Let

G

be a graph and μ(

G

x) denote the matching polynomial of

G

. The sum of the absolute values of all the roots (all the coefficients) of μ(G

x) is called the matching energy (the Hosoya index). Let

C

a+1

and

C

b+1

be two cycles with a+1 vertices and b+1 vertices

respectively. The 8-shape graph ∞(a

b) is the graph with a+b+1 vertices obtained from

C

a+1

∪

C

b+1

by identifying a vertex of

C

a+1

with a vertex of

C

b+1

. A new method for comparing matching energies between two graphs is deduced. By using this new method

the matching energy and Hosoya index of the 8-shape graphs is studied. And a completely order of matching energy and Hosoya index of the 8-shape graphs with

n

vertices is obtained.