IKANGAI Solutions. e.u.

Mobile Business Solutions

Posts Tagged ‘Twitter’

Infection modeling: The SIR model

April 3rd, 2012 by Michael No Comments

In the branching process model, a very simplified network structure is assumed. For real-world networks, a more general model should be applied. In order to allow for arbitrary graphs with cycles, we have to distinguish three states for each node:

Susceptible nodes have not been infected yet and are therefore available for infection. They do not infect other nodes.
Infectious nodes have been infected and infect other nodes with a certain probability.
Removed (recovered) nodes have gone through an infectious period and cannot take part in further infection (neither actively nor passively).

Using these three states S, I, and R, and the length of the infectious period t_I as an aditional parameter, a SIR model [1][2] can describe infections in any network structure: Susceptible nodes are infected with a certain probability and infected nodes are removed from the model after the infectious period.

A SIR model assumes that a disease can be caught at most once by each node and is therefore adequate for the modelling of the tweetflow discovery phase. SIS (susceptible – infectious – susceptible) models allow re-infections and apply to many real-world diseases.

References:

[1] Hethcote (1989): Three basic epidemiological models
[2] Easley and Kleinberg (2010): Networks, Crowds, and Markets, p.572

Infection modeling: The branching process model

April 3rd, 2012 by Michael No Comments

When examining the spread of diseases inside a population, not only the contagiousness of the disease, but also the structure of the network connecting the population determine the progress of the infection, as Easley and Kleinberg describe in [1]. Because messages in a social network spread in a very similar way as diseases or ideas, we try to model the discovery phase of a tweetflow invocation using infection modelling.

In tweetflow terms, the contagiousness of a disease for a node corresponds to the payoff (reward – effort) of the tweetflow and the skill of the node. The length of the infectious period corresponds to the period of validity (time to live, ttl). The severity of the infection could match the priority of a tweetflow, if applicable.

Diseases spread in a population as members of the population infect other members (biological contagion). Ideas can spread in the same way inside a social network (social contagion). However, there is an important difference in the way these types of infections are usually analyzed: In biological contagion, there is no decision-making, but a random choice (infection or no infection). Sometimes, these randomized models are useful for social contagion too, if the decision processes are too complex to model or have too many unknown parameters.

The simplest model for infections is the branching process. The contact network is considered a regular tree with k children per node, and the distance from the root is measured in waves. Beginning from this root, the (infected) originator, each infected person passes on the infection to each of the k people in the subsequent wave with probability p. The basic reproductive number R₀ = pk is the expected number of new infections caused by a single infected node. If R₀ > 1, the disease persists in the network, if R₀ < 1, it will die out after a finite number of waves. So both a high infection probability and high numbers of connected nodes are factors of persistence of the disease.

References:

[1] Easley and Kleinberg (2010): Networks, Crowds, and Markets

Infection Phase of Tweetflow Execution

March 10th, 2012 by Michael No Comments

Before a tweetflow can be executed, the requesting node must distribute it among its followers. We call this the infection phase: Starting from the requestor, each node in the follower network has three choices:

Ignore: The infection stops at this node, none of its followers receives the request.
Accept: The infection stops at this node, none of its followers receives the request, but the node signals that it is willing to fulfill the request.
Retweet: The infection continues across this node, and all of its followers receive the request.

I have written a small python program that posts a message in a follower network. It then selects one of the 3 choices mentioned above randomly for each node that receives the message. The result can be drawn as a graph, where red stands for “ignore”, yellow means “retweet” and green stands for “accept”.

It is clearly visible that in order to reach a high infection rate:

High follower counts are most important for nodes with a small distance to the requestor.
Retweeting the information is most important for nodes with a small distance to the requestor.

The infection rate of a follower network can be seen as a random variable, so an expected value for the infection rate can be calculated if there are usable estimates for the probabilities of each choice (accept, retweet, ignore).

Analyzing Bought Twitter Followers

January 11th, 2012 by Martin No Comments

After analyzing the 1000 bought Twitter followers, one can safely assume that all of them can be regarded as fake (“fake” meaning not representing a human user or a company) and that they were created for this purpose. The content of a typical follower has little or no meaning and is never directed to anybody else (which of course true for a lot of Tweets ). Here are some examples from the dataset:

Marietteszm – I luv ur slippers!!
Krystleia – Highlight of the day: DONT TOUCH THAT! WE DONT KNOW WHAT IT IS! .. Wtf mum, its your car.
Sherlyp52 – O değilde arka planım çoğ seksi hgadfhgdfh
Darnellct92 – My kids had a problem listening to me today,my husband was being an ass and even though my tubes are tied i might be pregnant.. what a day!
Clotildetan – asked by about saying about himself being an underdog

Another evidence for the assumption that these followers are fake, is the fact that these Twitter followers never retweet. They are completely passive. Furthermore, all of their Tweets were either posted between October 15th and 20th, on October 25th or on November 13th 2011 which cannot be a coincidence. This suggests that some kind of database in combination with a tool was used to generate these Tweets.

However, the creator of the Twitter users has put some effort into making the Twitter follower appear human. All of them had pictures and locations and short descriptions (some with sexual references) like this:

well i think i have the longest list of people who hate me ever, i call myself a villain because i fuck shit up, you aint got nothing to do ? shit give me head

The structure of network itself does not exhibit any clustering behavior: all bought Twitter followers just point to MartinTreiber_ and have only a few connections among each other. This is reflected in statistics of the network structure:

Number of vertices: 1010
Number of edges: 1179
Average degree: 2.335
Clustering coefficient: 0.112
Average embeddedness: 0.433
Graph density: 0.001
Connected components (weak/strong): 1/1010

If we move the MartinTreiber_ node to the center, apply the noverlap algorithm and zoom in, it is clearly observable that the vast majority of followers are fake, as the ratio of the number of relations to MartinTreiber_ with respect to the number of relations among the other 100 nodes is negligible.

So, what can we learn from this? Actually, it is pretty simple: if you want to boost your Twitter network stats, you can buy Twitter followers. But, if you want to extend your true reach in your Twitter network, you cannot rely on external services that boost your just numbers. You will have to make the effort to look for real people that are actually interested in your Tweets.

your ikangai science team

Buying Twitter Followers

January 8th, 2012 by Martin No Comments

After some considerations, I decided not to use the ikangai Twitter account. Instead, I created a new Twitter account MartinTreiber_ and decided to buy 1000 Twitter followers for it. This morning I got the notification that the account has 1000 new followers. Now it is time to look at the network structure and the followers in more detail.
The first thing I noticed – after a random sample – was that many of them tweeted on November 13th for the last time. Furthermore, lots of the new followers have a low number of followers (around 15-50) and higher number of people they follow (around 140-450) – a factor approximately around 1:10. When I looked at some of the profiles in more detail (specifically at the picture), I found pictures of attractive women and descriptions that contained sexual references. Apparently, this attracts some followers .

Here is a nice graphical representation of the follower network that I bought on Twitter:

Actually, it looks really cool, in comparison with the content. Basically, almost all nodes point to one single node and there are almost no connections between bought followers. My suspicion is that the companies that offer followers to buy just created several thousand of fake Twitter users, added some Tweets to each of them (in batches) to make them look “real” and that’s it. Interestingly, the network is similar to the network that is jokingly considered as Apple’s company structure:

your ikangai science team

A Twitter Experiment

January 6th, 2012 by Martin No Comments

For a course at university, I need to perform an analysis of a social network. My idea is to look at the Twitter network of ikangai and analyze it with NodeXL. After this initial work, comes the interesting part . I’m willing to buy 1000 Twitter followers and then to a look at the Twitter network again and compare its characteristics with the original one. My goal is to investigate the quality of Twitter followers that you can buy. I’m suspecting that the followers you buy form itself some kind of cluster, but that needs to be confirmed by the experiment.

My experiment starts with the following basic Twitter data:

6255

843

1493

As soon as the initial analysis is done, I’ll publish the results here.

your ikangai science team