Influenza has the lowest maximum hub score (0.29).
Fig. 5 Authority scores distribution, European Union Fig. 6 Hub scores distribution, European Union.
The relationships between authority scores and hub scores are shown as follows.
The authority and hub scores are based on a mutually reinforcing relationship where good authorities are pointed by good hubs and good hubs point to good authorities (Kleinberg 1999).9 We thus have a circular definition of hubs and authorities.
Authority and hub scores are a generalization of the eigenvector centrality for directed networks.
The authority scores are characterized by Eq. 14, and hub scores are defined by Eq. 15 below (Kleinberg 1999).
This sector displayed high authority and hub scores at the European level and in 9 member countries: Belgium, France, Germany, Ireland, Italy, Lithuania, Netherlands, Poland, and Romania.
To get around this problem, Kleinberg (1999) proposed to compute authority and hub scores for directed networks.
This is important because we found that input-output linkages and authority and hub scores are highly skewed distributed.
