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Updated: Aug 24, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
Published on: October 13, 2023
Two-peak and three-peak optimal complex networks
André X C N Valente1, Abhijit Sarkar, Howard A Stone
1Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA. andre@deas.harvard.edu
Abstract:
A central issue in complex networks is tolerance of random failures and intentional attacks. Current literature emphasizes the dichotomy between networks with a power-law node connectivity distribution, which are robust to random failures but fragile to targeted attacks, versus networks with an exponentially decaying connectivity distribution, which are less tolerant to failures but more resilient to attacks. We prove analytically that the optimal network configuration under a classic measure of robustness is altogether different from both of the above: in all cases, failure and/or attack, there are no more than three distinct node connectivities in the optimal network.
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