Finding the core and the periphery

A core is a set of vertices that are densely linked to each other and to everything else; the periphery hangs off the core and barely links to itself. Draw a graph from one of the paper's block models and watch five detectors try to recover the planted split.

After Cucuringu, Rombach, Lee & Porter, Detection of core–periphery structure in networks using spectral methods and geodesic paths, Euro. J. Appl. Math. 27 (2016).

The graph

Scorelowhighmisclassified

Adjacency matrix, sorted by score

core–core edgecore–peripheryperiphery–peripherydetected cut

Scores in decreasing order

planted coreplanted periphery

Find-Cut objective along each score ordering

Find-Cut sorts vertices by score and tries every split into the top c as core and the rest as periphery, keeping the c that maximises Φ = ρ(C,C) + ρ(C,P) − ρ(P,P), where ρ is edge density. Grey bands lie outside [b, n−b]; the dashed line is the planted core size. Watch the maximum drift to the band edge: this is the boundary effect described in Section 7.

Inside the method

All five methods on this graph

MethodCore sizeCore called peripheryPeriphery called coreAccuracyObjective ΦTime

Click a row to switch method. Planted core size is .

How similar are the rankings?

Spearman rank correlation between score vectors, as in the paper's Table D1. Degree-, Path- and LowRank-Core tend to agree; the Laplacian eigenvector ranks vertices very differently.

Accuracy across an ensemble

Reproduces the experiments of Figures 8–10 with n = 100 and half the vertices in the core, using the minimum set size b from the sidebar. Accuracy is the fraction of vertices assigned to their planted set.