AUTHOR=Qian Yu , Cao Jiahui , Han Jing , Zhang Siyi , Chen Wentao , Lei Zhao , Cui Xiaohua , Zheng Zhigang TITLE=A statistical analysis method for probability distributions in Erdös–Rényi random networks with preferential cutting–rewiring operation JOURNAL=Frontiers in Network Physiology VOLUME=4 YEAR=2024 URL=https://www.frontiersin.org/journals/network-physiology/articles/10.3389/fnetp.2024.1390319 DOI=10.3389/fnetp.2024.1390319 ISSN=2674-0109 ABSTRACT=

The study of specific physiological processes from the perspective of network physiology has gained recent attention. Modeling the global information integration among the separated functionalized modules in structural and functional brain networks is a central problem. In this article, the preferentially cutting–rewiring operation (PCRO) is introduced to approximatively describe the above physiological process, which consists of the cutting procedure and the rewiring procedure with specific preferential constraints. By applying the PCRO on the classical Erdös–Rényi random network (ERRN), three types of isolated nodes are generated, based on which the common leaves (CLs) are formed between the two hubs. This makes the initially homogeneous ERRN experience drastic changes and become heterogeneous. Importantly, a statistical analysis method is proposed to theoretically analyze the statistical properties of an ERRN with a PCRO. Specifically, the probability distributions of these three types of isolated nodes are derived, based on which the probability distribution of the CLs can be obtained easily. Furthermore, the validity and universality of our statistical analysis method have been confirmed in numerical experiments. Our contributions may shed light on a new perspective in the interdisciplinary field of complexity science and biological science and would be of great and general interest to network physiology.