Speaker
Description
Two competing types of interactions often play an important part in shaping system behaviour, such as activatory or inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. However, the primary focus of the literature is on the unweighted and structurally balanced ones, where all cycles have an even number of negative edges. Hence here, we first introduce a classification of signed networks into balanced, antibalanced or strictly balanced ones, and illustrate the shared spectral properties within each type. We then apply the results to characterise the dynamics of random walks on signed networks, where local consensus can be achieved asymptotically when the graph is structurally balanced, while global consensus will be obtained when it is strictly unbalanced. Finally, we will show that the results can be generalised to networks with complex-valued weights.
