"Core-Periphery Structure in Networks (Revisited)"

One of my papers just came out in published form. In fact, it's a SIAM Review reboot (with some new sections and other updates) of our paper from a few years ago. Here are the details.

Title: Core-Periphery Structure in Networks (Revisited)

Authors: Puck Rombach, Mason A. Porter, James H. Fowler, and Peter J. Mucha

Abstract: Intermediate-scale (or “meso-scale”) structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of such features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as
core-periphery structure, which entails identifying densely connected core nodes and sparsely connected peripheral nodes. In contrast to communities, the nodes in a core are also reasonably well-connected to those in a network’s periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes into account different possible core structures. We illustrate the differences between our method and several existing methods for identifying which nodes belong to a core, and we use our technique to examine core-periphery structure in examples of friendship, collaboration, transportation, and voting networks. For this new SIGEST version of our paper, we also discuss our work’s relevance in the context of recent developments in the study of core-periphery structure.

Tales from the ArXiv: A "Topological Middle Class"

This new arXiv paper, by Dani Bassett and company, has a lovely turn of phrase, a "topological middle class", which twist on the classical term rich-club phenomenon. Previously, in this paper, my collaborators and I introduced the term "poor-club phenomenon" via a similar play on words.

"Detection of Core–Periphery Structure in Networks Using Spectral Methods and Geodesic Paths"

The special issue in European Journal of Applied Mathematics on "Network Analysis and Modelling" that I co-edited also includes a research paper that I coauthored. Here are some details about that paper.

Title: Detection of Core–Periphery Structure in Networks Using Spectral Methods and Geodesic Paths

Authors: Mihai Cucuringu, Puck Rombach, Sang Hoon Lee, and Mason A. Porter

Abstract: We introduce several novel and computationally efficient methods for detecting "core–periphery structure" in networks. Core–periphery structure is a type of mesoscale structure that consists of densely connected core vertices and sparsely connected peripheral vertices. Core vertices tend to be well-connected both among themselves and to peripheral vertices, which tend not to be well-connected to other vertices. Our first method, which is based on transportation in networks, aggregates information from many geodesic paths in a network and yields a score for each vertex that reflects the likelihood that that vertex is a core vertex. Our second method is based on a low-rank approximation of a network’s adjacency matrix, which we express as a perturbation of a tensor-product matrix. Our third approach uses the bottom eigenvector of the random-walk Laplacian to infer a coreness score and a classification into core and peripheral vertices. We also design an objective function to (1) help classify vertices into core or peripheral vertices and (2) provide a goodness-of-fit criterion for classifications into core versus peripheral vertices. To examine the performance of our methods, we apply our algorithms to both synthetically generated networks and a variety of networks constructed from real-world data sets.

An Awesome 19th-Century Visualization of a Railroad Network

This 19th-century visualization of the New York and Erie Railroad is spectacular. Visually, it accentuates a possible core–periphery structure. (One expects railroad networks to have such a structure, although visualizations on their own can be very misleading, so one would need to check this to be sure.)

(Tip of the cap to Edward Tufte.)

Update: Here is an embedded version of the tweet so that you can see the picture without clicking on the link above.

160-year old geo/network hierarchical organizational diagram of the New York and Erie Railroad. pic.twitter.com/B3rvAXsbxx

— Elijah Meeks (@Elijah_Meeks) May 14, 2016