Show that the graph convolution product satisfies the following properties:

(a) It is commutative, that is,f?g=g?f.
(b) It is distributive, that is,f?(g+h) =f?g+f?h.
(c) It is associative, that is,f?(g?h) = (f?g)?h.
(d)L(f?g) =f?(Lg) = (Lf)?g


(a)
Proof.
![12229|78x52](upload://pUiE3YlOSFwMfWfWdwrvj33EOjG.png)
(b)
Proof.
![12230|154x84](upload://tzhoOw0WuoxTH034Orkx68VXKh0.png)
(c)
Proof.
![12231|267x237](upload://zoKpFoT4b19hVHGp3yrTaniCD1O.png)
(d)
Proof.
![12232|127x92](upload://e6JV1KwBZUXDzUsIUptbdsGsF5E.png)

Computer Science & Information Technology

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