Temporally correlated zero-range process with open boundaries: Steady state and fluctuations

19 pages, 14 figures, v2: minor revisions, close to final published version at http://dx.doi.org/10.1103/PhysRevE.92.02213

Multiplex PageRank

(15 pages, 6 figures

The World Trade network in 1990.

<p>(A) The unweighted undirected network which represents trade relationships between the countries. The core has 106 countries. (B) The weighted directed network representing the exchange of wealth between the countries. The 7 countries in core are listed.</p

Comparison on the connectivity of the core between the empirical data and the null model for <i>C. elegans</i>.

<p>(A) The shaded area marks two standard deviations from the sample mean. Neurone RIAR is found to have an anomalous connectivity with the highest ranked nodes. (B) Comparison on the core size between the empirical data (blue line) and the null model (red line). Similarly, the shaded area shows two standard deviations.</p

Relative size of the core in different kinds of real networks.

<p>Man-made (square): US airports (Airports) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref022" target="_blank">22</a>], Amazon.com recommendation (Amazon) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref023" target="_blank">23</a>], Californian (CA) roads [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref021" target="_blank">21</a>], Internet [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref024" target="_blank">24</a>] and Power grid (Power) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref020" target="_blank">20</a>]. Social (circle): Astrophysics collaborations (Astro) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref025" target="_blank">25</a>], Condensed Matter collaborations (CondMat) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref025" target="_blank">25</a>], American College football (Football) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref026" target="_blank">26</a>] and the Zachary Karate club (Karate) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref019" target="_blank">19</a>]. Biological (triangle): <i>C. elegans</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref020" target="_blank">20</a>] and Protein [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119678#pone.0119678.ref027" target="_blank">27</a>].</p

The distribution of the Additive, Multiplicative, Combined, and Neutral versions of Multiplex PageRank for users in the IM-forum multiplex network dataset.

<p>The damping factors used for the IM and forum data are .</p

The estimated ranks of users according to the sum and product of their in-degrees and degrees plotted against the values of their Additive and Multiplicative Multiplex PageRank, respectively.

<p>In the figure and . Note that the node with rank is the most important node of the network, and therefore the Additive and Multiplicative Multiplex PageRanks of the most important nodes of the online social network are correlated, respectively, with a linear combination or the product of the users’ in-degrees and degrees.</p

Data versus theory for the Additive, Multiplicative, and Combined versions of PageRank.

<p>In each of the three panels, the PageRank of the data is plotted against the corresponding value obtained through our theoretical approximation. Multiplex PageRank was evaluated using an iterative procedure with the standard values . The accuracy of the algorithm was set at .</p