Algorithms in Nature Network robustness Slides adapted from Carl - - PowerPoint PPT Presentation

Algorithms in Nature

Network robustness

Slides adapted from Carl Kingsford

Network robustness

Many complex systems show a surprising degree of tolerance to errors: Biological networks persist despite environmental noise, failures, attacks Communication networks often deal with malfunction, attacks, construction (usually local failures don’t lead to catastrophic global failures) What network structures enable such robust response?

Random vs. scale-free network

What is the effect of these two structures on the network’s robustness?

fraction of nodes removed diameter

diameter

Network fragmentation

S = fractional size of the largest cluster (important for connectivity) <s> = average size of isolated clusters

Initially, only small clusters with one isolated node form. Then, at critical point, the main cluster breaks into many smaller pieces and <s> peaks. Then, we keep removing more nodes and continue isolating nodes leading to decreasing <s>

Network fragmentation

SF: for random failures, S slowly decreases but <s> stays near 1 (all nodes break off one by one) SF: for attacks, once the hubs are removed, the network falls apart

increasing f increasing f

S = fractional size of the largest cluster <s> = average size of isolated clusters

[Jeong et al. Nature 2000]

Avg # incoming links / node Avg # outgoing links / node

# of substrates removed

Conclusions

Real-world networks are robust to random failures, but less able to deal with targeted attacks on high-degree nodes Two assumptions made:

• 1. Every node is equally likely to fail or be targeted (is this

realistic?)

• 2. The entire network is required at all times (are all proteins

involved in every biological process?)

• 3. Do attacks only affect a single node? (what about a

propagating virus?)