Temporal PageRank

Abstract

PageRank is one of the most popular measures for ranking the nodes of a network according to their importance. However, Page-Rank is defined as a steady state of a random walk, which implies that the underlying network needs to be fixed and static. Thus, to extend PageRank to networks with a temporal dimension, the available temporal information has to be judiciously incorporated into the model. Although numerous recent works study the problem of computing Page-Rank on dynamic graphs, most of them consider the case of updating static PageRank under node/edge insertions/deletions. In other words, PageRank is always defined as the static PageRank of the current instance of the graph. In this paper we introduce temporal PageRank, a generalization of Page-Rank for temporal networks, where activity is represented as a sequence of time-stamped edges. Our model uses the random-walk interpretation of static PageRank, generalized by the concept of temporal random walk. By highlighting the actual information flow in the network, temporal PageRank captures more accurately the network dynamics. A main feature of temporal PageRank is that it adapts to concept drifts: the importance of nodes may change during the lifetime of the network, according to changes in the distribution of edges. On the other hand, if the distribution of edges remains constant, temporal PageRank is equivalent to static PageRank. We present temporal PageRank along with an efficient algorithm, suitable for online streaming scenarios. We conduct experiments on various real and semi-real datasets, and provide empirical evidence that temporal PageRank is a flexible measure that adjusts to changes in the network dynamics.

Node embeddings in dynamic graphs

“…The concept was perhaps introduced in (Moody 2002) for analyzing diffusion in networks. In another terminology, temporal walks were used to construct time-aware centrality metrics in (Rozenshtein and Gionis 2016;Béres et al 2018).…”

“…In other words, the embedding of a node should be similar to the embedding of nodes in its temporal neighborhood. We define time respecting temporal walks (Rozenshtein and Gionis 2016) in order to sample for each node u at any time t nodes from its temporal neighborhood. As seen in Fig.…”

“…Present work. StreamWalk, our first algorithm updates the node embedding online to track and measure node properties and similarity from a graph stream (Rozenshtein and Gionis 2016). StreamWalk is based on the recent concept of temporal walks containing edges ordered in time.…”

“…Our algorithm performs online machine learning (Bifet et al 2010) by continuously updating a model as we read the graph stream. Its key ingredients are online gradient descent optimization (Juang and Lin 1998) and time respecting temporal walks (Rozenshtein and Gionis 2016).…”

2scent

“…Temporal graphs, also know as interaction [14,23] or temporal networks [7], are being studied using multiple approaches. One approach is to extend global properties from static graph theory such as page rank [8,22], shortest path [17,24,29], or centrality measures [1,21] to temporal networks and to introduce efficient algorithms to compute them. Other works focus on better understanding the nature and evolution of such temporal graphs.…”