Spectral methods and network communities

Subset of nodes more densely linked among themselves than to the rest of the network. COMMUNITY STRUCTURE: • Allows coarse-graining of network structure, provides reduced complexity and simplified visualization. • Important for search engines. • In social networks reflects social structure and is related to opinion dynamics or rumor propagation. • In biochemical and neural networks is related to functional units [Ravasz et al. and Guimerá-Amaral]. Communities in Complex Networks COMMUNITY (or modulus): • Subset of nodes more densely linked among themselves than

to the rest of the network. COMMUNITY STRUCTURE: • Allows coarse-graining of network structure, provides reduced complexity and simplified visualization. • Important for search engines. • In social networks reflects social structure and is related to opinion dynamics or rumor propagation. • In biochemical and neural networks is related to functional units [Ravasz et al. and Guimerá-Amaral]. After Song,Havlin,Makse: WWW schematic representation. Methods for community detection Some methods are divisive while others are agglomerative • Girvan-Newman : removal of links with high betweenness. • Radicchi et al. divisive algorithm, based on triangles. • Super-paramagnetic clustering. Reichardt-Bornholdt. • Guimerá-Amaral, and Danon et al. simulated annealing modularity optimization. Very good results but slow. • Greedy algorithm by Newman. Very fast. • Arenas-Duch. Extremal optimization. Works very well. • Pons-Latapy. Walk-trap algorithm. Trapped random-walks. • Newman. Spectral method with a “modularity matrix”. Very fast and reliable. • ... (this list is non-exhaustive). Methods for community detection Some methods are divisive while others are agglomerative • Girvan-Newman : removal of links with high betweenness. • Radicchi et al. divisive algorithm, based on triangles. • Super-paramagnetic clustering. Reichardt-Bornholdt. • Guimerá-Amaral, and Danon et al. simulated annealing modularity optimization. Very good results but slow. • Greedy algorithm by Newman. Very fast. • Arenas-Duch. Extremal optimization. Works very well. • Pons-Latapy. Walk-trap algorithm. Trapped random-walks. • Newman. Spectral method with a “modularity matrix”. Very fast and reliable. • ... (this list is non-exhaustive). Methods for community detection Some methods are divisive while others are agglomerative • Girvan-Newman : removal of links with high betweenness. • Radicchi et al. divisive algorithm, based on triangles. • Super-paramagnetic clustering. Reichardt-Bornholdt. • Guimerá-Amaral, and Danon et al. simulated annealing modularity optimization. Very good results but slow. • Greedy algorithm by Newman. Very fast. • Arenas-Duch. Extremal optimization. Works very well. • Pons-Latapy. Walk-trap algorithm. Trapped random-walks. • Newman. Spectral method with a “modularity matrix”. Very fast and reliable. • ... (this list is non-exhaustive). Methods for community detection Some methods are divisive while others are agglomerative • Girvan-Newman : removal of links with high betweenness. • Radicchi et al. divisive algorithm, based on triangles. • Super-paramagnetic clustering. Reichardt-Bornholdt. • Guimerá-Amaral, and Danon et al. simulated annealing modularity optimization. Very good results but slow. • Greedy algorithm by Newman. Very fast. • Arenas-Duch. Extremal optimization. Works very well. • Pons-Latapy. Walk-trap algorithm. Trapped random-walks. • Newman. Spectral method with a “modularity matrix”....

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