homomorphism density

[[concept]]

homomorphism density

Let $G=(V,E)$ and $F=(V^{\prime },E^{\prime })$ be graphs. The homomorphism density from $F$ to $G$, denoted $t(F,G)$ is given as $t(F,G)=\frac{\text{hom}(F,G)}{|V{|}^{|V^{\prime }|}}$ Where $\text{hom}(F,G)$ is the the total number of homomorphisms from $F$ to $G$.

We can think of this as the probability of sampling a version of $F$ from the graph $G$.

Mentions

TABLE
FROM [[]]
 
FLATTEN choice(contains(artist, this.file.link), 1, "") + choice(contains(author, this.file.link), 1, "") + choice(contains(director, this.file.link), 1, "") + choice(contains(source, this.file.link), 1, "") as direct_source
 
WHERE !direct_source