Figure 1.
Data versus theory
for the Additive, Multiplicative, and Combined versions of PageRank.
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
.
Figure 2.
Sketch of the multiplex online social network in which users communicate by exchanging instant messages and by posting messages to a forum.
Figure 3.
The Additive, Multiplicative, Combined, and Neutral users’ Multiplex PageRanks plotted against the mean field expectation
(solid line) for the IM-forum multiplex network dataset.
The damping factors used for the IM and forum data are .
Figure 4.
The time evolution of the values of Additive, Multiplicative, Combined, and Neutral Multiplex PageRank for the
top-ranked users.
The damping factors used for the IM and forum network data are . Each time step reflects the cumulative interactions in a three-week time window.
Figure 5.
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.
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.
Figure 6.
The distribution of the Additive, Multiplicative, Combined, and Neutral versions of Multiplex PageRank
for users in the IM-forum multiplex network dataset.
The damping factors used for the IM and forum data are .