Orbit representative 44.

<p>The central vertex is marked and called vertex 0, to indicate that it cannot be interchanged with any other vertex.</p

All graphlets up to order 5.

<p>The numbers in normal font are Pržulj’s graphlet ordering. Within each graphlet, the vertices with equal color are in the same orbit. The numbers in italic font are Pržulj’s orbit ordering.</p

The number of graphlets for each order.

<p>The logarithm of the number of graphlets is plotted against the number of vertices in each graphlet. The curve is an exponential fit: <i>f</i>(<i>n</i>) = 0.022<i>n</i>^2.50, which has a coefficient of determination <i>R</i>² = 0.9989.</p

All graphlets up to order 5.

<p>The numbers in normal font are the graphlet ordering generated by the algorithm, the numbers in italic font are Pržulj’s ordering.</p

Graphlet 18.

<p>The black outer vertices form orbit 43, the white inner vertex is orbit 44.</p

Use of an equation.

<p>(A) The explored graph in which <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147078#pone.0147078.e016" target="_blank">Eq (14)</a> is tested. Vertex <i>x</i>, colored white, is the inspected vertex. (B-F) The graph is shown in dotted lines, edges in full lines show all different graphlets where vertex <i>x</i> touches orbit 3. Vertices on a gray background are common neighbors of both other vertices of those graphlets. (G-H) The two graphlets in which vertex <i>x</i> touches orbit 14.</p

Matrix form, triangular matrix form and string form of graphlet 18.

<p>These forms correspond to graphlet 18 as it is shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147078#pone.0147078.g005" target="_blank">Fig 5</a>. The string form is not the lexicographically smallest possible for this graphlet.</p

Construction of an equation.

<p>(A) <i>G</i>(<i>x</i>)≃ Orbit representative 2. (B) <i>G</i>′(<i>x</i>) = <i>G</i>(<i>x</i>)∪{{<i>y</i>, <i>x</i>}, {<i>y</i>, <i>a</i>}}≃ Orbit representative 11. (C) <i>G</i>′(<i>x</i>)∪{<i>y</i>, <i>b</i>}≃ Orbit representative 13. (D) <i>G</i>′′(<i>x</i>) = <i>G</i>(<i>x</i>)∪{{<i>y</i>, <i>x</i>}, {<i>y</i>, <i>b</i>}}≃ Orbit representative 11. (E) <i>G</i>′′(<i>x</i>)∪{<i>y</i>, <i>a</i>} = <i>G</i>′(<i>x</i>)∪{<i>y</i>, <i>b</i>}.</p

Size search tree.

<p>Comparison of the number of nodes in the search tree of the RSMA and the ISMA algorithm for finding 3-node motifs in the PGS network. The search tree reduction factor is defined as the size of the search tree of RSMA divided by the size of the search tree of ISMA.</p

Data Structures.

<p>(a) The checklist. In the ISMA algorithm, the circles represent motif nodes (b) The motif iterator. (c) The priority queue map. (d) The priority object. It is assumed that the motif has k nodes.</p