Abstract
We address the problem of determining the natural neighbourhood of a given node i in a large nonunifom network G in a way that uses only local computations, i.e. without recourse to the full adjacency matrix of G. We view the problem as that of computing potential values in a diffusive system, where node i is fixed at zero potential, and the potentials at the other nodes are then induced by the adjacency relation of G. This point of view leads to a constrained spectral clustering approach. We observe that a gradient method for computing the respective Fiedler vector values at each node can be implemented in a local manner, leading to our eventual algorithm. The algorithm is evaluated experimentally using three types of nonuniform networks: randomised “caveman graphs”, a scientific collaboration network, and a small social interaction network.
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Orponen, P., Schaeffer, S.E. (2005). Local Clustering of Large Graphs by Approximate Fiedler Vectors. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_45
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DOI: https://doi.org/10.1007/11427186_45
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