Mean number of the four closed triples for nodes with the same indegree in the Epinions social network and the model.

<p>Results for the mean number of closed triples corresponding to (a) , (b) , (c) , and (d) loops for nodes with the same indegree are shown for the Epinions social network (black squares) and simulated network (red circles) based on the model. Analytic treatment (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e328" target="_blank">Eq. (28)</a>) gives a scaling behavior with an exponent , as indicated by the dash lines. Data points are averages over the logarithmic bins of the indegree .</p

Mean number of the four closed triples for nodes with the same outdegree in the Epinions social network and the model.

<p>Results for the mean number of closed triples corresponding to (a) , (b) , (c) , and (d) loops for nodes with the same outdegree are shown for the Epinions social network (black squares) and simulated network (red circles) based on the model. Analytic treatment (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e328" target="_blank">Eq. (28)</a>) gives a scaling behavior with an exponent , as indicated by the dash lines. Data points are averages over the logarithmic bins of the outdegree .</p

Mean reciprocal degree of nodes with (a) the same indegree and (b) the same outdegree in the Epinions social network and in the model.

<p>Results of the Epinions social network (black squares) and simulation results (red circles) based on the model are shown in a log-log scale in the main panels. Analytic treatment suggests that is linearly dependent on and , and the blue dash lines of slope 1 show its dependence. The inset in each panel shows the results in a linear scale and the dash line has a slope of , as given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e276" target="_blank">Eqs. (20)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e352" target="_blank">(31)</a>. Data points are averages over the logarithmic bins of the indegree and outdegree , respectively.</p

Distributions of four basic closed triples in the Epinions social network and the model.

<p>Distributions of closed triples corresponding to (a) , (b) , (c) , and (d) loops in the Epinions social network (black squares) and in the simulated network based on the model (red circles). Analytic treatment (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e337" target="_blank">Eqs. (30)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e352" target="_blank">(31)</a>) suggests a scaling behavior with an exponent , as shown by the dash lines. Data points are averages over the logarithmic bins of the , , and , respectively.</p

Reciprocal degree distributions of the Epinions social network and the model.

<p>Results of the Epinions social network (black squares) and simulation results (red circles) based on the model are shown. Analytic treatment (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e266" target="_blank">Eqs. (17)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050702#pone.0050702.e352" target="_blank">(31)</a>) suggests a scaling behavior with an exponent , as shown by the dash line. Data points are averages over the logarithmic bins of the reciprocal degree .</p

Degree correlations in the Epinions social network and the model.

<p>Results of degree correlations as measured by four quantities corresponding to the average nearest neighbor degree (squares), (circles), (triangles), and (inverted triangles) for (a) the Epinions social network and (b) simulated network based on the model. Data points are averages over the logarithmic bins of the indegree or outdegree .</p

Relationship between the indegree and the outdegree of nodes in the Epinions social network and the model.

<p>Results of the Epinions social network (black squares) and simulation results (red circles) based on the model are shown. The blue dash line represents the relation function . Data points are averages over the logarithmic bins of the indegree .</p

Three possible unclosed triples and four basic closed triples for a focal node (red).

<p>The basic closed triples correspond to one feedback () loop and three feedforward () loops. The three feedforward loops differ in the indegree of the focal node: for , for and for . The numbers of the three feedforward loops are equal because every loop from the perspective of the focal node constitutes a loop and a loop from the perspective of the another two nodes, but the loops may arise from different growth histories.</p