*Graphs of binary relations between things, if not graph theory itself so much, crop up throughout biology. Sometimes we don't stick rigorously to dusty terminology, so sometimes they're called networks, sometimes they ought to be called multigraphs. But they're a neat way to represent protein-protein interactions, gene rearrangements, molecular structures, phylogeny, inheritance, and a ton of other things.
Formal boring stuff that's been written a million times: a graph \(G=(V, E)\) is an ordered pair of sets: \(V\), a set of vertices (or nodes), and \(E\), a set of edges (interactions, links, relations, ...) each of which joins a pair \(v_1, v_2\) of vertices from \(V\).
As an example, the human interactome is a graph with \(V\) being the set of human proteins and \(E\) the interactions that occur between those proteins. In the interactome, the edges that connect proteins typically have no directionality: SNAP25 binds to STX1A and STX1A binds to SNAP25. So, for the interactome at least, it makes no difference whether an edge in \(E\) between proteins \(a\) and \(b\) is written \(a-b\) or \(b-a\), indeed we can equate the two representations. That is, the interactome is an undirected graph.
Not all binary relations are undirected though: for example, if edges represented the phosphorylation of a substrate by a protein kinase then the graph (and the edges within it) would necessarily be directed.
To be continued..
* early attempts to get mathjax to work should be taken with good humour
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