Properties of the most influential social sensors

Abstract

In the influence maximization problem one is to find a subset of vertexes with the highest influence among the node sets of the same cardinality, where a model representing the spread of influence is also given. In [6] two of the most commonly used model were introduced and it was shown that in both cases the problem becomes NP-hard. On the other hand, it was also proven that the greedy algorithm always guarantees a solution performing at most as bad as 1 - 1/e times the optimal solution. Focusing on the Independent Cascade Model we enhance the greedy algorithm to be able to remember not only the locally best solution but b other sets as well, whose influence was the second, third etc. best in the previous step. Surprisingly, contrast to the extended search space this method performs indistinguishably the same as the optimized greedy algorithm of [1] even for relatively large values of b. This shows that there are several different node sets, whose influence is indistinguishably the same as that of the node set returned by the greedy algorithm. Inspired by this result we characterize the most influential sets from two different perspective. Firstly, we try to determine the distribution of three different centrality measures on the members. It turns out that for the eigenvector centrality [12] this distribution can be closely approximated by the normal distribution. Secondly, we examine how the age of a node, i.e., the time passed after becoming a member of the network, correlates to its chance of being chosen by the greedy algorithm. Surprisingly, we found that for graphs with 100, 000 nodes generated by the forest fire model [8] [7], most of the times even the “youngest” node belongs to the first 50, 000 users who have joined the network. It may be even more striking that the fourth youngest elements are among the 10 percent of these nodes in average.