The role of hidden influentials in the diffusion of online information cascades

EPJ Data Science

Table 2 Network properties summary

	grassroots	elections
Network descriptor
$N_{v}$	115,459	84,386
$N_{e}$	10,191,105	7,427,825
WCC	113,671	83,331
SCC	102,750	76,941
$max (k_{in} + k_{out})$	38,028	32,073
$max (k_{in})$	8,262	7,924
$max (k_{out})$	37,810	31,402
$max (k_{c})$ (undirected)	228	210
L	3.175	3.092
D	10	9
r	−0.116	−0.124
ρ	0.455	0.489
Mesoscale characterization
Q	0.413	0.448
$N_{com}$	5,838	4,665
$S_{\max} / N$	0.196	0.110

$N_{v}$ number of vertices, and $N_{e}$ number of edges. WCC stands for the size of the weakly connected component; SCC is the size of the strongly connected component. Next we report the maximum degree and core values considering both in- and out-connectivity ( $k_{in} + k_{out}$ ), the network of friends ( $k_{in}$ ), and the network of followers ( $k_{out}$ ). Average shortest path L and diameter D (the largest shortest path in the network) provide some hints about how deep in the structure can a cascade travel. r stands for the degree-degree correlation index (assortativity). Remarkably, r<0 (in accordance with other reported assortativity values for OSNs, but clearly in contrast with other types of social networks [30]). Reciprocity ρ is a type of correlation expressing the tendency of vertex pairs to form mutual connections. Notably, results for the datasets in this works are higher than those for social networks in [28], and are actually comparable to reciprocity in neural networks. In our context, it reinforces the idea that Twitter may be used both as a microblogging system and a message interchange service. Finally, we report on some quantities regarding the Walktrap community detection outcome. Q stands for the best modularity value attained by the heuristics; $N_{com}$ expresses the number of modules in the Q-optimal partition. The quotient of the largest community’s size and the network size, $S^{\max} / N$ , is also shown.