Information Delivering Path

We assume that attackers can assess the desired data, and the phishing link disguises in-teresting website successfully. Or, people feel free to assess the desired data, and spread the rumours intentionally. We trace the real data whether the information disseminates as we an-ticipate. While the information originates from different users, several phenomena deserve people’s attention.

In this thesis, we demonstrate four cases of our method. Then, we utilize the real data to testify our method. Besides, we define that information delivering path as the average of path starting from contagious user to every active user. We record the information delivering paths to comprehend the effect of different users on information dissemination. For instance, we illustrate every participant as a node and the edge between two user as ‘friends’ in Figure 4.2.

The edges between users represent the real connections on Facebook. Since the number of the participants and their friends are too many to display, we only illustrate the participants in this thesis. The properties can be observed in the same way for all the participants and their friends.

For case study, we define D as the average length of information delivering path (IDP).

D(c) = P

v∈af f ected usersIDP_(c→v) number of af f ected users,

where user c is contagious, user v is an affected user and c → v represents the directed infor-mation delivering path from user c to user v .

In case 1, we presume that contagious user max carries a specific piece of information with responding threshold 0.1. When r^(ij) ≥ th, we consider information would be de-livered from user i toward user j . Marking the contagious user as black node and the af-fected user as gray node, we illustrate the result of case 1 in Figure 4.3. In this case, while

Figure 4.2: The real connections on Facebook.

stone, viola, ryan, mao, bzero, f lower, claire, terry, mei, jay ∈ F_max, max spreads a specific piece of information through viola to stone indirectly. Real data reveal this predicted information delivering path existing, showed in Figure 4.4 and Figure 4.5. Therefore, al-though stone, viola, alphar, peter, channing, hsuan, min ∈ F_lun, lun, who is not a friend of max, has an opportunity to be affected by max via stone and viola. Whereas not all actions are recorded in accessible database that some users get used to click the share button to share a piece of information and the others don’t, we do our best to prove our predicted path set is efficient.

Figure 4.3: The expected information diffusion of case one.

As a result, there are 6 affected user and the information delivering path is 1²₃.

D(max) = 1(max→viola)+ 1_(max→ryan)+ 1_(max→mao)+ 2(max→bzero)+ 2(max→stone)+ 3_(max→lun) 6

= 12 3

In case 2, we presume that contagious user max carries a specific piece of information with responding threshold 0.05. We illustrate the result of case 2 in Figure 4.6. Besides the duplicate paths we have testified in case one, we show the rests in Figure 4.7, in Figure 4.8 and in Figure 4.9. According to the proposed method, viola affect lun directly because of r((viola)(lun)) reaching the responding threshold. Also, bzero is affected by max, instead of indirectly by ryan. As a result, there are 14 affected user and the information delivering path is

Figure 4.4:Real data testify for the diffusion path existing from max to ryan.

Figure 4.5:Real data testify for the diffusion path existing from max to lun.

1₁₂⁵ .

D(max) = 5 × 1 + 8 × 2 + 3 × 1

14 = 1 5

12

max’s influence has a chance to cause the information diffusion in breadth through our partici-pant network.

According to case 1 and case 2, the number of affected users rises as the responding thresh-old descends. The number of users directed affected increases as well. By verifying with the real data, the proposed method discovers the possible delivering paths from 9550 relationships.

We claim that the information certainly propagates in a selected set. On the other hand, we can derive an efficient target set for diffusion of a specific piece of information. we can derive the

Figure 4.6:expected information diffusion of case two

diffusion coverage of a piece of information from a specified individual as well.

In case 3, we presume that the contagious user alphar carries a specific piece of information with responding threshold 0.03. We illustrate the result of case 3 in Figure 4.10. Besides the duplicate paths we have testified in case 1, we show the rests in Figure 4.11. We examine a strong individual responding rate r((alphar)(viola)), which represents the top 3 responding rate for alphar, to form the information delivering path steadily. Even though the content of topics are not similar, the information spreads along this path more times than others as shown in Figure 4.12. As a result, there are 6 affected users and the information delivering path is 1²₃.

In the past few years, researchers have studied scale-free networks and have found the

Figure 4.7:Real data testify for the diffusion path existing from viola to alphar.

vulnerabilities to attacks are rooted in the inhomogeneity of the connectivity distribution. In such networks, removing some highly connected nodes, which ensure the connectivity, may alter the network’s topology and decrease the communication abilities of the remaining nodes dramatically [26]. Due to the testifications above, we figure out that attack survivability is not equivalent to the connectivity any more while human behaviours are included in scale-free network if the information users carry with contains malicious link. Take Figure 4.13 as an example, viola is the most connected user to all other 23 participants while the information with th = 0.1 from viola affects 2 users among the participants and the information delivering path is 1¹₂. Although terry is not the most connected user, the information with th = 0.1 from terry affects 2 users among the participants and the information delivering path is 3⁵₉.

Analyzed by different angle, stone, who is the most connected user to his friends among the participants, has 960 friends. alphar has 325 friends and terry has 276 friends only. However, the information with th = 0.1 from alphar affects 72 users among this connected component and the information with th = 0.1 from terry affects 94 users among this connected component.

But the information with th = 0.1 from stone affects 27 users only, due to fewer interactions between stone and his friends. More detail will be introduced in following subsection.

Figure 4.8:Real data testify for the diffusion path existing from viola to gk.