Network operators use the Border Gateway Protocol (BGP) to control the global visibility of their networks. When withdrawing an IP prefix from the Internet, an origin network sends BGP withdraw messages, which are expected to propagate to all BGP routers that hold an entry for that IP prefix in their routing table. Yet network operators occasionally report issues where routers maintain routes to IP prefixes withdrawn by their origin network. We refer to this problem as BGP zombies and characterize their appearance using RIS BGP beacons, a set of prefixes withdrawn every four hours.Across the 27 monitored beacon prefixes, we observe usually more than one zombie outbreak per day. But their presence is highly volatile, on average a monitored peer misses 1.8% withdraws for an IPv4 beacon (2.7% for IPv6). We also discovered that BGP zombies can propagate to other ASes, for example, zombies in a transit network are inevitably affecting its customer networks. We employ a graph-based semi-supervised machine learning technique to estimate the scope of zombies propagation, and found that most of the observed zombie outbreaks are small (i.e. on average 10% of monitored ASes for IPv4 and 17% for IPv6). We also report some large zombie outbreaks with almost all monitored ASes affected.

Abstract-Graph-based semi-supervised learning for classification endorses a nice interpretation in terms of diffusive random walks, where the regularisation factor in the original optimisation formulation plays the role of a restarting probability. Recently, a new type of biased random walks for characterising certain dynamics on networks have been defined and rely on the γ-th power of the standard Laplacian matrix L γ , with γ > 0. In particular, these processes embed long range transitions, the Lévy flights, that are capable of one-step jumps between fardistant states (nodes) of the graph. The present contribution envisions to build upon these volatile random walks to propose a new version of graph based semi-supervised learning algorithms whose classification outcome could benefit from the dynamics induced by the fractional transition matrix.

PageRank for Semi-Supervised Learning has shown to leverage data structures and limited tagged examples to yield meaningful classification. Despite successes, classification performance can still be improved, particularly in cases of fuzzy graphs or unbalanced labeled data. To address such limitations, a novel approach based on powers of the Laplacian matrix L γ (γ > 0), referred to as L γ -PageRank, is proposed. Its theoretical study shows that it operates on signed graphs, where nodes belonging to one same class are more likely to share positive edges while nodes from different classes are more likely to be connected with negative edges. It is shown that by selecting an optimal γ, classification performance can be significantly enhanced. A procedure for the automated estimation of the optimal γ, from a unique observation of data, is devised and assessed. Experiments on several datasets demonstrate the effectiveness of both L γ -PageRank classification and the optimal γ estimation.