  Memory plays a vital role in the temporal evolution of interactions of
complex systems. To address the impact of memory on the temporal pattern of
networks, we propose a simple preferential connection model, in which nodes
have a preferential tendency to establish links with most active nodes. Node
activity is measured by the number of links a node observes in a given time
interval. Memory is investigated using a time-fractional order derivative
equation, which has proven to be a powerful method to understand phenomena with
long-term memory. The memoryless case reveals a characteristic time where node
activity behaves differently below and above it. We also observe that dense
temporal networks (high number of events) show a clearer characteristic time
than sparse ones. Interestingly, we also find that memory leads to decay of the
node activity; thus, the chances of a node to receive new connections reduce
with the node's age. Finally, we discuss the statistical properties of the
networks for various memory-length.
