What are Boolean Networks?

Question

I was reading this SO question and I got intrigued by what are Boolean Networks, I've looked it up in Wikipedia but the explanation is too vague IMO. Can anyone explain me what Boolean Networks are? And if possible with some examples too?

Answer 1

Boolean networks represent a class of networks where the nodes have states and the edges represent transitions between states. In the simplest case, these states are either 1 or 0 – i.e. boolean.

Transitions may be simple activations or inactivations. For example, consider nodes a and b with an edge from a to b.

     f
a ------> b

Here, f is a transition function. In the case of activation, f may be defined as:

f(x) = x

i.e. b's value is 1 if and only if a's value is 1. Conversely, an inactivation (or repression) might look like this:

f(x) = NOT x

More complex networks use more involved boolean functions. E.g. consider:

a       b
 \     /
  \   /
   \ /
    v
    c

Here, we've got edges from a to c and from b to c. c might be defined in terms of a and b as follows.

f(a, b) = a AND NOT b

Thus, c is activated only if a is active and b is inactive, at the same time.

Such networks can be used to model all kinds of relations. One that I know of is in systems biology where they are used to model (huge) interaction networks of chemicals in living cells. These networks effectively model how certain aspects of the cells work and they can be used to find deficiencies, points of attack for drugs and similarities between unrelated components that point to functional equivalence. This is fundamentally important in understanding how life works.