### Article Source

# The Dynamics of Active Sensing in Social Networks

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- By Nathan de Lara (Telecom ParisTech / Thalès) - 2018, Nov. 14th

## Abstract

We introduce a novel embedding of *directed graphs* derived from the **singular value decomposition (SVD)** of the *normalized adjacency matrix*. Specifically, we show that, after proper *normalization* of the singular vectors, the distances between vectors in the embedding space are proportional to the *mean commute times* between the corresponding nodes by a *forward-backward random walk* in the graph, which follows the edges alternately in forward and backward directions.
In particular, two nodes having many *common successors* in the graph tend to be represented by close vectors in the embedding space. More formally, we prove that our representation of the
graph is equivalent to the *spectral embedding* of some co-citation graph, where nodes are linked with respect to their common set of successors in the original graph. The interest of our approach is that it does **not require** to build this *co-citation graph*, which is typically *much denser* than the original graph. Experiments on real datasets show the efficiency of the approach.