An important part of the network analysis are network partitioning  problems, which come in the forms of partitioning, finding maximum cut and detecting communities. There are well known, simple spectral heuristics for all three problems, which assign nodes to an appropriate part based on the sign of the eigenvector corresponding to an extremal eigenvalue of a particular network matrix. We will discuss a general framework in which these heuristics work and suggests a way for their further improvement.

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