  We address the problem of determining a natural local neighbourhood or
"cluster" associated to a given seed vertex in an undirected graph. We
formulate the task in terms of absorption times of random walks from other
vertices to the vertex of interest, and observe that these times are well
approximated by the components of the principal eigenvector of the
corresponding fundamental matrix of the graph's adjacency matrix. We further
present a locally computable gradient-descent method to estimate this
Dirichlet-Fiedler vector, based on minimising the respective Rayleigh quotient.
Experimental evaluation shows that the approximations behave well and yield
well-defined local clusters.

Discrete Mathematics;Data Structures and Algorithms