Abstract
Many biological, social and man-made systems are better described in terms of temporal networks, i.e. networks whose links are only present at certain points in time, rather than by static ones. In particular, it has been found that non-Markovianity is a necessary ingredient to capture the non-trivial temporal patterns of real-world networks. However, our understanding of how memory can affect the properties of dynamical processes taking place over temporal networks is still very limited, being especially constrained to the case of short-term memory. Here, by introducing a model for temporal networks in which we can precisely control the link density and the strength and length of memory for each link, we unveil the role played by memory on the dynamics of epidemic spreading processes. Surprisingly, we find that the average spreading time in our temporal networks is often non-monotonically dependent on the length of the memory, and that the optimal value of the memory length which maximizes the spreading time depends on the strength of the memory and on the density of links in the network. Through analytical arguments we then explore the effect that changing the number and length of network paths connecting any two nodes has on the value of optimal memory.
Highlights
When a system is composed of many individual entities and pairwise interactions between them, it is natural to describe its underlying structure as a complex network
By considering a standard susceptible-infected (SI) epidemic over networks generated by the proposed model, we study how the range of the memory affects the rate at which infection is spread across the network
We can see that the infection spreading in the temporal network with no memory is faster than when any memory is taken into account
Summary
When a system is composed of many individual entities and pairwise interactions between them, it is natural to describe its underlying structure as a complex network. Often in real world systems this underlying structure is in its self dynamic, and so it is better described in terms of networks in which links among a fixed set of nodes change over time [3,4,5,6] Examples of such temporal networks include human contacts, which vary as individuals move over space [7,8,9], online social interactions that take place at certain points in time [10], or functional brain networks where correlations among the different areas of the human brain fluctuate over time [11, 12]. Non-Markovianity turns out to be useful in the definition of flow-based communities [26]
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