Inferring Local Node Degree in ER Random Network

Beverly Gemao^1,2*, Pik-Yin Lai¹

¹Physics Department, National Central University, Zhongli, Taoyuan, Taiwan
²Physics Department, Mindanao State University - Iligan Institue of Technology, Iligan City, Philippines

* Presenter:Beverly Gemao, email:beverly.gemao@gmail.com

Complex systems, which are present in various areas of study, are best represented as networks with components as vertices or nodes and their associated interactions as edges or links. In many systems, some nodes and their corresponding links are not measured. To understand this incomplete systems better, there have been increasing interest on network inverse problems and network reconstruction procedure for incomplete networks. In this work, we look into a simple case and extract local node degree from a bidirectional network with some nodes missing.

The system considered is an Erdős–Rényi random network of N identical nodes under Gaussian white noise and is described by a set of coupled differential equations. We chose the coupling between nodes to be linear with strength that can be varied. Near the synchronized state, we linearized about the noise-free stable fixed point and analyzed the dynamics of the network in the presence of weak noise. For this case, we found that the collective effect of the measured nodes and also that of the missing nodes are dependent on the structure of the network and can be approximated as a function of the local node degree and the number of measured and unmeasured nodes.

Keywords: local node degree, incomplete network, missing nodes