Abstract
Many graph mining tasks can be viewed as classification problems on high dimensional data. Within this class we consider the issue of discovering core-periphery structure, which has wide applications in the economic and social sciences. In contrast to many current approaches, we allow for weighted and directed edges and we do not assume that the overall network is connected. Our approach extends recent work on a relevant relaxed nonlinear optimization problem. In the directed, weighted setting, we derive and analyze a globally convergent iterative algorithm. We also relate the algorithm to a maximum likelihood reordering problem on an appropriate core-periphery random graph model. We illustrate the effectiveness of the new algorithm on a large scale directed email network.
Highlights
Graph theory gives a common framework for formulating and tackling a range of problems arising in data science
In this work we study the different, but closely related, issue of identifying core–periphery structure; we seek a set of nodes that are highly connected internally and with the rest of the network, forming the core, and a set of peripheral nodes that are strongly connected to the core but have only sparse internal connections
Even though all core nodes typically have high centrality score, not all nodes with high centrality measures belong to the core and it is possible to Tudisco and Higham Applied Network Science
Summary
Graph theory gives a common framework for formulating and tackling a range of problems arising in data science. We have introduced in (Tudisco and Higham 2019) a scalable nonlinear optimization method with global quality guarantees for core– periphery detection in binary, undirected and connected graphs.
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