networks: build-interaction-graph → build-syntactic-interaction-graph.

The interaction graph is *not* usually defined in this way.

example/example.org

@@ -356,7 +356,7 @@ tab
    Some functions in =dds= build graphs:
 
    #+BEGIN_SRC racket :results output drawer :var bf=munch-sexp(another-test-table)
-(build-interaction-graph (unorgv bf))
+(build-syntactic-interaction-graph (unorgv bf))
    #+END_SRC
 
    #+RESULTS:
@@ -372,7 +372,7 @@ tab
 
    #+NAME: igraph
    #+BEGIN_SRC racket :results output drawer :var bf=munch-sexp(another-test-table)
-(display (graphviz (build-interaction-graph (unorgv bf))))
+(display (graphviz (build-syntactic-interaction-graph (unorgv bf))))
    #+END_SRC
 
    #+RESULTS: igraph
@@ -433,10 +433,10 @@ tab
    because 0 is not #f.  For example, =(if 0 1 2)= evaluates to 1, and
    not to 2.
 
-   Here's the unsigned interaction graph of this network:
+   Here's the unsigned syntactic interaction graph of this network:
    #+NAME: simple-bn-ig
    #+BEGIN_SRC racket :results silent :var simple-bn=munch-sexp(simple-bn)
-(dotit (build-interaction-graph (unorgv simple-bn)))
+(dotit (build-syntactic-interaction-graph (unorgv simple-bn)))
    #+END_SRC
 
    #+BEGIN_SRC dot :file dots/examplejTo8XT.svg :results raw drawer :cmd sfdp :noweb yes
@@ -448,6 +448,15 @@ tab
    [[file:dots/examplejTo8XT.svg]]
    :END:
 
+   Note that, while this definition is an easy one to check
+   structurally, this is *not* how interaction graphs are typically
+   defined.  An interaction graph is usually defined based on the
+   dynamics of the network: an arrow from a variable x to a variable
+   y means that varying x and only x may have an influence on the
+   value of y.  It is easy to imagine a situation in which the
+   syntactic interaction graph does not in fact agree with this
+   criterion, the simplest example being the network y = x \wedge \neg x.
+
    Here's the signed interaction graph of this network:
 
    #+NAME: simple-bn-sig

networks.rkt

@@ -29,7 +29,7 @@
                [make-network-from-forms (-> (listof (cons/c symbol? update-function-form?))
                                             network?)]
                [list-interactions (-> network-form? variable? (listof variable?))]
-               [build-interaction-graph (-> network-form? graph?)]
+               [build-syntactic-interaction-graph (-> network-form? graph?)]
                [build-all-states (-> domain-mapping/c (listof state?))]
                [make-same-domains (-> (listof variable?) generic-set? domain-mapping/c)]
                [make-boolean-domains (-> (listof variable?) (hash/c variable? (list/c #f #t)))]
@@ -304,16 +304,26 @@
 ;;; Builds the graph in which the vertices are the variables of a
 ;;; given network, and which contains an arrow from a to b whenever a
 ;;; appears in (list-interactions a).
-(define (build-interaction-graph n)
+;;;
+;;; Note that, while this definition is an easy one to check
+;;; structurally, this is *not* how interaction graphs are typically
+;;; defined.  An interaction graph is usually defined based on the
+;;; dynamics of the network: an arrow from a variable x to a variable
+;;; y means that varying x and only x may have an influence on the
+;;; value of y.  It is easy to imagine a situation in which the
+;;; syntactic interaction graph does not in fact agree with this
+;;; criterion, the simplest example being the network y = x AND (NOT
+;;; x).
+(define (build-syntactic-interaction-graph n)
   (transpose
    (unweighted-graph/adj
     (for/list ([(var _) n]) (cons var (list-interactions n var))))))
 
 (module+ test
-  (test-case "build-interaction-graph"
+  (test-case "build-syntactic-interaction-graph"
     (define n #hash((a . (+ a b c))
              (b . (- b c))))
-    (define ig (build-interaction-graph n))
+    (define ig (build-syntactic-interaction-graph n))
     (check-true (has-vertex? ig 'a))
     (check-true (has-vertex? ig 'b))
     (check-false (has-vertex? ig 'c))
@@ -456,7 +466,7 @@
 ;;; network for every arrow in the unsigned interaction graph, so its
 ;;; performance decreases very quickly with the size of the network.
 (define (build-signed-interaction-graph/form network-form doms)
-  (let ([ig (build-interaction-graph network-form)]
+  (let ([ig (build-syntactic-interaction-graph network-form)]
         [network (network-form->network network-form)])
     ;; Label every edge of the interaction graph with the sign.
     (define sig
@@ -567,7 +577,7 @@
 (module+ test
   (test-case "Interaction must graphs always contain all nodes."
     (define n #hash((a . #t) (b . #t)))
-    (define ig (build-interaction-graph n))
+    (define ig (build-syntactic-interaction-graph n))
     (define sig-nf (build-boolean-signed-interaction-graph/form n))
     (define sig (build-boolean-signed-interaction-graph (network-form->network n)))
     (check-equal? (get-vertices ig) '(b a))