Network Measures

The igraph package can also calculate network measures.

Several network measures exist that correspond to different node characteristics. Here we want to focus on two of them that are particularly useful for legal citation analysis:

1. Authority scores measure the importance of a node in a network based on the inward ties it attracts. In a legal citation network, this indicate that the case is a particularly important precedent.
2. Hub scores measure the importance of a node in a network based on the outward ties it sends. In a legal citation network, this would correspond to a decision that cites all relevant authorities.

We start by calculating the authority scores of our nodes to find the most important precedents.

authority_score_network <- authority_score(citation_network, scale = TRUE, weights = NULL, options = arpack_defaults)

citation_authority <- as.data.frame(sort(authority_score_network$vector, decreasing=TRUE))

Let’s compare the raw scores based on the number of citations with the authority scores. You will notice that the ranking is a bit different since authority scores weigh the importance of inward citations based on the importance of the citing node.

head(most_cited)

 ## Var1 Freq

head(citation_authority)

 ## sort(authority_score_network$vector, decreasing = TRUE)

We then turn to hub scores to find decision that well describes the status of the law by citing all relevant authorities.

hub_score_network <- hub_score(citation_network, scale = TRUE, weights = NULL, options = arpack_defaults)

citation_hub <- as.data.frame(sort(hub_score_network$vector, decreasing=TRUE))

Let’s again compare the raw scores based on the number of outward citations with the hub scores. You notice again that the ranking is a bit different, because hub scores weigh the importance of outward citations based on the importance of the cited node.

head(most_citing)

 ## Var1 Freq

head(citation_hub)

 ## sort(hub_score_network$vector, decreasing = TRUE)

Which network metrics best describe the varying characteristics of a legal case is an area of ongoing research. Generally, however, different network measures correspond to different attributes of a case. As a result, selecting an appropriate network measure depends on what you are trying to assess.