Figure 1.
Out-degree(followers) and in-degree (
followees) distributions of the two observed data sets.
Most users are ordinary beings who have relative small number of followers and keep only a small fraction of celebrities.
Table 1.
Basic statistics of the two observed data sets.
Table 2.
Comparisons of the average number of common followees () and followers (
) for reciprocal and non-reciprocal node pairs, respectively.
Figure 2.
The fraction of influenced nodes as the function of the fraction of removed links .
is transmission probability.
In each subgraph, the red and green curves correspond to results of removing reciprocal and non-reciprocal links, respectively. Compared with removing non-reciprocal links, the fraction of influenced nodes decays much faster when we remove the same amount of reciprocal links.
Figure 3.
The fraction of influenced nodes as the function of observed time-step , where
is the fraction of removed links and
is transmission probability.
The red and green curves correspond to results of removing reciprocal links and non-reciprocal links, respectively. Compared with removing non-reciprocal links, the diffusion speed is also affected much remarkably when removing reciprocal links.
Figure 4.
The fraction of giant component size () and the susceptibility (
) as the function of the fraction of removed links (
) on the two observed datasets, (A) Sina Weibo and (B) Douban.
In each subgraph, the red and green curves correspond to the results of reciprocal and non-reciprocal links, respectively. The size of strongly connected giant component () decreases more sharply when removing reciprocal links than deleting non-reciprocal ones. Accordingly, the network susceptibility (
) increase quicker when removing reciprocal links than that of deleting non-reciprocal links. That is to say, reciprocal links play a more important role in maintaining the connectivity of directed networks than non-reciprocal links.
Figure 5.
The average network distance () as the function of removed links (
) on the two observed datasets, (left panel) Sina Weibo and (right panel) Douban.
The red and green curves correspond to the results of removing reciprocal and non-reciprocal links, respectively. The average network distance () increases much faster when removing reciprocal links than deleting nonreciprocal ones. That is to say, reciprocal links also play a more important role in keeping the efficiency of directed networks than non-reciprocal links.