The concept of Equality Point.

<p>Positive and negative equality points are illustrated respectively in the left and the right charts. The vertical axis <i>t</i> indicates the total time of algorithms and the horizontal axis <i>r</i> shows the number of random networks used for motif detection.</p

Steps taken during classifying a subgraph which has reached a previously existing leaf in the quaternary tree.

<p>1) The quaternary tree is searched and the corresponding leaf is identified 2) Using the identified leaf’s pointer to the corresponding leaf from binary tree, the latter’s counter is augmented.</p

Algorithm 1.

<p>Algorithm 1.</p

Experimental Results for QuateXelero vs. Kavosh.

<p>Experimental Results for QuateXelero vs. Kavosh.</p

QuateXelero (QX) vs. G-Tries in smaller motifs.

<p>10, 100, 100, and 100 random networks were used respectively for Yeast, Social, E.coli, and Electronic networks.</p

Steps taken to search the quaternary tree during expanding (enumerating) a sample subgraph.

<p>In this figure, −1 indicates one way connection from the existing vertex to added vertex, 0 indicates no connection between them, 1 stands for a one way connection in the reverse direction, and 2 shows a two way connection. The order of numbers in the input string is the same order as the corresponding vertices are added during expanding the subgraph (that is 1, 2, 3, and then 4 in this example).</p

Experimental Limitations.

<p>Experimental Limitations.</p

Trends of random network census time ratio (left) and Equality Point (right) for undirected networks.

<p>The ratio in the left chart indicates the ratio of average time spent by QuateXelero for census on random networks to the same time required for G-Tries.</p

Experimental Datasets.

<p>Experimental Datasets.</p

QuateXelero (QX) vs. G-Tries in larger motifs.

<p>5 random networks were used in all experiments. Bolded italic values for Yeast network are estimated with respect to the results in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0068073#pone-0068073-t005" target="_blank">Table 5</a>.</p