Bullivant and Sadewo said in their paper that their network maps "support the view that it is meaningful to talk in terms of there being defined 'cliques' of bishops," and influential bishops who meaningfully shape networks. They aimed to calculate that influence.
The weighted scale of network map influence, called an "indegree" measurement, averaged 1.24 for U.S. bishops.
McCarrick, however, measured 17 on the scale, behind only Philadelphia's archbishop emeritus Cardinal Justin Rigali at 22. McCarrick's measurement was equal to that of Cardinal Adam Maida, archbishop emeritus of Detroit. Cardinal Sean O'Malley of Boston ranked 15, followed by Archbishop Jose Gomez of Los Angeles, former Washington archbishop Cardinal Donald Wuerl, Cardinal Timothy Dolan of New York, then-Archbishop of Philadelphia Charles J. Chaput, former Los Angeles archbishop Cardinal Roger Mahony, and Cardinal Blase Cupich of Chicago, who was ranked 11.
The metropolitan archbishop can be a key figure in the appointment of a bishop. However, under new Vatican norms the metropolitan bishop is also a key figure in investigating other suffragan bishops who are accused of abuse, the very men who are part of his social network cluster.
"(G)iven the structure of episcopal networks, there would seem to be a very low probability of any metropolitan being 'free of conflicts of interest' if asked to investigate other bishops, past or present, of his own diocese or province," the paper said. "Even where no direct ties exist, there will frequently be other close ties between mutual subordinates or superiors, protégés or mentors."
The paper also touches briefly on the deeply controversial topic of homosexual relations among Catholic clergy. Heterosexual relationships can only take place outside of all-male priestly networks, but homosexual relations are different.
"There is clear potential for mutually compromised networks of homosexually active (or once-active) priests, such as McCarrick appears to have cultivated among his 'nephews'," the paper said.
Social network analysis could be a basis for further work. Bullivant hopes to analyze the U.S. bishops based on the apparent phenomenon of bishops transferring sexually abusive priests between dioceses.
"Just to map which bishops were in-the-know enough to send priests to and from each other would be interesting, for example," he said.
Another topic for inquiry is financial corruption and episcopal social networks, such as the allegations against Bishop Michael Bransfield, who formerly headed the Diocese of Wheeling-Charleston, West Virginia. He is accused of sexual harassment and assault of seminarians, priests and other adults, as well as making hundreds of cash "gifts." With the right data, these transfers of money could reveal more information about Bransfield's network.
Applying the social network analysis back in time could shed light on the origins of clergymen like McCarrick.
"We are interested, if we ever find resources, money and time to do it, to do that 'family tree' or a 'genealogy' if you like," Bullivant said. "It makes sense if you have particularly important 'kingmakers' in one generation, picking the bishops the next generation, especially the way that the big archdioceses do, there's a 'family tradition' almost."
This approach to the Church is not simply a story of corruption, he said. Rather, it's "a tool of sociological and historical inquiry into the way in which a very important decision-making class functions."
Besides a bishop's service in a diocese, there are many other "meaningful proxies" to analyze in a churchman's social networks: the bishops who co-consecrated him, shared seminary or university background, or shared service on certain committees or boards of directors.
Bullivant said on Twitter July 15 that the document is a "working paper" seeking comments, questions and suggestions for future work. He said the question was "awkward" for placement in a journal, with a "very slow process." The authors wanted their work published before any promised report on McCarrick, for background and context.
The release of the Vatican's investigation on McCarrick was reportedly delayed due to the coronavirus pandemic.
In October 2018, just months after sexual abuse allegations against McCarrick first emerged, the Vatican said that Pope Francis had commissioned a study of McCarrick's career. Cardinal O'Malley told the U.S. bishops' conference in November 2019 that the Vatican intended to publish the report "soon, if not before Christmas, soon in the new year."
Kevin J. Jones is a senior staff writer with Catholic News Agency. He was a recipient of a 2014 Catholic Relief Services' Egan Journalism Fellowship.