The transfer function for the given signal flow graph is

1
\(\frac{{{G_1}{G_4}\left( {{G_2} + {G_3}} \right)}}{{1 - {G_1}{G_4}{H_1} + {G_1}{G_2}{G_4}{H_2}}}\)
2
\(\frac{{{G_1}{G_4}\left( {{G_2} + {G_3}} \right)}}{{1 - {G_1}{G_4}{H_1} + {G_1}{G_3}{G_4} + {G_1}{G_2}{G_4}{H_2}}}\)
3
\(\frac{{{G_1}{G_4}\left( {{G_2} + {G_3}} \right)}}{{1 - {G_1}{G_4}{H_1} + {G_1}{G_3}{G_4}{H_2} + {G_1}{G_2}{G_4}{H_2}}}\)
4
\(\frac{{{G_1}{G_4}\left( {{G_2} + {G_3}} \right)}}{{1 + {G_1}{G_4}{H_1} - {G_1}{G_3}{G_4} - {G_1}{G_2}{G_4}{H_2}}}\)

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