A new method based on the concept of betweenness centrality was developed for chemical network analysis and skeletal reduction. After establishing the graphical representation of a chemical network, the betweenness centrality is defined to rank species for removal. It then shows that such a definition takes into account of the fluxes between species as well as their positioning within a chemical network, which are not fully considered by existing methods. Autoignition using GRI 3.0 detailed mechanism of methane oxidation is then used to demonstrate the concept as well as the reduction procedure. The index of importance based on the betweenness centrality is calculated to show the controlling chemistry. Skeletal mechanisms of different sizes based on such an index with further optimization are constructed for each case. Based on the retention frequency of each species in all cases, a global skeletal mechanism is eventually constructed and validated for autoignition, perfectly stirred reactors and laminar flames in a large parameter range of pressure from 0.1 to 30 atm, temperature from 1000 to 1600K, and equivalence ratio from 0.5 to 1.5, showing satisfactory performance.