Applying social network Analysis to the Information in CVS RepositoriesAbstractThe huge quantities of data available in the CVS repositories of large, long-lived lib re (free, open source) software projects, and the many interrelationships among those data offer opportunities for extracting large amounts of valuable information about their structure, evolution and internal processes. Unfortunately, the sheer volume of that information renders it almost unusable without applying methodologies which highlight the relevant information for a given aspect of the project. In this paper, we propose the use of well known set of methodologies (social network analysis) for characterizing lib re software projects, their evolution over time and their internal structure. In addition, we show how we have applied such methodologies to real cases, and extract some preliminary conclusions from that experience. Keywords: source code repositories, visualization techniques, complex networks, lib re software engineering 1 Introduction The study and characterization of complex systems is an active research area, with many interesting open problems. Special attention has been paid recently to techniques based on network analysis, thanks to their power to capture some important characteristics and relationships.
Network characterization is widely used in many scientific and technological disciplines, ranging from neurobiology [14] to computer networks [1] [3] or linguistics [9] (to mention just some examples).
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In this paper we apply this kind of analysis to software projects, using as a base the data available in their source code versioning repository (usually CVS).
Fortunately, most large (both in code size and number of developers) lib re (free, open source) software projects maintain such repositories, and grant public access to them. The information in the CVS repositories of lib re software projects has been gathered and analyzed using several methodologies [12] [5], but still many other approaches are possible. Among them, we explore here how to apply some techniques already common in the traditional (social) network analysis. The proposed approach is based on considering either modules (usually CVS directories) or developers (commit ers to the CVS) as vertices, and the number of common commits as the weight of the link between any two vertices (see section 3 for a more detailed definition).
This way, we end up with a weighted graph which captures some relationships between developers or modules, in which characteristics as information flow or communities can be studied. There have been some other works analyzing social networks in the lib re software world. [7] hypothesizes that the organization of lib re software projects can be modeled as self-organizing social networks and shows that this seems to be true at least when studying SourceForge projects. [6] proposes also a sort of network analysis for lib re software projects, but considering source dependencies between modules.
Our approach explores how to apply those network analysis techniques in a more comprehensive and complete way. To expose it, we will start by introducing some basic concepts of social network analysis which a reused later (section 2), and the definition of the networks we consider 3. In section 4 we introduce the characterization we propose for those networks, and later, in section 5, we show some examples of the application of that characterization to Apache, GNOME and KDE. To finish, we offer some conclusions and discuss some future work.
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2 Basic concepts on Social Network Analysis The Theory of Complex Networks is based on representing complex systems as graphs. There are many examples in the literature where this approach has been successfully used in very different scientific and technological disciplines, identifying vertices and links as relevant for each specific domain. For example, in ecological networks each vertex may represent a particular specie, with a link between two species if one of them “eats” the other. When dealing with social networks, we may identify vertices with persons or groups of people, considering a link when there is some kind of relationship between them.
Among the different kinds of networks that can be considered, in this paper, we use affiliation networks. In affiliation networks there are two types of vertices: actors and groups. When we represent the network in terms of actors, each vertex is associated with a particular person and two vertices are linked together when they belong to the same group of people. When we represent the network in terms of groups, each vertex is associated with a group and two groups are linked through an edge when there is, at least, one person belonging to both at the same time.
Social networks can be directed (when the relationship between any two vertices is one way, like “is a boss of”) or undirected (when it is bidirectional, like “live together”).
In addition, they can be weighted (each edge has an associated numeric value) or unweighted (each edge exists or not).
3 Definition of the networks of developers and modules In the approach we propose, for each project we build two networks using the commit information of the CVS system. Both correspond to the two sides of an affiliation network obtained when we consider commit ers and modules software projects.
In both cases we consider weighted undirected networks as follows: Commuter network. Each vertex corresponds to particular commit er (usually, a developer of the project).
Two commit ers are linked when they have contributed to at least one common module, being the weight of the corresponding edge the number of commits performed by both developers to all common modules. Module network. Vertices represent a software module of the project. Two modules are linked when there is at least one commit er who has contributed to both of them.
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Edges are weighted by the total number of commits performed by common commit ers to both modules. The definition of what is a module will be different from project to project, but usually will correspond to top level directories in the CVS repository. In the case of both networks, the weight of each edge (degree of relationship) re-fleets the closeness of two vertices. The higher it is, the stronger the relationship between the given two vertices. We may also define the cost of relationship between any two vertices as the inverse of the degree of relationship.
That cost of relationship is a measure of the “distance” between them, in the sense that the higher this parameter the more difficult to reach one vertex from the other. For this reason we use the cost of relationship as the base for defining a distance in our networks. Given a pair of vertices i and j, we define the distance between them as di j = e 2 Pi; j ce, where Pi; j is the set of all the edges in the shortest path from i to, and ce is the cost of relationship of edge e of such path. 4 Characterization of the networks considered for each project For our analysis, we have considered a number of parameters characterizing the topology of the networks. In particular, we use the following definitions (which are common in the analysis of affiliation networks): Degree of a vertex (k): number of edges connected to that vertex. In the case of commit er networks, for it represents the number of companion commit ers, contributing to the same modules as the given one.
In the case of module networks, it is the total number of modules with which the given one. Weighted degree of a vertex: sum of the weights of all edges connected to that particular vertex. This can be interpreted as the degree of relationship of a given vertex with its direct neighborhood. Distance centrality of a vertex [13] (Dc): proximity to the rest of vertices in the network. It is also called closeness centrality: the higher its value, the closer that vertex is to the others (on average).
Given a vertex v and a graph G, it can be defined as: Dc (v) = 1 t 2 G dG (v; t); (1) where dG (v; t) is the minimum distance from vertex v to vertex t (the sum of the costs of relationship of all edges in the shortest path from v to t).
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The distance centrality can be interpreted as a measurement of the influence of a vertex in a graph: the higher its value, the easiest it is for that vertex to spread information into that network. Let’s observe that when a given vertex is “far” from the others, it has a low degree of relationship (i. e. a high cost of relationship) with the rest. In that case the term t 2 G dG (v; t) will be high, meaning that the vertex is not placed in a central position in the network, being its distance centrality low. This parameter can be used to identify modules or are well related in a project.
Between ness centrality of a vertex [4, 2]: The of a vertex Bc is a measurement of the number of shortest paths traversing that particular vertex. Given a vertex v and a graph G, it can be defined as: Bc (v) = s 6 = v 6 = t = inG st (v) st; (2) 2 Degree 0 50 100 150 200 250 300 350 400 450020406080100120 Figure 1. Distribution of the degrees of Apache, circa February 2004 where st (v) is the number of shortest paths from s tot going through v, and st is the total number of shortest paths between s and t. The between ness centrality of a vertex can be interpreted as a measurement of the importance of a vertex in a given graph, in the sense that vertices with a high value of this parameter are intermediate nodes for the communication of the rest. Inthe case of weighted networks, multiple shortest paths between any pair of vertices are highly improbable. So, the term st (v) st takes usually only two values: 1, if the shortest path between s and t goes through v, or 0 otherwise.
Therefore, the between ness centrality is just a measurement of the number of shortest paths traversing a given vertex. Clustering coefficient of a vertex [14]: The clustering coefficient c of a vertex measures the connectivity of its direct neighborhood. Given a vertex v in a graph G, it can be defined as the probability that any two neighbors of v be connected. Hence (v) = E (v) kv (kv 1); (3) where kv is the number of neighbors of v and E (v) is the number of edges between those neighbors. A high clustering coefficient in a network indicates that this network has a tendency to form cliques.
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Observe that the clustering coefficient does not consider the weight of edges. Weighted clustering coefficient of a vertex [10]: The weighted clustering coefficient cw of a vertex is an attempt to generalize the concept of clustering chef- to weighted networks. Given a vertex v in a weighted graph G it can be defined as: cw (v) = i 6 = j 2 NG (v) wi j 1 kv (kv 1); (4) cc (clustering coefficient) 0. 3 0. 4 0. 5 0.
6 0. 7 0. 8 0. 9 1 1. 1051015202530 cc (clustering coefficient) 0. 6 0.
65 0. 7 0. 75 0. 8 0. 85 0. 9 0.
95 1 1. 05020406080100120 Figure 2. Clustering coefficient of modules in Apache (top) and GNOME (bottom), circa February 2004 (distribution) where NG (v) is the neighborhood of v in G (the all vertices connected to v), wi j is the degree of relationship of the link between neighbor i and neighbor j (wi j = 0 if there are no link), and kv is the number of neighbors. The weighted clustering -cent can be interpreted as a measurement of the local efficiency of the network around a particular vertex. For our networks, remark that the term i 6 = j 2 NG (v) wi j can be seen as the total degree of relationship in the neighborhood of vertex v, while 1 kv (kv 1) is the total number of relationships that could exists in that neighborhood. 5 Case studies: Apache, GNOME and KDEmodulesApache, GNOME and KDE are all well known lib re software projects, large in size (each well above the million lines of code), in which several sub projects (modules) can be identified.
They have already been studied (for instance in [11] and [8]) from several points of view. We have used them to apply our methodology, and in this section some results of that application are shown (just an example of how a project can be characterized from several points of view).
In figure 1 the distribution of the degree of relationship for each commit er in the Apache project is shown as an ex-3 Weighted clustering coefficient 0 5000 10000 15000 20000051015202530 Weighted clustering coefficient 0 20000 40000 60000 80000 100000 120000 140000050100150200250 Weighted clustering coefficient 0 20000 40000 60000 80000 10000002468101214 Figure 3. Weighted clustering coefficient of modules in Apache (top), GNOME (middle), and KDE (bottom), circa February 2004 (distribution) ample of how developers can be characterized by how they relate to each other. It is easy to appreciate how that distributions shows two peaks, one between 20-40 and other around 70-90. Only a handful of developers has direct relationship with more than 200 companions.
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Finally there is a comparison off all the three software projects studied. The methodology followed in writing this term paper is reading the following reference materials available in the internet and extracting the key points for the failures of the software projects. The papers referenced for writing the following term paper are 1. H. Goldstein. Who Killed the Virtual Case File? IEEE Spectrum, ...
In figure 2 the distribution of the clustering coefficient of modules in Apache and GNOME is compared. Although in both cases there is a peak in 1 (meaning that in many cases the direct neighborhood of a module is completely linked together), there is an interesting peak in GNOME around 0. 77, which should be studied but probably corresponds to sparse-connected cluster. Figure 3 shows how, despite differences in the distribution of the clustering coefficient, the distribution of the weighted clustering coefficient has more similar shapes, with a quick rise from zero to a maximum, and a slower, asymptotic decline later. This would mean than in the three projects most nodes (those near the peak) are in clusters with a similar interconnection structure. As a final example, on the evolution of a project, figure 4 shows the distribution of the connection degree of four snapshots of the Apache project.
It can be seen how there isa tremendous growth in the connection degree of the most connected module (from 34 in 2001 to more than 100 in 2004), while the shape of the distribution changes over time: from 2001 to 2002 a two-peak structure develops, which slowly changes into a one-peak distribution through 2003 and 2004. For lack of space we do not offer it here, but the analysis of the top modules and developers for each parameter considered gives a lot of insight on which ones are helping to maintain the projects together, to deal with information flows, or are the of clusters. 6 Conclusions and further work In this paper we have shown a methodology which applies affiliation network analysis to data gathered from CVS repositories. We also offer some examples of how it can be applied to characterize lib re software projects. From amore general point of view, we have learned (demonstration not shown in this paper) that in the three analyzed cases (Apache, GNOME and KDE), both the commit ers and the modules networks are small-world networks, which means that all the theory developed for them applies here.
Our group is still starting to explore the many paths open by this methodology. Currently, we are interested in analyzing a large number of projects, looking for correlations which can help us to make estimations and predictions of the future evolution of projects. We are also looking for characterizations of projects based on the parameters of the curves that interpolate the distributions of the parameters we are studying. And of course, applying other techniques 4 Degree 0 5 10 15 20 25 30 35012345678 Degree 0 10 20 30 40 50 60 70024681012 Degree 0 10 20 30 40 50 60 70 80 9002468101214 Degree 0 20 40 60 80 100 12002468101214 Figure 4. Connection degree of modules in Apache circa February from 2001 (top) to 2004 (bottom) (distribution) usual in small-world and other social networks. We feel that these research paths will allow for the more complete understanding of how lib re software projects differentiate from each other, and also will help to identify common patterns and invariants.
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