Example 5Eva, Wong, Yumi and Kim are students who are staying in a backpacker's hostel. Because they speak differentlanguages they can have problems communicating. The situation they have to deal with is that:a)b)d)e)8)f)...c) Find (²..Eva speaks English onlyYumi speaks Japanese onlyKim speaks Korean onlyWong speaks English, Japanese and Korean.Summarise this information in a network diagram.Construct a communication matrix, C, to represent the situation, where rows represent the speakers andcolumns the receivers.Interpret the element (1, 1) in C²Can you find an example of a redundant link in the previous matrix?Can you think of a legitimate situation where a redundant link may actually be feasible?Calculate T for our communications matrix. (T=C+C².)5| PageExample 6Four fire towers T1, T2, T3 and T4, can communicatewith one another as shown in the diagram opposite. Inthis diagram an arrow indicates that a direct channelof communication exists between a pair of fire towers.The matrix C² is shown opposite.d Explain the meaning of the 1 inrow T3, column T1e How many of the two-stepcommunication links shown in thematrix C² are redundant?TIFor example, a person at tower 1 can directly communicate with a person in tower 2and vice versa.The communication matrix C can bealso used to represent this information.a Explain the meaning of a zero inthe communication matrix.b Which two towers cancommunicate directly with T2?c Write down the values of the two missing elements in the matrix.C =C²=0072T1 T2 T3 T40 11010A0111T1101073T2 T3 T4010210200 TI0 721 T30 T40711 T20T31 T4f Construct a matrix that shows the total number of one and two-step communicationlinks between each pair of towers.g Which of the four towers need a three-step link to communicate with each other?T46| Page Dominance matricesDominance matrix is a square binary matrix in which 1s represent one-step dominance between membersof a group.In many group situations, certain individuals are said to be dominant. Problems of identifying dominantindividuals in a group can be analysed using the same approach we used to analyse communicationnetworks.This method is used to rank teams or players who are playing competition against each other.D represents one-step dominanceD² represents two-step dominanceTotal dominance scores, T = D + D²Example 7Five tennis players - Anna, Birgit, Cas, Di and Emma-compete in a round-robin tournament (each player plays everyother player once). Who is the best player? Another way of asking this might be: Who is the DOMINANT player?The results are:Anna defeated Cas and DiBirgit defeated Anna, Cas and EmmaCas defeated Di. Di defeated Birgit.Emma defeated Anna, Cas and Di.a) Summarise this information in a network diagram, with arrows moving from the winner to the loser..b) Construct a one-step dominance matrix, D, to represent the situation, where players are listed in alphabeticalorder. Enter a '1' in each ROW to show who the player on the left won against. Find the DOMINANCE SCORE foreach player by summing the values in each row.ABD =from CDEtoABCD0 0 1 1E0This is a one step Domination matrix because it tells us whodefeated who, or who dominated over who, in theirindividual game. If we add the elements in each row, we getthe total number of wins (one-step dominances) of eachplayer.7| PageNow we can also take into account two step dominances in order to rank the players. A two step dominance occurswhen for example A defeats C who then defeats D. A is said to have a two step dominance over D.We can find the two-step dominance matrix by squaring D. Once we have done this, we can add together the oneand two-step dominances to get a total dominance score.Find D², the two-step dominance matrix and also find the total for each row.c)d)fromTotal dominance matrix = T =D+D²8CA8C D ECalculate the total dominance score for each player by first finding T and hence rank the players.Example 8The graph shows the one-step dominances between four farmdogs, Kip, Lab, Max and Nim. In this graph, an arrow from Labto Kip indicates that Lab has a one-step dominance over Kip.From this graph, it can be concluded that Kip has a two-stepdominance overA Max only.B Nim only.D all of the other three dogs. E none of the other three dogs.NimC Lab and Nim only.MAX8 | Page

Question

Accepted Answer

a) summarize the info in a network diagram