Robustness and resilience are often defined in terms of a system’s capacity to maintain functionality in the face of external perturbations. In this model we give an overview to network robustness looking at what happens when we remove links and node, both strategically and randomly
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</p><p>Transcription excerpt:
</p><p>Robustness &amp; resilience are often thought of in terms of a systems capacity to maintain functionality in the face of external perturbations. We see some extraordinary example of this, ecological networks that persist despite extreme environmental changes, Communication networks like the internet can often deal with malfunction, errors and attacks, without these local events lead to catastrophic global failures, but we also see the opposite where some small failure in say a financial system can propagate to affect the whole systems. Trying to understand how and why this happens is the study of network robustness.
</p><p>Robustness can be correlated with connectivity in that connectivity enables system integration, as we previously noted without connectivity parts to the system may become disconnected and disintegrated. If blood stops flowing to some part of the body then it will become atrophied and waste away or if a child stops talking to their parents then the family unit disintegrates through lack of communications. Thus when we are talking about robustness &amp; resilience we are often asking what will happen to the networks overall connectivity and integration if we remove some components or connections and equally how will this failure then spread within the network system.
</p><p>We can think about failure either with respect to the networks nodes asking what will happen if we remove a certain amount, this is called node percolation, but we can also talk about failure in terms of the removal of edges, that is edge percolation and another key factor here is whether the attack is random or strategic. When we talking about robustness with respect to the nodes in the network then a key factor is the degree distribution between the nodes, the higher that degree distribution, meaning there will be more hubs, the more vulnerable it is to strategic attack, but if it is a random attack then the degree distribution is not so important, as these hubs that are part of centralized network will be particularly vulnerable to strategic attack. Thus as we have previously noted distributed networks will be robust to strategic attack but scale free centralize networks are particularly susceptible. A strategic attack on large hubs will drastically reduce the number of connections within the system increase the average path length significantly, which is a key measure of the systems overall integration. This has been conferred in empirical data from the internet and world wide web which show robustness to random attack but are significantly affected by strategic attract due to the presence of major hubs in the network.
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Next edge percolating, that is when connections fail or are removed, an important factor here is the degree of betweenness to the network, if we remember betweenness is really measuring the number of bridging edges, that represent the critical, irreplaceable connections between one cluster and other. An example of this might be the Malacca Straits, a stretch of sea between the cost of Malaysia and Indonesia that connects maritime transport in Asia with the Middle East and Europe. Approximately 40 percent of the world's trade and 25 percent of all crude petroleum is thought to pass through this critical link in the global logistics network. This is an example of a bridging link that reduces the systems robustness and makes it much more susceptible to strategic attack.
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