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The graph-theoretical task of determining most likely inter-community edgesbased on disconnected subgraphs' intra-community connectivity is proposed. Analgorithm is developed for this edge augmentation task, based on elevating thezero eigenvalues of graph's spectrum. Upper bounds for eigenvalue elevationamplitude and for the corresponding augmented edge density are derived and areauthenticated with simulation on random graphs. The algorithm worksconsistently across synthetic and real networks, yielding desirable performanceat connecting graph components. Edge augmentation reverse-engineers graphpartition under different community detection methods (Girvan-Newman method,greedy modularity maximization, label propagation, Louvain method, and fluidcommunity), in most cases producing inter-community edges at >50% frequency.

Edge Augmentation on Disconnected Graphs via Eigenvalue Elevation