Mere minutes after I announced to my friends that I would research networks in grad school, we found ourselves deep in conversation about how Facebook, the then-upstart social networking company, should go about tagging groups of people who know each other “in real life.” We quickly boiled the question down to finding tightly connected groups of people—a problem called community detection, as I would later learn—and started brainstorming. The problem is just this magnetic. Put a few budding scientists together in a room, and they’ll devise a dozen ways to solve it in no time, even if they know next to nothing about networks. It is no surprise that a bewildering literature on this topic has grown steadily since.
Let me make a disclosure: as a card-carrying physicist, I gravitate toward unifying theories and elegant methods while shying away from any unnecessary complications I can avoid. A few chapters slant this way resolutely, like the brilliant Chapter 4 and its exposition on the leading school of thoughts on community detection, their differences, and surprising similarities, or Chapter 13 with its—sometimes unequal—overview of dynamical approaches to the problem. Honorable mentions also go to Chapter 5 for its in-depth overview of label propagation methods and Chapter 12 for its expedited but broad-ranging tour of Bayesian approaches to stochastic block modeling.
Between these segments are nearly a dozen chapters on topics ranging from in-the-trench graph theory to community detection, various flavors of generalized blockmodeling, and methodologies. Some border on the tedium—one chapter lists definitions reproduced elsewhere with more context—while others are quite readable and informative. Of note is a series of chapters on blockmodeling approaches to various types of networks such as multi-mode networks (generalizing two-modes or bipartite networks), signed networks, and linked networks (a combination of hierarchical and multiplex networks in a physicists-speak).
The prescient Chapter 7 delves into the impact of data imperfection on clustering results and shows how various pre-processing steps can alter scientific conclusions markedly. It is exploratory, but its message is strong and has already been echoed in the statistical network literature, making it a must-read.
Two self-referential case studies bookend the volume and look into the social networks supporting the scientific production on networks, clustering, and blockmodeling. These chapters will confirm the intuition of many who have spent some time in this field: Network research is overwhelmingly produced in silos, with the social network community on one side and the natural scientists on the other. This frames the book as a rare, genuinely interdisciplinary e ort to buck that trend.
And while the book does a fair job of juxtaposing a range of perspectives, at least one significant voice is missing: graph machine learning is largely absent from its pages. Much like physicists ignored social scientists and vice-versa—often justifiably but also to the detriment of both—history repeats itself in
The volume also misses a golden opportunity to weigh in with a definitive and informed judgment on what approaches to clustering are more—or less!—fruitful.
Clustering and blockmodeling have attracted contributions like no other topics in the scholarly research on networks because these problems are intuitive and invite creative solutions. Such abundance is most welcome and refreshing. With the hindsight of five decades of research, however, one would hope we would have already sifted through these methodological proposals to retain the directions worthwhile of future research. As a matter of fact, abundant rigorous work has gone in this direction (Peel et al. 2017; Peixoto 2021), from algorithmic bounds on the quality of algorithms to optimal compression theorems. Yet, the book suspends all verdicts and instead elects to present its dizzying array of approaches on equal footings.
As for my grad school friends, they will have to wait for the next anthology to find a definitive answer to the problem we grappled with all these years ago.