  We propose a linear clustering process on a network consisting of two
opposite forces: attraction and repulsion between adjacent nodes. Each node is
mapped to a position on a one-dimensional line. The attraction and repulsion
forces move the nodal position on the line, depending on how similar or
different the neighbourhoods of two adjacent nodes are. Based on each node
position, the number of clusters in a network, together with each node's
cluster membership, is estimated. The performance of the proposed linear
clustering process is benchmarked on synthetic networks against widely accepted
clustering algorithms such as modularity, the Louvain method and the non-back
tracking matrix. The proposed linear clustering process outperforms the most
popular modularity-based methods, such as the Louvain method, while possessing
a comparable computational complexity.
