整个句子框架结构：The narrator indicates that.......and the night......is the first night......

The narrator indicates that he hasn’t been sleeping well since the cat’s arrival, and the night(that关系副词省略) the cat disappears is the first night of sound sleep (that关系代词省略)he’s had since bringing the cat into the house.

分句(1):The narrator indicates that he hasn’t been sleeping well since the cat’s arrival

并列连词:and

分句(2):the night the cat disappears is the first night of sound sleep he’s had since bringing the cat into the house.

备注:分句(1)和分句(2)由并列连词and连接的两个并列句

分句(1):The narrator indicates that he hasn’t been sleeping well since the cat’s arrival

主句:the narrator indicates

从句:that he hasn’t been sleeping well since the cat’s arrival

备注:分句1为that引导宾语从句,宾语从句用现在完成进行时，since为介词与后面名词短语the cat’s arrival构成介词短语作时间状语，修饰hasn’t been sleeping well

分句(2):the night the cat disappears is the first night of sound sleep he’s had since bringing the cat into the house. 【主干是 The night is the first night】

主语:the night the cat disappears

系动词:is

表语:the first night of sound sleep he’s had since bringing the cat into the house.

备注:主语为一个带有定语从句名词短语，表语为带有of介词短语，定语从句，和一个since介词短语作时间状语。

备注(1): the first night为表语中心名词

备注(2):of sound sleep he has had since bring the cat into the house为介词短语作后置定语修饰前面中心名词the first night

备注(3):he has had since bringing the cat into the house为定语从句修饰前面名词sound sleep，关系代词that在定语从句作宾语省略了。

备注(4):since bringing the cat into the house为介词since+动名词短语bringing the cat into the house构成介词短语作时间状语。