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This paper studies the “age of information” in a general multi-source multi-hop wireless network with explicit channel contention. Specifically, the scenario considered in this paper assumes that each node in the network is both a source and a monitor of information, that all nodes wish to receive fresh status updates from all other nodes in the network, and that only one node can transmit in each time slot. Lower bounds for peak and average age of information are derived and expressed in terms of fundamental graph properties including the connected domination number. An algorithm to generate near-optimal periodic status update schedules based on sequential optimal flooding is also developed. These schedules are analytically shown to exactly achieve the peak age bound and also achieve the average age bound within an additive gap scaling linearly with the size of the network. Moreover, the results are sufficiently general to apply to any connected network topology. Illustrative numerical examples are presented which serve to verify the analysis for several canonical network topologies of arbitrary size, as well as every connected network with nine or fewer nodes.