node follows a power law: most nodes have few connections, a small number have very many. They explained this through growth and preferential attachment: new nodes preferably attach to nodes that are already well connected (Barabási & Albert, 1999).

Steyvers and Tenenbaum found a similar pattern in semantic networks, including free word associations. Most words there have few connections and are linked to each other through a small number of hubs (Steyvers & Tenenbaum, 2005).

These findings concern large language networks. A network around a single choice is much smaller and collected differently; whether it has clear hubs is an empirical question in each study.

Henderson, Iacobucci and Calder describe how cognitive theories represent consumers' brand associations as networks, and how network analysis can clarify branding issues such as segmentation, cannibalisation, brand dilution and brand confusion (Henderson et al., 1998).

Neurofactor applies the same network logic to a specific choice rather than to a brand. This application builds on brand research, but is not validated by it. How to collect associations is explained in How do you measure associations?

Communication space is limited, so you want to know which nodes have the greatest reach:

• Reach within the network. A message that touches a hub touches an association connected to many others.
• Connecting themes. A bridge node lets you link a theme where your offer is strong to a theme where doubt exists.
• Risks that spread. If a hub or bridge node carries a negative valence, that doubt can affect several themes.

This is reasoning from network structure. Whether a message on such a node actually changes how other themes are perceived needs investigating; see From target group insights to testable messages.

1. Define the choice context. A network applies to one defined choice and one target group.
2. Document the network construction. Decide what a node is, when two associations are connected (for example, when one respondent mentions both) and what the weight is (for example, how many respondents mention both). Record thresholds and coding rules.
3. Calculate degree and strength. A node that scores high on strength alone may rest on a single very strong connection (Opsahl et al., 2010).
4. Determine the clusters. Choose themes in advance based on content or determine them with a cluster analysis, and record which.
5. Calculate bridge measures. Look at connections with other clusters (bridge strength) and, additionally, at the position on paths between clusters (bridge betweenness) (Jones et al., 2021).
6. Check stability. Repeat the analysis on subsamples or with a bootstrap (Epskamp et al., 2018).
7. Combine position with valence and salience. A negatively charged hub calls for a different approach than a positively charged one.
8. Test what you want to do with it. A hub or bridge node is a starting point for a testable message, not a proven lever.

An association can be both a hub and a bridge node: many strong connections spread across several clusters.

This example is fictional. The content is illustrative and not a research finding.

Situation and choice question. A leasing company wants to understand what plays a role when lease drivers decide whether their next lease car will be electric.

Available information. An open association task produces coded associations. Two associations are connected if one respondent mentions both; the weight is how many respondents do so.

Suitable approach. The researchers define clusters, calculate degree, strength and bridge strength and check stability. A possible network:

Possible interpretation. 'Charging' would colour the network; 'charging at home' would touch costs, convenience and sustainability at once. But drivers without their own driveway may give 'charging at home' a negative valence: the position says nothing yet about the direction.

Next step. The leasing company examines valence per subgroup and then tests messages about charging against a general message.

• Centrality depends on how the network is built. The associations you include, how you define connections, your threshold and your clustering determine which nodes come out as central (Bringmann et al., 2019).
• Centrality depends on the sample. The ranking can shift when you re-estimate the network with fewer observations; with low stability, differences cannot be interpreted (Epskamp et al., 2018).
• A hub is not a cause of behaviour. A central position describes structure in related answers, not causation.
• A group network is not an individual network. An aggregated network can show structures that do not occur in that form for any individual.
• They remain working concepts. There are no validated thresholds for a hub. Only compare across studies when the network construction is the same.

• Calling the most frequently mentioned association a hub. Frequency describes the association itself, not its connections.
• Confusing position with valence. A hub can be positive, negative or ambivalent; looking only at position may reinforce a risk.
• Presenting a hub as a driver. A central association indicates where to look, not a proven motive for the choice.

Hubs and bridge nodes show which associations have the greatest reach in a network: a hub through many strong connections, a bridge node by connecting themes. Use them as working concepts: document the network construction, check stability, look at valence and test whether communication on these nodes works as expected.