Social Network Analysis (SNA)

Suppose that after a hurricane passes through, a community suddenly needs shelter operations, medical support and road repairs all at once. City hall, the fire department, the public health department, hospitals and volunteer organizations respond while exchanging information with one another.

Looking only at each agency's staff or budget tells you its capacity, but it is hard to tell which agency links the collaboration together and where information flow is at risk of breaking down.

Social network analysis (SNA) is a method that represents the relationships between actors such as people or organizations as data and analyzes the structure of their connections. In this article we use an information-sharing network of disaster response agencies to look at centrality, density, communities, vulnerabilities in connections and how to report the results.

The actors that make up a network are called nodes, and the relationship between two of them is called an edge or tie. For example, if the fire department passed disaster situation information to the health department, you can record that an information-passing relationship exists between the two agencies.

SNA is useful for identifying agencies with many connections, agencies that link different organizations, the overall cohesion of the network, tightly knit subgroups and so on. However, having many connections does not by itself mean an agency has higher actual performance or authority.

If you recorded only that two agencies have a working relationship, it can be represented as an undirected tie. A directed network, on the other hand, distinguishes who sent information to whom. Just because city hall sent information to the hospital, you cannot assume the hospital sent the same information to city hall.

Ties can also be given weights that represent strength or frequency. If you do not want to treat an agency contacted once a month the same as one contacted 20 times, you can use the number of information exchanges as the weight. But how indicators are computed and interpreted depends on whether the weight is contact frequency, satisfaction with the collaboration, travel time or something else.

The agencies include city hall, the fire department, the police department, the public health department, the local hospital, a shelter operator, a volunteer organization and others. The aim of the analysis is to identify the agencies that exchange a lot of information and the key paths that connect different groups of agencies.

The figures in this article are based on a network built for illustration. For the density calculation below, we use a binary directed network that ignores weights and uses only whether a relationship exists.

An edge list records the sending agency and the receiving agency row by row.

In an adjacency matrix, rows are sending agencies and columns are receiving agencies, and you can enter 1 if a relationship exists and 0 if not. For a weighted network, enter the number of times information was passed instead of 1. In a directed network the matrix is generally not symmetric.

Before the analysis, standardize the names of the same agency and check for duplicate records and gaps in the survey. The fact that there are no data must be distinguished from the fact that there is actually no relationship.

In a directed network, you distinguish in-degree, the ties through which information is received, from out-degree, the ties through which it is sent.

For example, if city hall sent information to 8 of the 12 agencies, its out-degree is 8. If ties to oneself are not allowed, the normalized out-degree is 8 ÷ (12 − 1) ≈ 0.727.

In other words, city hall passed information directly to about 72.7% of the other 11 agencies. This means city hall's reach as a sender of information is wide; it does not prove that what it passed on was accurate or that it is the most influential agency.

An agency that links different groups of organizations can have high betweenness centrality even without many direct ties.

For example, if the health department lies on the main path linking the fire agencies with the hospital and welfare agencies, its betweenness centrality can come out high. Concentrating information-passing work in such an agency can make collaboration smoother, but it also carries the risk that connections weaken if that agency's response stops.

However, there is no guarantee that shortest paths are the same as the actual paths information travels. When the network is disconnected or weights are used, state how shortest paths are defined and how the measure is normalized.

In a directed network, however, the results vary greatly depending on which direction of distance is used and whether some nodes are unreachable. For disconnected networks, alternatives such as harmonic centrality can be considered.

Eigenvector centrality does not simply count ties; it gives more weight to ties with other nodes that are themselves highly central. However, in directed or disconnected networks there can be computational limits and interpretation problems. Other measures such as PageRank are sometimes more appropriate.

No single centrality measure is best. Choose one that fits what you are evaluating: information spread, coordination of collaboration or vulnerability of connections.

In a directed network with no self-ties and n nodes, the number of possible ties is n(n−1). In this example, suppose a total of 42 distinct directed ties were observed among the 12 agencies.

So the density of the binary directed network is about 0.318; that is, about 31.8% of the possible ties were observed. A high density means connections are relatively dense, but a network is not better just because every agency contacts every other agency directly.

Given the division of duties and information overload, the right connection structure depends on the situation.

In a disaster response network, emergency rescue agencies, medical and health agencies, and community support agencies may each form close-knit groups.

Typical methods include modularity-based approaches such as Louvain and Leiden; check whether they support direction and weights. Community detection results can vary with the algorithm and the resolution setting.

For example, finding three communities does not mean the disaster response system must be organized into three departments. It is important to compare the results with actual operations and check whether enough information passes between different communities.

In-degree and out-degree are numbers of direct ties, and betweenness centrality is shown as a normalized measure for illustration.

In this table, city hall has the highest out-degree, indicating a wide reach for passing on information directly. The health department, by contrast, does not have the highest out-degree, but its high betweenness centrality suggests it may hold an important position on the paths connecting groups of agencies.

These results do not measure the agencies' formal authority or response performance; they summarize the structural features of the recorded information-sharing relationships. Whether highly central agencies actually process information more accurately has to be checked with separate data.

Sizing nodes in proportion to centrality or coloring them by community lets you quickly see the key agencies and the group structure.

Also, the agency that sits visually at the center may not always be the one with the highest mathematical centrality. So it is best to use the graph as a complement to the centrality figures and the network definition.

Analyzing only 12 agencies can miss connections that run through the federal government or outside support agencies beyond the area. Density and centrality also change depending on how the list of agencies was drawn up.

How relationships are measured also matters.

Even if information is passed many times, the accuracy and usefulness of that information can differ. State which data you used, such as call logs, survey responses or official documents.

Consider change over time as well.

The network right after a disaster may differ from the network during the recovery phase, so a single monthly network should not be used to explain the collaboration structure for every period. Where needed, you can consider longitudinal network analysis that compares networks across time points.

Centrality is not a causal effect.

Finding that a particular agency has high betweenness centrality does not let you conclude that the disaster response improved because of that agency. Other factors, such as the organization's role and the scale of its resources, should be examined.

In actual studies, it is good to also present the network graph, a centrality table for all agencies, the settings and results of community detection, and the limitations of the data.

Depending on the purpose, you can use degree centrality, which shows the number of direct ties; betweenness centrality, which shows position on paths between groups; density, which summarizes the overall level of connection; and community detection, which finds tightly knit subgroups.

But the results depend on how ties were defined and which actors were included in the network. So rather than drawing firm conclusions about an agency's influence and performance from centrality figures or network graphs alone, examine the actual operational context and the quality of the data as well.