Advances in Network Clustering and Blockmodeling

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.

Advances in Network Clustering and Blockmodeling (Wiley, 2019) takes on the gargantuan task of looking back to half a century of research to highlight the most recent and exciting ideas in network clustering and blockmodeling. The edited volume is ambitious and shines at its best but, in the end, strains under the breadth of its subject matter. Research on network clustering and blockmodeling is filled with the ideas of countless fields, and the book aims to survey it all. Unfortunately, it ends up losing itself in some of the details while remaining too superficial at critical junctures. As a result, I was left wanting more while simultaneously fighting the urge to skim profusely.

Advances makes a laudable e ort to bridge communities of researchers who have seldom dialogued in the past by interspersing chapters authored by mathematical sociologists, computer scientists, statisticians, and physicists. True to their diverse origins, these chapters range from deeply methodological investigations to case studies of networked systems through the lens of blockmodeling.

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 Advances. At the time of publication in 2019, graph machine learning was not the behemoth it is now. Still, it was already making significant progress on graph learning “tasks” at scale, making this a critical omission. A reader looking for a complete overview will need to look elsewhere for the latest on embedding techniques and their application to network clustering (Wu et al. 2021; Xu 2021).

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.

In sum, Advances in Network Clustering and Blockmodeling almost lives up to its title. Sociologists and natural scientists alike stand to learn something from giving it a read—perhaps chiefly for the sake of cross-pollination. Experts will be familiar with the content of its pages, while beginners will sometimes struggle to make sense of its succession of compact chapters.

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.