Abstract: It is commonly recognized that, as to a general network, the network reliability will be increasingly enhanced when network arcs are growing. However, this argument is not entirely correct. For some researches on networks that mainly focus on shortest path length, the conclusions can be got as follows. First, if network G suffers from random attacks, the network shortest path entropy is utilized as a criterion judging the network reliability and will be computed before and after an extra arc is added when the network node or arc is attacked and thus fails. In this case, the larger the entropy value is, the weaker the reliability becomes. Second, if network G suffers from malicious attacks, a newly-defined reliability indicator is applied in accordance with pessimistic principle, which is positively correlated with network reliability. The result further shows that: when G is identical to G' in the shortest path length, then the reliability of G' is not weaker than G's; when G is not equal to G' in the shortest path length, their reliability's relative value is not unique. This study helps cultivate an in-depth understanding of the influence of network arc's growth on the network's reliability. Finally, a simplified inter-city expressway network graph of Jiangsu province is exemplified to demonstrate the effectiveness and practicability of this approach.

Key words: random failures, mailcious attacks, network reliability, network shortest path entropy, pessimistic principle