Wave Localization on Complex Networks

Communicability in time-varying networks with memory

“…One of such physical metaphors is the use of tight-binding Hamiltonians (TBHs) to study network properties. Although such physical model comes from the study of electronic properties of molecules and solids [11], it is used in network theory without the necessity of considering that electrons are really moving through the nodes and edges of the network [12][13][14][15][16][17][18]. For instance, Sade et al [12] studied the spectral statistics of complex networks and relate them via a TBH with features of the Anderson metal insulator transition for a wide range of different networks.…”

“…Similarly, Zhu et al [13] studied the structural characteristics of complex networks using the representative eigenvectors of the adjacency matrix and found with the use of the TBH that the networks have nontrivial localization properties due to the nontrivial topological structures. Berkovits et al [14] described networks by a TBH, which was used to determine the properties of the Anderson transition according to the statistical properties of its eigenvalues. They concluded that the use of this approach on new complex topologies of networks lead to novel physics, specifically that clustering may lead to localization.…”