Link creation and information spreading over social and communication ties in an interest-based online social network

EPJ Data Science

Table 1 Statistics concerning the friendship and neighborhood networks, their union ( i.e. , the full social network) and the communication network in April 2011

	Friendship	Neighborhood	Union	Communication
Nodes	126,858	77,356	140,686	80,303
Links	557,258	633,635	1,187,650	574,285
Loops	0	0	0	22,579
Reciprocation	0.60	0.43	0.54	0.61
$〈 k_{out} 〉$	4.4	8.2	8.4	7.2
〈w〉	-	-	-	1.8
〈m〉	-	-	-	12.9
WCC size	121,143	76,760	140,686	75,965
SCC size	81,292	41,063	100,492	38,336
Density	3.4⋅10⁻⁵	1.1⋅10⁻⁴	6.0⋅10⁻⁵	8.9⋅10⁻⁵
Average SPL	7.3	4.7	5.3	4.8
Diameter	25	15	20	17
Degree centr. [53]	0.0072	0.0875	0.0486	0.0650

$SPL = shortest path length$ ; $WCC = weakly connected component$ ; $SCC = strongly connected component$ ; $〈 k_{out} 〉$ average out degree, 〈w〉 average edge weight (only for the communication network, see Section 4.3), 〈m〉 average number of messages in the shoutbox. Degree centralization is given by Freeman’s formula $C_{D} = \frac{\sum_{i \in G} (k_{\max} - k_{i})}{(| G - 1 | \cdot | G - 2 |)}$ .