Analytic and simulation results of SM.

<p>(<b>A</b>) Plot of against of SM on the complete graph. The data both from the exact enumerations and simulations are shown. The curve represents the analytic result . (<b>B</b>-<b>D</b>) Scaling plots of the simulation data for of SM against on the scale-free network (<b>B</b>), on the random network (<b>C</b>) and on the square lattice (<b>D</b>). Inset of <b>D</b> shows the plots of for various against .</p

Scaling plot of and a snapshot in DM.

<p>(<b>A</b>) Scaling plot of against of DM on a square lattice with and . Inset: plot of against . (<b>B</b>) A snapshot of a steady state configuration of DM on the square lattice with the size . Black dots denote agents with a dominant idea . White dots denotes those with ideas different from .</p

Schematic diagram for the evolution of configurations in SM on CG.

<p><b>A</b> is a configuration with and . The next propagation process (a), (or the -th propagation) at , changes <b>A</b> into <b>B</b> with all and . Successive innovation processes (b) change <b>B</b> into <b>C</b> with with and . The propagation process (c), which cannot be executed by the probability , leaves <b>C</b> as it is. The propagation process (d) at initiated from an agent with drives <b>C</b> into <b>D</b> with all and . An innovation process (e) drives <b>D</b> into <b>E</b> with ( and ).</p

Analytic and simulation results of DM.

<p>Scaling plots of against of DM (<b>A</b>) on the complete graph with , (<b>B</b>) on a scale-free network (<b>C</b>) on a random network and (<b>D</b>) on a square lattice. Curves in the figures show the analytic results <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070928#pone.0070928.e160" target="_blank">Equation (6</a>) and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0070928#pone.0070928.e220" target="_blank">Equation (9</a>). All the simulation data in <b>B</b>, <b>C</b> and <b>D</b> are obtained by use of . Inset of <b>D</b> shows the plots of for various against .</p

Z-score of the Kullback-Leibler (KL) divergence as a function of the number of legislators <i>k</i> that a Twitter user follows in the U.S. (A), and in Korea (B).

<p>The radius of each circle is proportional to the log of the number of Twitter users with given <i>k</i>. <i>Z</i>_<i>D</i> ≳ 1 implies a statistically significant level of partisanship (political bias). We see that partisanship is widespread in both countries, except for high-degree Twitter users for whom <i>D</i> → 0.</p

Degree distributions in the data.

<p>(A) The distribution of the number of Twitter followers for each legislator. (B) The distribution of the number of legislators that Twitter users follow. All distribtuions are heavy-tailed.</p

Schematic illustrations for the data employed in our study.

<p>(A) The legislators are included in two distinct bipartite networks. On the left is the legislator–Twitter user network, and on the right the legislator–legislative bill network. Of the two types of edges—a ‘nay’ vote and a ‘yea’ vote—we consider the ‘nay’, since they are believed to carry more information in determining the legislators’ political spectra (see the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0124722#sec007" target="_blank">Method</a> section for more detail). The structure of each bipartite network can reveal differences in political positions of the legislators, which is the origin of the online-offline discrepancy. Here, for example, the upper two legislators occupy similar positions that are different from that of the the lower one since their follower sets are disjoint. The two groups’ voting patterns may show less clear differences. In this study we use Multidimensional Scaling (MDS) and Kendall’s ranking correlation coefficient to quantify the spectra and their discrepancies. (B) A sample of the U.S. senator–Twitter followership network consisting of ten legislators and their Twitter followers. The red squares are Republican (GOP) senators, and the blue squares are the Democratic (DEM) senators. All other nodes are Twitter users.</p