Developing a Framework for Linking Clustering Coefficient to Loose Coupling of Hardware and Software Systems

This paper will discuss the concept of the Clustering Coefficient as is used with regard to the connectivity between people or organizations. The paper will use an example of a hypothetical group of people as would be found on a small project team to determine a possible best range for the coupling coefficient to resolve the optimal number of tight and loose connections. The concept of diminishing marginal returns and the tradeoff between tight and loose connections will be examined to determine how tight connections may actually destroy options on exchanging information with other people, and thus lower the value of the organization. The concept of the coupling coefficient will then be applied to discuss the concept of Loose Coupling as is often applied to hardware and software systems, or systems of systems. The goal of this section of the paper will be to determine a framework to examine the level of coupling between subsystems in a system of systems, and to then determine to what degree a system is coupled, with possible implications to the difficulty and costs for spiral developing the subsystems. Coupling to standards will be presented as analogous to limiting the tight connections between people. Introduction: As part of looking at valuing networks and applying this concept to organizational design, the concept of clustering and the clustering coefficient became apparent. Unfortunately, while the concept is discussed, rarely is a formula found to readily apply to an organization or an actual network. Additionally, the application of the clustering coefficient is scratched upon but not deeply investigated. This paper uses a previously developed method for calculating the coupling coefficient and applying it to a hypothetical group to determine the levels of a coupling coefficient that aid and hinder group performance. This author believes that social networking theory and systems engineering concepts can be closely linked. As such, this paper attempts to move past the idea of a coupling coefficient to provide a possible method to evaluate loose coupling between technical systems. Clustering: Clustering is a measure, or at least a heuristic, to define the level of connectivity between a group of people. The Clustering Coefficient (CC) is the measure for this level of connectivity. As described in “Linked”m (Barabasi, 2002), if 4 people are all closely connected then the CC = 1.0. Essentially: CC = number of close links/ number of possible close links Number of possible close links = N(N-1)/2 As an example, “Linked” says that if there are 4 people then there are 6 possible close links. Some readers may confuse this with what is commonly referred to as the “N(N-1), or the N problem.” This problem is how people describe the pre-networking challenge that occurred when the DoD tried to have all of the nodes in a certain mission area connect to all other nodes in that mission area. The N(N-1) was based on using half©2007 The MITRE Corporation. All Rights Reserved. 2 DRAFT Developing a Framework for Linking Clustering Coefficient to Loose Coupling of Hardware and Software Systems John W. Dahlgren [email protected] Approved for Public Release. Distribution Unlimited. # 07-0202 Connections Coefficient Hops Hops of Network duplex radios and needing to be able to transmit and receive at the same time. In “Linked” they show only 6 links between 4 nodes because they appear to assume full duplex links. This explains why the above formula divides the N(N-1) by 2. Figure 1 Linkage between 4 Close Friends From the above example, if each of the 4 people are all close friends, then CC = 6/6 = 1.0. In reality everyone won’t be close friends. If only 4 of those links were considered to be among close friends, then the CC = 4/6 = .667. Generally speaking, many people would look at these examples and believe having a CC = 1.0 is optimal. Surprisingly that is not the case. When everyone in a group is very close to each other, they usually primarily exchange information with each other. This limits their information sources and limits the knowledge the group has access to. As pointed out in “Linked” and “The Agile Organization” it is optimal to have some closeness within a group along with having what are called weak connections to outside groups, thereby making more information available to more people. “Linked” related this to the results of job searches, and that most people don’t learn about job openings from their close friends but really learn about openings from “friends of friends”. This mixture of a close knit group of people along with weaker outside links to other groups is referred to as a Small World Network. Optimal Clustering Coefficient While various readings have discussed the CC, the author has yet to find one that goes deeply into discussing how to optimize network performance to have a Small World Network that takes into account: How the formula for CC can be amended to take into account the optimal range of tight connections. How the formula for CC can be amended to take into account the benefits of medium and weak connections. How the answers to the CC and the above questions relate to the survivability of a Small World Network. How a formula can evaluate the gradual degradation of performance as various links are removed in a Small World Network. The next challenge is to determine the optimal CC, or at least a range for the CC to provide an optimal Small World Network as judged by performance. The below table shows the range of CC values for the number of close connections in a group of 4 people. Close Clustering Maximum # of Average # of Resiliency ©2007 The MITRE Corporation. All Rights Reserved. 3 DRAFT Developing a Framework for Linking Clustering Coefficient to Loose Coupling of Hardware and Software Systems John W. Dahlgren [email protected] Approved for Public Release. Distribution Unlimited. # 07-0202 rminable rminable 1 .167 Undete Undete 0 2 .333 Undeterminable Undeterminable 0 3 .5 2 1.5 Minimal to 0 4 .667 2 1.33 Good 5 .833 2 1.17 Best 6 1.0 1 1 Good to Avg Table 1 Range of Clustering Coefficient Values able 1 introduces the concept of resiliency of the network. For this paper, resiliency is