期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 115, 期 27, 页码 6911-6915出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1801588115
关键词
resilience; community structure; percolation; universality; external field
资金
- NSF [PHY-1505000, CMMI-1125290, CHE-1213217]
- Defense Threat Reduction Agency Grant [HDTRA1-14-1-0017]
- Major Program of National Natural Science Foundation of China [71690242, 91546118]
- National Natural Science Foundation of China [61403171, 71403105, 2015M581738, 1501100B]
- Key Research Program of Frontier Sciences, Chinese Academy of Sciences [QYZDJ-SSW-SYS019]
- Planning and Budgeting Committee of the Council for Higher Education of Israel
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1125290] Funding Source: National Science Foundation
Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic- paramagnetic spin system. We also study universality class by defining the analogous critical exponents delta and gamma, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.
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