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| Signed graphs generalize network models by admitting positive and negative signs on the links, thus allowing two different types of interactions between the entities modeled by the nodes. This talk will study the Laplace operator on weighted signed graphs and its spectral properties. The operation of motif replication and its effect on the spectrum will be presented. A motif refers to a small subgraph whose occurrence in a graph is much higher (or lower) than a comparable random graph. Because of the deviation from a random graph, the presence of such motifs are often believed to be related to the function of biological and chemical networks. Based on a generic dynamical system defined on the graph, I will present analytical results on the role of different motifs on the dynamical behavior. |
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