CAPACITY BUILDING WORKSHOP ON ACTORS AND SOCIAL NETWORK ANALYSES (Jena, Germany, 5-6 July 2006)

Transcription

1 CAPACITY BUILDING WORKSHOP ON ACTORS AND SOCIAL NETWORK ANALYSES (Jena, Germany, 5-6 July 2006) NetSyMoD Network Analysis Creative System Modelling Decision Support Step I Actor Analysis 3. Analysing Network Data

2 A step-by-step guide to Analysing network data with AGNA and R for implementing the NetSyMoD methodological framework PART I: SNA with AGNA In this tutorial, you will perform a social network analysis, following the steps discussed yesterday. The data set you will use contains the results of the survey we conducted yesterday; the data have been saved as an Excel file (brahma.xls), located on the desktop of your computer. Open it: you can see that there are several worksheets, one per section. The first worksheet is dedicated to characteristics of actors, the second one to their relations, the third one to their opinion and the last one named Legend reports the coding aspects. Each partner is associated with its number in the BrahmaTwinn s Description of Work. In the first and third worksheets the actors are listed in rows and the variables in columns; in the second worksheet the actors are listed both in rows and columns following the same order; the value at the crossway of a row and a column indicates the presence of a relation, and eventually its strengths. If the network is directed, the exact meaning of the matrix is that the actor listed in the row is involved in a relation towards the actor listed into the column (e.g. FSU calls FEEM ). This Excel file contains all the data collected yesterday: its aim is to give you a fast picture of the data we are going to analyse today but we will use separate specific agna files format during our exercises. Now you can close the Excel window. Step 1: Input data in AGNA After opening the AGNA software (double click on Agna.exe), you will see a screenshot as this one. The left side contains the matrix of relations, while the right side contains the outputs, statistics and calculations: they are obviously both blank for the moment. Now go to File/New Network: Agna will ask you how many nodes you wish to enter. This number obviously correspond to the number of actors you have in your Matrix of relations (number of rows or columns in the 2 nd worksheet of the excel file) which is 17.

3 Enter the number of nodes, and click OK. The size of the matrix displayed on the left-hand side now corresponds to this number of rows and columns, and you are now ready to directly insert the values which characterise the relationships between actors. Now try to insert single values in the cells and then save your Network example with the name you prefer by going to File/Save Network. Unfortunately, AGNA does not handle multiple relations. We will thus need to conduct the following analysis on separate files, each representing one specific type of relation: each analysis will then be saved in a separate *.agn file, as you just did. Unfortunately, AGNA does not handle multiple relations. We will thus need to conduct the following analysis on separate files, each representing one specific type of relation: each analysis will then be saved in a separate *.agn file, as you just did. To save your time today, we have already inserted the data collected yesterday in dedicated files. We will start our analysis with undirected binary relations, that is matrix agn that you can find in the default Agna directory: therefore go to File/Open Network and open agn. You should now see the matrix of relations (corresponding to question 2.1.2) displayed on the left hand side of the Agna window. By just clicking on the heading of a row (numbers from 1 to 17) you could change the name of the actors (nodes) which will then appear both in the rows and in the columns. We suggest however not to modify the name of the actors, as we will need the file for analysis with a separate software. Rather, make sure you keep a clear labelling of the nodes, in the Excel file for instance. You can now go to the menu Network where you can easily re-arrange your matrix if needed; for instance you could need to: Symmetrize your matrix in the case of accidental asymmetry: For this methodology, the matrix for undirected and binary relations can be symmetrised using union rule (maximum in AGNA). Transpose the matrix: In case you did a mistake while reporting directed data in your excel file, this function allows you to transpose the matrix in order to meet the requirements which do state that the actors listed in the rows are having a directed relations toward the one listed in the columns. Binarize the matrix: This function can be used if you have valued relations, but want to transform them into binary for more powerful analysis. In this case, you should choose a cut-off point in your scale of strength. Remove outsiders: This function allows you to automatically delete the actors not involved in the Network (not interested by any ties/relations) Go to Network/ Symmetrize Go to Network/ Transpose Go to Network/ Binarize Go to Network/ Remove Outsiders

4 IMPORTANT: If you have tried one of this functions (Symmetrize, Transpose, Binarize, Remove outsiders), do save the file with a different name (File/Save Network As ), close it and re-open the original agn file. Step 2: Visualise your network We will begin our analysis by looking at the graphical representation of our network. To visualise the network, go to View/Network viewer. This function enables a pop-up window (as in the screenshot aside) which offers many features, as the search window on the left, or graphical options under the different menus. The network should first be displayed in circular form; you can try to display it in a random form by clicking the fourth button starting from the left, as represented below. You may like to use this function several times to investigate which of the shapes suits better to your network. You can drag and move individual nodes the links between nodes will be updated automatically. Play around with different shapes of the network, but bear in mind that in this network representation location of nodes and proximity have no bearing on the real distance between nodes! Now try to add more information to the network. You can for instance change the appearance of all the nodes (colour, shape). To do this, go to Image/All Faces and select the symbol you prefer into the Light Background folder; you can obviously change single nodes appearances to highlight certain characteristics of your network by selecting a single node (click on it ) and then go to Node/ Face/Light background and select the symbol you prefer. Similarly you can change the size of all the nodes (Image/All Faces width ) or of the single nodes (Node/Face width). Try therefore to assign different node-shapes to the actors, depending on the category of actors they belong to (refer to the information provided in the first worksheet). For instance FSU certainly covers a central position for this network (which will be better analysed later on) so you can try to change the shape, size and colour of this particular node. 1. Move the node at the centre of your network, for instance: do you think this layout has improved the representation of our network data?

5 When you are satisfied with the shape and colour of the network, go to File/Export image/ and save the image as svg which is the format that allows you to modify again the image later on if you wish. In the same menu, you can also save it as a jpeg file if you need to export it later in a report for instance. Lastly, go to File/Insert In Output to save the diagram in the output window: this will allow us to compare the different graphical representations of the different network we are going to analyse today. AGNA will ask you to save the whole output window save it as Output.html, confirm and go to the next actions below. Repeat step 1 and 2 for the other matrix of section 2.1, that is, matrix agn that you can find as well in the default Agna directory (File/Open Network). This is a weighted, undirected network which means that the frequency of interactions is also reported, but the relation is reflexive. Remember to check for consistency of the data matrix and symmetrise it if needed. Now save this 2nd output in the output window (File/Insert In Output) and save your output window: Go to File/ Save Output. Once you are done, minimize the AGNA window, and browse your folders until you find the html output file that you can open by double-clicking it. Now have a look at the 2 networks displayed and try to answer the following questions. Table 1: Network visualisation

6 Step 3: Perform simple statistical analyses with AGNA Under the menu Analysis : you can find different features which allows basic analyses of the properties of the network; the results are all going to be displayed into the right hand side window. Open one of the previously displayed network (2.1.1.agn or agn) and start with the Basic description (Analysis/Basic Description) which tells you the number of nodes, of outsiders, of edges and the type of network ((un)weighted and (un)directed). All the other options under this Analysis menu describe the network, the power of actors and their position. In particular, and as explained yesterday we are interested in: Network density: the number of existing ties, expressed as percentage of the number of ordered/unordered pairs which could theoretically be possible. In more dense, compact networks, information is more likely to spread fast. Diameter of the network: the maximum distance between any two nodes. More formally, the diameter is calculated as the length of the longest geodesic path in the network, where a geodesic path is a path between any two given nodes that is the shortest possible link between those two nodes. That is, the geodesic path can be interpreted as the most efficient path between two nodes. The diameter of a network tells us how many steps are necessary to go from one side of the network to the other. Cohesion of the network: the number of mutual connections in the network divided by the maximum possible number of such connections. Go to Analysis/Distance/ Diameter and see the results in the output window Go to Analysis/ Distance/Diameter and see the results in the output window Go to Analysis/Distance/ Cohesion and see the results in the output window Save your output window and repeat these steps for the other network we already started to analyse (2.1.1.agn or agn). Now, you should be able to reply to other simple questions concerning these networks; see next page.

7 Table 2: Basic statistics 14. Can you tell something about the actors, by comparing the different graphs and network measures? If no, why not? If yes, what can you tell? We are now ready to calculate individual measures of actors position within the network, as detailed in the next steps.

8 Step 4: Calculate centrality with AGNA Open the first network (2.1.1.agn) containing undirected data. As a benchmark measure for nondirected relations, we will calculate the degree of each actor, as well as its Betweenness centrality measure: Degree centrality: is the number of direct ties that involve a given node; degree centrality represents the level of communication activity or the ability to communicate directly with others; it can also be interpreted as the opportunity to influence (and be influenced) directly. The nodal degree can be normalised by dividing the degree number by the maximum number of ties possible, allowing to calculate the NormNodalDegree named relative degree in AGNA s output. Betweeness centrality: It reflects the intermediary location of a node along indirect relationships linking other nodes. For a given node i, this index is computed as the sum of the ratios of the number of geodesic paths between all possible pairs of nodes j and k involving node i to the number of all geodesic paths between j and k. Go to Analysis/ Sociometrics/Nodal Degree and see the results in the output window. Go to Analysis/ Centrality/ Betweeness Repeat step 1, 3 and 4 for the other undirected data (2.2.1.agn, agn) you have in your default Agna Directory. Display the relative networks (step 2), undertake the basic statistical analysis and the centrality analysis, save the outputs and try to answer to the following questions. Table 3 : Centrality measures for undirected networks

9 20. Do you think that the graphical shape of the network you choose in step 2 conveys well the structure of the networks, as emerging from this analysis? If not, re-open the corresponding svg file and draw a better graph; finally save it with a different name. Step 5: Calculate prestige measures for directed network In the current and next step, we are going to analyse the matrixes which we did not open yet, that is agn and agn. Repeat therefore Steps 1 and 3 for the file agn. Now we are going to see how to calculate the centrality of a directed network. For directed relations, one can compute measure of Betweeness centrality but not of Degree centrality (as in step 4): incoming relations may have a different interpretation than outgoing relations. Indeed, in the case of directed graphs, one speaks of out-degree and in-degree measures. Out-degree: It is the sum of all connections from the actor to others: it is important because it tells us how many connections an actor has, and it usually measures how influential an actor is. For a binary network, the out-degree of a node is the total number of edges incident from it divided by the number of all other nodes. In-degree: On the other hand, in-degree computes the number of ties to a given actor. Actors who have a high in-degree are considered more prestigious or supported. The in-degree of a node is thus the sum of all values corresponding to the ties incident to a node, divided by the number of all other nodes in the network. Go to Analysis/ Sociometrics/ Outdegree Go to Analysis/ Sociometrics/ Indegree The Betweeness Centrality index can be calculated for both directional and non directional relations, but scholars advise to consider only in-degree, out-degree and closeness but for our purposes in-degree and out-degree measures are sufficient. Try now to answer to the following, keeping in mind the network of reference ( How many s did you send to representative of the following institutions?): 21. Consider the out-degree measure: which actor has the highest out-degree? What are the implications?

10 22. Consider the in-degree measure: which actor has the highest in-degree? 23. What are the implications? 24. Which measures do you think conveys best actors : Prestige Influence Now that you have complete information on this network, you may want to display its graphical representation as in step 2, maybe editing shapes and colours according to the findings of your analysis.

11 Step 6: Analyse independently a weighted directed network with AGNA Now open the last network we did not analysed yet (2.3.2.agn) and repeat all the steps previously explained. Have a look at all the statistics displayed in the output window and related to: Network density Diameter of the network Out-degree In-degree Now try to answer the following, keeping in mind the network of reference ( How many s did you send to representative of the following institutions?): 25. Consider the out-degree measure: which actor has the highest out-degree? 26. What are the implications? 27. Consider the in-degree measure: which actor has the highest in-degree?

12 28. What are the implications? 29. Which measures do you think conveys best actors : Prestige Influence 30. While analysing your outputs, which are the main differences between binary and weighted networks? 31. Do actors have different roles in terms of their centrality, depending on the type of relation? Try to investigate the most significant statistics and measures of prestige and then prepare a brief report just by copying from the Output AGNA window to a word file the relevant findings of your analysis. If you think this is necessary, you can accompany your report with a representation of your network: create therefore a visualisation of your network, as explained in step 2, re-arrange it, save it as svg and finally as jpg, in order to include it in your report if you wish.

13 Step 7: Structural equivalence In addition to the general description of the network (which also points out the centrality of certain actors) it is also important for the purpose of our analysis to assess the Structural equivalence of actors, if any. Structural equivalence: Actors are structurally equivalent if they have identical ties to and from all other actors, and on all types of relations structurally equivalent actors are, therefore, substitutable and, if two or more actors are structurally equivalent, there is no loss in generality in aggregating them. This analysis is thus carried out on relational data. We need to compare the basic measures which we have discussed earlier. To recap, these are: o Betweenness (non directed relations, that is, 2.1.1, 2.2.1, and 2.3.1) o Nodal degree for presence/absence of relations (non directed relations, that is, 2.1.1, 2.2.1, and 2.3.1) o In-degree or out-degree, depending on the measure you think conveys better the idea of actors influence (see questions in Step 5) (directed, binary and valued relations, that is, 2.1.2, 2.2.2, 2.3.2) Please fill in table 4 attached at the end of the present document. Are there actors who are structurally equivalent? Do you think there are actors who are embedded in the network similarly enough that they are substitutable? To assess the Structural equivalence of actors, we will also need to look at the socio-matrix to find out which actors are related to the same actors, and in the same way. Actors who occupy the same position within the network, can be substituted. This findings has to be completed with the cluster analysis of opinions which will be performed in next section.

14 Part II: Positional equivalence with R The following exercise will show you how to perform a simple cluster analysis with R, an open source application freely available on the WWW ( Several other commercial applications as SPSS, SAS, EViews, Stata offer much more friendly interface to perform the analyses we are interested in, but the licence is usually expensive. If you institution already own such an application, you may want to rely on it. Step 1: Export your data in a txt file First of all you will need to export the data in a format that R is able to handle such as txt or csv. Open the Windows notepad (Start\Programmes\accessories\notepad) and paste the data from the 3 rd excel worksheet directly into the notepad window, including row and column names. Save the file on the desktop with this name brahma.txt and go to next step. Step 2: Open R and import your database Double click on the R desktop icon and import your database by writing the following command in the main window named R-Console, or by pasting it directly from below. Of course you will need to change the file path and name of the file, and to delete the first arrow > if you are copying the command from below. > test<- read.table ('C:/Documents and Settings/Jac/Desktop/brahma.txt') Press enter: test is now the name associated to your database. You can display it by typing the name in the main window and by pressing Enter. > test Step 3: Calculate distances with R Create a new database containing distances between the actors by writing in the Console window the following command: > distances<- dist(test, method = "euclidean") Press Enter. The default method for calculating distances is Euclidean. You can choose between different methods by simply substituting euclidean (Usual square distance between the two vectors - 2 norm) with one of the following: "maximum"', '"manhattan"', '"canberra"', "binary"' or '"minkowski". Now you can display the distances you have calculated by simply writing the name of the database created. In our example: > distances

15 Step 4: Calculate clusters with R Now, once you have calculated the distances, you can cluster them by writing the following command: > cluster<- hclust(distances, method= complete ) On the basis of the distances calculated in the previous step, this function performs a hierarchical cluster analysis using a set of dissimilarities for the n objects being clustered. Initially, each object is assigned to its own cluster and then the algorithm proceeds iteratively, at each stage joining the two most similar clusters, continuing until there is just a single cluster. At each stage distances between clusters are recomputed by the Lance-Williams dissimilarity update formula according to the particular clustering method being used. A number of different clustering methods are provided. Ward's minimum variance method aims at finding compact, spherical clusters. The complete linkage method finds similar clusters. The single linkage method (which is closely related to the minimal spanning tree) adopts a 'friends of friends' clustering strategy. The other methods can be regarded as aiming for clusters with characteristics somewhere between the single and complete link methods. Note however, that methods '"median"' and '"centroid"' are not leading to a monotone distance measure, or equivalently the resulting dendrograms can have so called inversions (which are hard to interpret). Now, you can display the dendogram by writing the following code: > plot(cluster) You should obtain this kind of output: The leaves grouped together indicate similar actors opinions; the distance is reported on the Y axis (Height), where the branches join each other indicate the distance between actors. On the basis of these evidences you are now able to assess the positional equivalence of actors involved and indicate the ones which may be substituted by others, on the basis of the Structural equivalence assessed earlier.

16 32. How many clusters are there in your network? 33. Are the clusters very different among themselves? 34. Consider also actors positional equivalence: do you think that there are actors who could be substituted? 35. Note: it may be interesting to perform the cluster analysis for each type of questions, and compare the results. If you have time, try to analyse clustering of the network with respect to one opinion question of your choice.

17 Annex I: Tips and tricks to use R All the documentation on this software package can be found in the default directory as pdf or html files: R\R-2.3.0\doc\manual First of all if you need some help on a particular R function, just write in the console window the following command help ( function name ) and press Enter. For instance: > Help (hclust) You can associate an output to each of the calculation you perform by using the following command: NameOutput <- function (matrix,, ), as in the following example: > test<- read.table ('C:/Documents and Settings/Crimi/Desktop/brahma.txt') As in the example, be aware that the path name in R is written with / and not with \ as in Windows explorer. You can include text comments in the command file, by opening and closing the comment statements with "#": #Step 4: Calculate clusters with R# cluster<- hclust(distances) The additional text contained between the hashes will not change the command. It will however add clarity to the file, and allow you to recall the meaning of each command later on. Each function in R (as read.table, dist, hclust etc ) is built with several arguments enclosed by parenthesis, separated by commas, which can be modified at will. The first arguments are the data on which the calculations are performed, while for the following, if no specification is made, the arguments are set to default. For instance, the complete default function on distances is the following: o dist(x, method = "euclidean", diag = FALSE, upper = FALSE, p = 2) x: a numeric matrix, data frame or '"dist"' object. method: the distance measure to be used. This must be one of "euclidean"', '"maximum"', '"manhattan"', '"canberra"', "binary"' or '"minkowski"'. Any unambiguous substring can be given. diag: logical value indicating whether the diagonal of the distance matrix should be printed by 'print.dist'. upper: logical value indicating whether the upper triangle of the distance matrix should be printed by 'print.dist'. p: The power of the Minkowski distance. m: An object with distance information to be converted to a "dist"' object. For the default method, a '"dist"' object, a matrix (of distances) or an object which can be coerced such a matrix using 'as.matrix()'. (Only the lower triangle of the matrix is used, the rest is ignored). o If we simply type in dist(test) as we did in our tutorial in step 3, the method will be by default set to Euclidean and the power of the Minkowski distance to 2 for instance. We can however specify different arguments as in the example below: dist(test, method = " manhattan ", p = 3) if you want some details on the meaning of the arguments, simply type in help (dist)