J Optim Theory Appl (2018) 176:492–508
A Novel Mixed Integer Linear Programming Model
for Clustering Relational Networks
· Burak Eksioglu
Fred W. Glover
Received: 7 June 2017 / Accepted: 26 December 2017 / Published online: 5 January 2018
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract Integer programming models for clustering have applications in diverse
ﬁelds addressing many problems such as market segmentation and location of facili-
ties. Integer programming models are ﬂexible in expressing objectives subject to some
special constraints of the clustering problem. They are also important for guiding clus-
tering algorithms that are capable of handling high-dimensional data. Here, we present
a novel mixed integer linear programming model especially for clustering relational
networks, which have important applications in social sciences and bioinformatics.
Our model is applied to several social network data sets to demonstrate its ability to
detect natural network structures.
Keywords Clustering · Mixed integer programming · Social networks
Mathematics Subject Classiﬁcation 05C12 · 68R05 · 68R10 · 90C05 · 90C11 ·
90C27 · 90C35 · 90C90
Communicated by Panos M. Pardalos.
Fred W. Glover
Systems Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi
Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA
College of Engineering and Applied Science, University of Colorado, Boulder, CO 80309, USA