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The formation of network structure is mainly influenced by an individual nodes activity and its memory, where activity can usually be interpreted as the individual inherent property and memory can be represented by the interaction strength between nodes. In our study, we define the activity through the appearance pattern in the time-aggregated network representation, and quantify the memory through the contact pattern of empirical temporal networks. To address the role of activity and memory in epidemics on time-varying networks, we propose temporal-pattern coarsening of activity-driven growing networks with memory. In particular, we focus on the relation between time-scale coarsening and spreading dynamics in the context of dynamic scaling and finite-size scaling. Finally, we discuss the universality issue of spreading dynamics on time-varying networks for various memory-causality tests.
We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself, but the a
The largest eigenvalue of a networks adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expre
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the networks adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks spectra. We fin
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a systems unitary components and its emergen
The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network [1]; or, if immunized, would preve