Abstract
A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k) = ck-α. We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, pr, that needs to be removed before the network disintegrates. We show analytically and numerically that for α ≤ 3 the transition never takes place, unless the network is finite. In the special case of the physical structure of the Internet (α = 2.5), we find that it is impressively robust, with pc > 0.99.
| Original language | English |
|---|---|
| Title of host publication | The Structure and Dynamics of Networks |
| Publisher | Princeton University Press |
| Pages | 507-509 |
| Number of pages | 3 |
| Volume | 9781400841356 |
| ISBN (Electronic) | 9781400841356 |
| ISBN (Print) | 0691113572, 9780691113579 |
| State | Published - 23 Oct 2011 |
Bibliographical note
Publisher Copyright:© 2000 The American Physical Society.