# Influence Maximization with Priority in Online Social Networks
## 5 Experiments
### Experimental Results  
We install IGS to compare with state-of-the-art algorithms such as BCT, DSSA, OPIM \(-\)\(C\) and Degree then calculate the spread of influence on all nodes and to \(U\), the priority set, \(U\subset V\). Results are shown in following tables and figures. _The Influence._ The Figure 2 and the Table 2 indicate IGS outperforms the others when influencing to priority nodes by a given threshold \(T\). The above figure gives information about the influence values in case \(k\) changes from 150 to 200, \(U\) includes 200 nodes and the threshold \(T\) is 100. The terms \"_infl_\", \"_inf_\" mean the influences to set \(U\) (\(\sigma_{U}(S)\) ) and to all nodes (\(\sigma(S)\)), respectively. These algorithms output differently on various databases. Looking at red bars, we can see IGS approximately affects the set \(U\) twice the value of the threshold \(T\) on most databases except Re-Tweet but still higher than \(T\). Conversely, the influence on \(U\) of the remaining sharply fluctuate according to the databases. While DSSA and BCT influence on U over \(T\) with netHEPT and ENRON, they work quite low with the others. OPIM \(-\)\(C\) and Degree often affect \(U\) much lower than \(T\). Besides, the \(\sigma(S)\) of BCT is highest on netHEPT whereas the one of IGS keeps at top in all other cases. In general, the values of \(\sigma(S)\) of DSSA, OPIM \(-\)\(C\) and Degree have similarities with each others. \begin{table}
\begin{tabular}{l r r r r} \hline \hline
**Database** & **\#Nodes** & **\#Edges** & **Types** & **Avg. Degree** \\ \hline netHEPT [15] & 15 K & 59 K & directed & 4.1 \\ ENRON [15] & 37 K & 184 K & directed & 5 \\ netPHY [15] & 37 K & 181 K & directed & 13.4 \\ DBLP [15] & 655 K & 2 M & directed & 6.1 \\ TWITTER RETWEET [42] & 1 M & 2 M & directed & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset’s statistics. Besides, Table 2 describes the experiment while \(T\) comes from 100 to 500, \(k=500\) and enlarge \(U\) up to 1K nodes. This setting is to check the case when U is large and when the threshold \(T\) is incremental. Certainly, the condition that \(k\geq T\) has to be maintained so we fixed \(k=500\). Looking at bold values, we can see although \(U\) and \(S\) both become large and \(T\) increments gradually, the influence on \(U\) of IGS is always significantly higher than \(T\), even up to more than ten times. DSSA, BCT and OPIM \(-\) C also give the outputs over threshold \(T\) in many cases, they still have values lower than \(T=500\) on netPHY, DBLP and RETWEET however. The \(\sigma_{U}(S)\) of Degree is lowest, especially, is only 22.77 on Re-Tweet. From Figure 2 and Table 2, we can see \(\sigma_{U}(S)\) of IGS is significantly higher than \(T\) and produces better results than the state-of-the-art algorithms. This is because IGS always prioritizes affecting \(U\) until over the threshold \(T\) then affects other nodes as well even with large values of \(k\), \(U\) size and \(T\). The other algorithms show that they are not always possible to influence U to exceed the desired threshold. On the whole, the state-of-the-art IM algorithms cannot influence the given priority set as well as IGS can. Figure 2: Comparisons of Influence Spreading with \(k=100\to 500\), T = 100 and U size = 200. Running time.Figure 3 compares running time of these algorithms. They indicate time of IGS gives lowest values on netHEPT, ENRON and netPHY databases. Nevertheless, IGS stays at top 3 on DBLP while it costs highest running time on the remaining of the dataset to find 150 and 160 seed sets but return to top 3 at the other values of budget \(k\). IGS only takes about 0.1 s to find out the seed set in most cases except RETWEET. Besides, the figures also give information about the other algorithms. First, BCT runs significantly slow on netHEPT than the others. This method often stays at top 3 or top 4 on ENRON, DBLP and RETWEET. Second, running time of DSSA and IGS look similiar, while that of OPIM-C and Degree is usually higher than the above two algorithms.