Abstract
The PageRank algorithm, which has been “bringing order to the web” for more than 20 years, computes the steady state of a classical random walk plus teleporting. Here we consider a variation of PageRank that uses a non-backtracking random walk. To do this, we first reformulate PageRank in terms of the associated line graph. A non-backtracking analog then emerges naturally. Comparing the resulting steady states, we find that, even for undirected graphs, non-backtracking generally leads to a different ranking of the nodes. We then focus on computational issues, deriving an explicit representation of the new algorithm that can exploit structure and sparsity in the underlying network. Finally, we assess effectiveness and efficiency of this approach on some real-world networks.
Highlights
Let A = ∈ Rn×n be the adjacency matrix of an unweighted, weakly connected, directed graph with n nodes and m directed edges
Non-backtracking has more recently been considered in the context of matrix computation, where it has been shown to form the basis of effective algorithms in network science for community detection, centrality and alignment [3,10,16,18,20,21,23,31]
Given that the PageRank algorithm [22] computes the steady state of a particular random walk, it is natural to ask whether there is any scope for designing and analysing a non-backtracking analog
Summary
The notion of a walk around a graph is both natural and useful. The walker may follow any available edge, with nodes and edges being revisited at any stage. Non-backtracking has more recently been considered in the context of matrix computation, where it has been shown to form the basis of effective algorithms in network science for community detection, centrality and alignment [3,10,16,18,20,21,23,31]. Given that the PageRank algorithm [22] computes the steady state of a particular (teleporting) random walk, it is natural to ask whether there is any scope for designing and analysing a non-backtracking analog. It is interesting to note a connection with the space syntax approach in the analysis of road networks, where edges in a graph represent crossroads and nodes are the streets [7]. We show that, even for undirected graphs, non-backtracking generally leads to a different ranking of the nodes.
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