Complex Networks

CHALLENGES IN THE NS REPORT 1. Dynamics, spatial location, and information propagation in networks. 2. Modeling and analysis of very large networks. 3. Design and synthesis of networks. 4. Increasing the level of rigor and mathematical structure. 5. Abstracting common concepts across fields. 6. Better experiments and measurements of network structure. 7. Robustness and security of networks. ORGANIZED COMPLEXITY SUMMARY 1. Complex systems are robust yet fragile, with unavoidable constraints and trade-offs. 2. High proof complexity implies problem fragility. 3. Thus robustness and its verifiability are compatible design objectives. 4. Potentially good news for the study of all forms of organized complexity. 5. Needs new math and technology not new science. 6. Encouraging beginnings but the math is not yet readily accessible making progress on both theory and education.