Market and Social Systems on the Internet

Student name
Professor name
Market and Social Systems on the Internet
Date
Part 1
4. Negative edge weights and Dijkstra’s algorithm:
Give an example of a directed graph with negative weight edges for which Dijkstra’s algorithm produces incorrect answers. (5 points)
Dijkstra’s algorithm works by updating distance between an existing point and a new point for neighboring points. The shortest path in the point is calculated when one of the value is negative when the two points are positive it assumes that the point does not exist. The algorithm has the limitation that the results cannot be negative results from negative points that brings negative results are not used (Easley et al., 2010).
Give an example of a directed graph with negative weight edges for which Dijkstra’s algorithm produces correct answers. (5 points)
Graph G (V, E) with vertices V = {A, B}, edges E = {(A, B), (B, A)} and weight w (A, B) = -1, w (B, A) = +3. From this example the negative weight is used. All the distance of the nodes are defined correctly.
Explain why Dijkstra’s works correctly in certain cases and incorrectly in others. (5 points)
Dijkstra’s algorithm works correctly by computing the distance between two points by using standard deviation. The algorithm works well when the value between the two points is positive which will give relatively similar values for multiple points. The algorithm gives an incorrect answer when the distance between the points is negative (Easley et al., 2010).

Part 2
Modify the simulator to do the following:
Decide on a sociological question that can be studied within the context of the model, which requires you to expand the set of parameters (E.g., consider larger populations, different movement policies, more groups, etc.).
The results give average homogenous values of 738 test which vary. There is a close relationship in all the values from the simulator program. The two ratio give close values for most of the test cases. Test using some sets of data does not bring results which means the points do not exist (Easley et al., 2010).

Figure SEQ Figure * ARABIC 1 visualization o the algorithm

Figure SEQ Figure * ARABIC 2 simulation o values
Formulate a hypothesis (e.g., consider a particular set of parameters that you think affects the outcome).
For a point P in a network, the shortest distance between the P node and next node, otherwise, the point is the shortest distance when all the path in the same network to a point is marked.
Modify the simulator to gather some data points to evaluate your hypothesis (and iterate on #2 until you have a hypothesis that is validated by the data).
When different values are used the values are used as the population, the calculation brings similar values. Most of the social network such as Twitter and Facebook has shown that the algorithm is applicable as the connection from one point to another that is one user to another relies on the shortest distance possible
Write a brief (perhaps 1-3 paragraphs) explanation of your hypothesis, your experimental methods, and your conclusions. Accompany them with a graph (line, chart, bar, pie,) supporting your case.
People using social network then connect to a close friend, who is connected to other close friends. The social network connection shows that the connection path starts from a close friend than to a friend of friends’ connection. Grouping in social media shows a close relationship to the shortest part in the node. The shortest path between nodes of a social network such as Facebook is known to utilize the algorithm. There is a destination node that the message starts from the destination where the message is delivered. Research shows that the message from one node to another uses the shortest path distance (Easley et al., 2010). The communication starts with closes community then it links to another community.

(Easley et al., 2010)
Figure 3 social network interconnection
Works cited
Easley, David, and Jon Kleinberg. Networks, crowds, and markets: Reasoning about a highly connected world. Cambridge University Press, 2010