The concept of network immunity, i.e., the robustness of the network
connectivity after a random deletion of edges or vertices, has been
investigated in biological or communication networks. We apply this concept to
a self-assembling, physical network of microemulsion droplets connected by
telechelic polymers, where more than one polymer can connect a pair of
droplets. The gel phase of this system has higher immunity if it is more likely
to survive (i.e., maintain a macroscopic, connected component) when some of the
polymers are randomly degraded. We consider the distribution p(σ) of the
number of polymers between a pair of droplets, and show that gel immunity
decreases as the variance of p(σ) increases. Repulsive interactions
between the polymers decrease the variance, while attractive interactions
increase the variance, and may result in a bimodal p(σ).Comment: Corrected typo