DOI: http://dx.doi.org/10.7551/978-0-262-33027-5-ch075 Planarity as a driver of Spatial Network structure Garvin Haslett and Markus Brede Institute for Complex Systems Simulation, School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom
[email protected] Downloaded from http://direct.mit.edu/isal/proceedings-pdf/ecal2015/27/423/1903775/978-0-262-33027-5-ch075.pdf by guest on 23 September 2021 Abstract include city science (Cardillo et al., 2006; Xie and Levin- son, 2007; Jiang, 2007; Barthelemy´ and Flammini, 2008; In this paper we introduce a new model of spatial network growth in which nodes are placed at randomly selected lo- Masucci et al., 2009; Chan et al., 2011; Courtat et al., 2011; cations in space over time, forming new connections to old Strano et al., 2012; Levinson, 2012; Rui et al., 2013; Gud- nodes subject to the constraint that edges do not cross. The mundsson and Mohajeri, 2013), electronic circuits (i Can- resulting network has a power law degree distribution, high cho et al., 2001; Bassett et al., 2010; Miralles et al., 2010; clustering and the small world property. We argue that these Tan et al., 2014), wireless networks (Huson and Sen, 1995; characteristics are a consequence of two features of our mech- anism, growth and planarity conservation. We further pro- Lotker and Peleg, 2010), leaf venation (Corson, 2010; Kat- pose that our model can be understood as a variant of ran- ifori et al., 2010), navigability (Kleinberg, 2000; Lee and dom Apollonian growth.