Relationship Between Cohesion and Coupling Metrics for Object-Oriented Systems

Abstract

Cohesion and coupling are regarded as fundamental features of the internal quality of object-oriented systems (OOS). Analyzing the relationships between cohesion and coupling metrics plays a significant role to develop efficient techniques for determining the external quality of an object-oriented system. Researchers have proposed several metrics to find cohesion and coupling in object-oriented systems. However, few of them have proposed an analysis of the relationship between cohesion and coupling. This paper empirically investigates the relationships among several cohesion and coupling metrics in object-oriented systems. This work attempts to find mutual relationships between those metrics by statistically analyzing the results of experiments. Three open-source Java systems were used for experimentation. The empirical study shows that cohesion and coupling metrics are inversely correlated.

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Appendices

Appendix

A Definitions of Cohesion Metrics:

LCOM1, (Lack of Cohesion in Methods 1), [16].

The number of pairs of methods in the class using no instance variables in common.

LCOM2, (Lack of Cohesion in Methods 2), [17].

$$\begin{aligned} LCOM2= \left\{ \begin{array}{cl} P-Q, &{} if \; P-Q \ge 0 \\ 0, &{} otherwise \\ \end{array} \right. \end{aligned}$$

where, P = number of pairs of methods without shared instance variables. Q = number of pair of methods with shared instance variables.

LCOM3, (Lack of Cohesion in Methods 3), [26].

Consider an undirected graph G, where the vertices are the methods of a class, and there is an edge between two vertices if the corresponding methods share at least one instance variable. Then $LCOM3=|connected \ components \ of \ G|$.

LCOM4, (Lack of Cohesion in Methods 4), [23].

LCOM4 is similar to LCOM3, where graph G additionally has an edge between vertices representing methods $M_i$ and $M_j$, if $M_i$ invokes $M_j$ or vice versa.

LCOM5, (Lack of Cohesion in Methods 5), [22].

Consider a set of methods $\{M_i \}(i=1...m)$ accessing a set of instance variables $\{A_j \}(j=1...a)$. Let $\mu (A_j )$ be the number of methods that reference $A_j$. Then $LCOM5= \frac{\frac{1}{a}\times \sum _{1\le j\le a}\,\times \,\mu (A_j)-m}{1-m}$.

CBMC, (Cohesion Based on Member Connectivity), [15].

The CBMC for a class C, CBMC(C), is defined to be the connectivity factor of its reference graph, $F_c (G_r (C))$, scaled by the structure factor of its reference graph, $F_s (G_r (C) )$. $CBMC(C)=F_c (G_r (C) )\times F_s (G_r (C) )=F_c (G_r (C) )\times \frac{1}{n} \sum _{i=1}^n CBMC({G_r}^i (C) )$ The connectivity factor of a reference graph $G_r, F_c (G_r)$, represents the degree of the connectivity among the members, and is defined to be the ratio of the number of glue methods $|M_g (G_r)|$ to the number of normal methods $|M_n (G_r)|$: $F_c (G_r)= \frac{|M_g (G_r)|}{|M_n (G_r)|}$.

The structure factor for a reference graph $G_r, F_s (G_r )$, is defined to be the average cohesion of its children in the structure tree: $F_s (G_r )$ = $\frac{1}{n}\times \sum _{i=1}^n CBMC({G_r}^i )$ where ${G_r}^i$ is one of the n children of $G_r$ in the structure tree, and $CBMC({G_r}^i )$ denotes the cohesion of a component ${G_r}^i$.

ICBMC, (Improved Cohesion Based on Member Connectivity), [33].

The cohesion for the reference graph $G_c = (N_c, E_c)$ of a class c is defined: $ICBMC(G_c )=$

$$\begin{aligned} \left\{ \begin{array}{cl} \frac{|M_g |}{|N_m (G(c))|\times |N_v (G(c))|}\times \frac{1}{2} \times \sum \nolimits _{i=1}^{2} ICBMC(G_{M_g}^i ) \, \mid \; Q \in CS(G), \end{array} \right\} \end{aligned}$$

(1)

where $N_m$ and $N_v$ denote the set of vertexes representing methods and the set of vertexes representing instance variables of class c, respectively; G is called an elementary component of $G_c$. If a graph $G' =(N',V')$ is a sub graph of the reference graph $G_c$ and its non-spanning graphs contain elementary components, then $G'$ is called a non-elementary component of $G_c$. $G_c = (N_c, E_c)$ is the reference graph of a class c. Q is the minimum set of edges.

$OL_n$, [34].

This metric can be defined as the common strength of attributes. The strength of the attribute can be defined as the common strength of the methods that approach that attribute. Where n are the numbers of iteration which are used to calculate OL. COM(m) and COV(v) are used to represent the strength of method m and instance variable v respectively in Yang’s cohesion measure. For a given class c, Yang first constructs a corresponding reference graph $G_c$. If $G_c$ is disjoint, then let its cohesion be 0, otherwise computes its cohesion value by the following steps: (1) Initialize the iteration count variable count to 0, i.e., let count = 0; (2) For every method $m_i$, set its initial strength to 1, i.e., let $COM (m_i) = 1$; (3) For every instance variable $v_i$, let $COV(v_i)=\frac{1}{N_m (G_c)} \times \sum _{j=1}^{l} COM (m_j)$ where $N_m (G_c)$ denotes the number of method vertexes in $G_c$ and $\lambda (m_j,c)$; (4) For every method $m_i$, let $COM(m_i)=\frac{1}{N_v (G_c)} \times \sum _{k=1}^{m} COM (v_k)$, where $N_v (G_c)$ denotes the number of instance variable vertices in $G_c$ and $v_{k \in \lambda (m_j,c)}$; (5) $count = count + 1$, if $count <n$ then Go to (3) (6) Compute the cohesion of class c, i.e., let $OL_n (c)$=$\frac{1}{N_v (G)} \times \sum _{r=1}^{N_v (G)}COV (v_r)$.

PCCC, (Path Connectivity Class Cohesion), [1].

$$\begin{aligned} PCCC(C)= \left\{ \begin{array}{cl} 0, &{} if \; l=0 \; and \; k>1 \\ 1, &{} if \; l>0 \; and \; k=1 \\ \frac{NSP(G_c)}{NSP(FG_c)}, &{} otherwise \\ \end{array} \right. \end{aligned}$$

Where l is the number of attributes, k is the number of methods and NSP is the number of simple paths in graph $G_c$; $FG_c=$ corresponding fully connected graph.

LSCC, (Low-level design Similarity-based Class Cohesion), [4].

$$\begin{aligned} LSCC(C)= \left\{ \begin{array}{cl} 0, &{} if \; k=0 \; or \; l=0 \\ 1, &{} if \; k=1 \\ \frac{\sum _{i=1}^{l} x_i (x_i-1)}{lk(k-1)}, &{} otherwise \\ \end{array} \right. \end{aligned}$$

Where l is the number of attributes, k is the number of methods and $x_i$ is the number of methods that referenced.

CC, (Class Cohesion), [12].

CC = Ratio of the summation of the similarities between all pairs of methods to the total number of pairs of methods. The similarity between methods i and j are defined as: $Similarity (i,j) =\frac{|I_i \cap I_j |}{|I_i \cup I_j |}$ where $I_i$ and $I_j$ are the sets of attributes referenced by methods i and j, respectively.

SCOM, (Sensitive Class Cohesion Metric), [18].

SCOM = Ratio of the summation of the similarities between all pairs of methods to the total number of pairs of methods. The similarity between methods i and j is defined as: $Similarity (i,j)=\frac{|I_i \cap I_j |}{(|I_i |,|I_j|)}\times \frac{|I_i \cup I_j |}{l}$, where l is the number of attributes.

TCC, (Tight Class Cohesion), [10].

Consider a class with N public methods. Let NP be the maximum number of public method pairs: $NP=[N \times (N-1)]/2$. Let NDC be the number of direct connections between public methods. Then TCC is defined as the relative number of directly connected public methods. Then, $TCC=NDC/NP$.

LCC, (Loose Class Cohesion), [10].

Consider a class with N public methods. Let NP be the maximum number of public method pairs: $NP=[N \times (N-1)]/2$. Let NIC be the number of direct or indirect connections between public methods. Then LCC is defined as the relative number of directly or indirectly connected public methods. $LCC=NIC/NP$.

B Definitions of Cohesion Metrics:

CBO_IUB, (CBO Is Used By), [24].

(CBO Is Used By: the part of CBO that consists of the classes using the target class): the definition of CBO merges two coupling directions: classes using the target class and classes used by the class. For changeability purposes, the former seems more relevant than the latter one, hence the split.

CBO_U, (CBO Using), [24].

(CBO Using: the part of CBO that consists of the classes used by the target class): introduced as a consequence of CBO_IUB, to cover the part of CBO not considered by CBO_IUB.

CBO, (Coupling between Object Classes), [16].

CBO for a class is the count of the number of other classes to which it is coupled. A class is coupled with another class if the method declared in one class uses method or instance variable defined by another class. CBO includes inheritance-based coupling (i.e. coupling between classes related via inheritance). For good software quality, high CBO is undesirable.

RFC, (Response for a Class), [16].

RFC can be defined as the set of methods that can potentially be executed in response to a message received by an object of that class. $RFC = |RS|$ where, RS = the response set for the class. The response set for the class can be defined as: $RS = \{M_i \} \bigcup _{all \, n} \{R_i\}$ where, $\{R_i\}$ is set of methods called by method $M_i$ and $\{M_i\}$ is set of all methods in the class. RFC of class A = Number of methods in class A + Number of distinct methods of other classes directly invoked by the methods of class A.

MPC, (Message Passing Coupling), [27].

The MPC metric gives an indication of how many messages are passed among objects of the classes: MPC = number of sent statements defined in a class. The number of messages sent out from a class may indicate how dependent the implementation of the local methods is on the methods in other classes. This may not be indicative of the number of messages received by the class.

DAC, (Data Abstraction Coupling), [27].

DAC or DAC1 is the number of attributes whose types are of other classes. DAC = number of ADTs (abstract data type) defined in a class. The number of variables having an ADT type may indicate the number of data structures dependent on the definitions of other classes. The more ADTs a class has, the more complex the coupling of that class with other classes. The goal in designing individual software components is to represent a concept in what will eventually be an executable form. The Abstract Data Type (ADT) is the object-based paradigm’s technique for capturing this conceptual information.

DAC2, (Data Abstraction Coupling 2), [27].

DAC2 is the number of distinct classes used as types of the attributes of the class.

OCMEC, (Cohesion Based on Member Connectivity), [13].

OCMEC is a number of distinct classes used as types of the parameters of the methods in the class.