Maximum transport capacity of a network

• Network capacity is less than the ratio of network size to average path length.
• Maximal transport capacity of a network is independent of routing strategies.
• Maximal transport capacity is found to be a natural property of networks.

The transport capacity of a network can be enhanced and the congestion can be controlled by improving routing algorithms. Its upper limit is, however, unknown in detail. This study shows that any connected network has a maximum transport capacity largely depending on the topological and structural properties of the network. Network transport capacity is limited and cannot be greater than the ratio of the sum of all the capacities of the nodes to the average path length of the network, regardless of the adopted routing algorithm. When the capacity of all nodes is equal to 1, the maximum transport capacity of the network is not greater than the ratio of the network size to the average path length. The results demonstrate that the maximum transport capacity of a network, which is the essential characteristic of the network, is mainly determined by the topological structure of the network and is independent of the routing strategies.