## 1. INTRODUCTION

Communication between the members of an organization involves members gathering and sharing information, and plays an important role in achieving common goals. Smooth communication within an organization is the foundation of maintaining competitive advantage in the case of a corporation (Nonaka *et al*., 1996). On the other hand, it must be recognized that information sharing involves the division of specific members of an organization into inner and outer members. From the perspective of inner members of an organization, there is information that may be shared with outer members, and information that must not be shared. Recent incidents of information leaks may be identified from this perspective. An example is the raised that South Korean president Park Geun Hye leaked the text of speeches and other confidential information to her old friend Choi Soon-sil, and for which she was arrested (Sang-Hun, 2016, 2017). This problem may be treated as one of information sharing between the inner and outer members of an organization, wherein information was shared with a friend not engaged in an official capacity and outside the president’s administration and the president. When leaks of confidential information similar to these at the national level occur in a private enterprise, then the confidential information is considered to be information on independently developed new technologies, strategic information on mergers or acquisitions, and the private information of customers. When this information is leaked outside of an organization, it leads to loss of corporate competitive advantage and damage to creditworthiness. Corporations and other organizations are presently seeking coexistent information sharing and information security measures (Cedillo-Campos *et al*., 2014; Vayrynen *et al*., 2013; Zhang and Li, 2006). Although the active sharing of confidential information may occur within an organization, organizations are not required to share their confidential information shared externally.

A network formed through communication is referred to as a communication network (CN), and many researchers such as Leavitt have previously embarked on studying the structure and characteristics of CN (Guetzkow and Dill, 1957; Leavitt, 1951; Shaw, 1954). Leavitt’s study of CN (Leavitt, 1951) established simple wheel type or Y type CN (Figure 1) as experimental patterns, and used working experiments to derive a relationship between the centrality of these networks and whether leaders appeared, the dissatisfaction of members, the amount of work, and the number of errors.

Thereafter, there have been many studies analyzing the characteristics of CN using such experiments. The authors’ research group has also proposed a series of analytical models for ascertaining the structure of CN through entropy (Ozeki *et al*., 1985a, 1985b; Ozeki and Katori, 1983; Yamashita, 1996; Yamashita, 2016; Yamashita and Kwon, 2015; Yamashita and Ozeki, 1994). However, past studies of CN aimed for as much active intra-organizational information sharing as possible, which involved specialized information sharing models. This meant that models tended to look at only one of the elements sought by the modern enterprise as described above—either information sharing or information security measures—and were thus divorced from reality.

Therefore, in this study, we will first begin by focusing upon both communication between the inner members of organizations and communication between inner and outer members. Then, we construct a model for ensuring information security outside of an organization while promoting internal information sharing. Next, based on the structure of CN and the characteristics of their members, we intend to find a solution to the problem of which members should receive information in advance for it to be effective in terms of both information sharing and information security measures. In particular, the authors will describe this problem using their proposed analytical model of a memory channel CN (Yamashita, 2016; Yamashita and Kwon, 2015) as a basis. Here, we assume that the probability of information enclosure *u _{i}* and the probability of blocking information

*υ*are each already known, and consider the problems of ① enlarging the amount of post-event information within an organization minus information outflow as much as possible, and ② estimating the percentage of information allocated in advance

_{i}*d*in order to equalize it as much as possible. This allows for an analytical model that simplifies the complicated structure of an actual CN, but enables estimation of the most effective advanced information allocation percentage

_{i}*d*in the CN, accounting for information security measures. Thus, by comparing the obtained

_{i}*d*to phenomena in actual organizations, we may study the validity of our proposed model.

_{i}## 2. INFORMATION SECURITY

In contrast to information sharing is information security. External information security measures must be put in place so that information sharing tightens relationships between members and encourages organizational activity. The previously mentioned information leak by the president of South Korea (Sang-Hun, 2016) and the use of a private e-mail address for official business by Hilary Clinton in the U.S. (Lichtblau and Myers, 2016; Zurcher, 2016) are problems that have affected the political lives of the politicians involved. Information sharing and information security measures conflict with one another. Active information sharing makes it difficult to ensure information security, while strictly tightening information security measures risks creating obstacles to active information sharing. The ideal situation is one where information that is allowed to be shared is actively exchanged among those members who should share it, while information that must not be shared was not.

Hanaoka argues that information “sharing” and “secreting” are mutually opposing concepts, and organizations are bound by the omnipresence of the two. Organizational boundaries must serve as secure walls blocking certain types of information, while simultaneously allowing other types of information to remain seamless and unfenced. For example, setting up supply chain management (SCM) sharing of commonly handled product information is an essential condition for corporations connected to the supply chain. On the other hand, each of the corporations has information that must be kept confidential from the other corporations. In such cases, while complete transparency may be desired for the fences bounding one corporation, complete blocking may also be required at the same time (Bowler, 1981; Hanaoka, 2001; Hanaoka, 2003).

In this study, we shall attempt to analyze the characteristics of individual CN structures by describing the state of their coexistent information sharing and information security measures.

## 3. CONCEPTUAL DESCRIPTIONS OF A CN

CN A system comprised of multiple members or departments linked through intra-group communication is generally called a CN, and in this study, the authors express this as $N=\{X;\hspace{0.17em}\Gamma \}$ based on prior research (Ozeki *et al*., 1985a). Here, if there are *n* members in a group, and the subscripts *i* and *j* are the members (individuals or departments) comprising an organization, then $X=\{{x}_{1},\hspace{0.17em}{x}_{2},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{x}_{i},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{x}_{j},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{x}_{n}\}.$. In addition, ** Γ** represents the possible communication in direct product space

*X*^{2}for group

**above, and $({x}_{i},\hspace{0.17em}{x}_{j})\in \Gamma $ holds when communication is possible between**

*X**x*and

_{i}*x*Furthermore, the value of the arc (

_{j}*x*,

_{i}*x*) in communication

_{j}**, if it is assumed that the probability of**

*Γ**x*passing on information to

_{i}*x*is,

_{j}*p*may be considered a framework for the value graph

_{ij}**' as in formula (1) below (Yamashita, 1996).**

*N*

where, if there is a group with no arc, and *p _{ij}* is generally

*p*＝0, then the matrix $P=({p}_{ij})$ assuming

_{ij}*p*≧ 0 as an element is generally the channel matrix (transition probability matrix) (Yamashita, 1996).

_{ij}## 4. PREVIOUS RESEARCHES OF CNS

The research into CNs focused upon in this study divides CN structures into several types, and includes a large amount of research into experimentally analyzing their individual characteristics. A pioneering study in this was the experimental research by Leavitt (Leavitt, 1951). In this study, Leavitt established four types of CN (circle type, chain type, Y type and wheel type) and analyzed individual CNs as to whether leaders appeared, the dissatisfaction of members, the amount of work, and the number of errors. The results confirmed that CNs with higher centrality such as wheel type and Y type tended to see clear leaders and fewer errors, though less work, and that those on the periphery of a CN tended to be very dissatisfied. Subsequently, the authors’ research group also commenced a series of studies to ascertain the structure of a CN according to stationary allocation vectors (Ozeki *et al*., 1985a, 1985b; Ozeki and Katori, 1983; Yamashita, 1996; Yamashita and Ozeki, 1994). In the course of such studies, the authors have proposed a series of CN allocation models based on the disposition of Markov chains for estimating stationary allocation vectors from a channel matrix, and quantitatively ascertaining the structure of the CN in terms of entropy. These CN analytical models assume a “memoryless channel” CN in which no information remains in the memory of the sender when information is sent. However, as most CNs are actually “memory channel” CNs in which much information remains in the memory of the sender even after sending, the models are therefore divorced from reality. Subsequent studies of memory channels conducted by the authors (Yamashita, 2016; Yamashita and Kwon, 2015) have served as the basis for the present study. As information remains in the memory of the sender, we have made the problem of information security the subject of this study. Next, we will explain research into memoryless channels, followed by research into memory channels.

## 5. ANALYTICAL MODEL OF MEMORYLESS CHANNEL CN

In order to address the problem of how information should be allocated when there is repeated communication in a CN, the authors have proposed the following analytical model of a memoryless channel CN to estimate the allocation of information when each member is free to repeatedly communicate (Yamashita, 1996).

First, if it is assumed that the previously described channel matrix $P=({p}_{ij})$ and initial vector $a=({a}_{i})$ are already known, and ** P** does not change in relation to time

*t*, then

is the stationary allocation vector $s=({s}_{i}),$ which expresses the allocation of information when there is freely repeated communication in a memoryless channel CN, provided that $s=({s}_{1},\hspace{0.17em}{s}_{2},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{s}_{i},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{s}_{n})$ and $a=({a}_{1},\hspace{0.17em}{a}_{2},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{a}_{i},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{a}_{n}),$ The above formula (2) expresses the probability that information is present with member *x _{i}* when there is freely repeated communication; in other words, the allocation of information within a CN. This means that as long as a member has a large element

*s*for stationary allocation vector

_{i}**, they are a critical member for whom a large amount of information is collected. If matrix**

*s***(channel matrix) information is compressed into vectors according to this stationary allocation vector**

*P***, then it is possible to simplify a CN structure in describing it (Yamashita, 1996).**

*s*However, although the right side of formula (2) converges in the case of an aperiodic CN, it does not converge in the case of a periodic CN; therefore, it is possible to consider dividing aperiodic and periodic cases.

### <Aperiodic>

Depending on the disposition of Markov chains, in aperiodic CN formula (2) converges, and satisfies formula (3) at this time (Ozeki *et al*., 1985a).

Consequently, by solving the simultaneous equation in formula (3), we can find the stationary allocation vector ** s**. In addition, since formula (3) returns to an characteristic value problem, if element

*n*(number of members) in

**is large, then if characteristic equation $({P}^{T}-\lambda \cdot I)\cdot {s}^{T}=0$ is solved, and characteristic vector**

*s*

*s*^{T}for characteristic value

*λ*=1 (this is the maximum characteristic value (Kunisawa, 1975) is standardized so that the sum of the element is 1, then it is possible to find a solution for stationary allocation vector

**.**

*s*### <Periodic>

In cases of a periodic CN, formula (2) does not converge; therefore, as in formula (4), the mean of each element *q _{i}*(

*t*) of the reliability vector

**(**

*q**t*) for time t must be the stationary allocation vector

**. When this happens, if the period is c, each element**

*s**s*of the stationary allocation vector may be expressed as in formula (4) (Yamashita, 1996).(5)

_{i}

These models are all of memoryless channels, in which no memory of information is left with the sender of information.

## 6. CN ANALYTICAL MODEL OF MEMORY CHANNEL CN

In the previous section, we explained a method of expanding a memoryless channel CN model into a memory channel CN model. In situations in which a memory of information is left with the sender, situations arise in which the sender themselves holds important information and other members do not; that is, there is asymmetry in the information. In such circumstances, the sender is placed in the advantageous state of holding important information, and would be expected to enclose information in order to maintain superiority. In other words, the sender maintains information asymmetry by “enclosing” the information. The analytical model of a memory channel CN proposed by the authors in prior research (Yamashita, 2016; Yamashita and Kwon, 2015) is one for estimating the “advanced information allocation percentage,” by which more information is passed onto members within the CN, based upon consideration of “information enclosure” in which an information holder attempts to maintain “information asymmetry.” We will explain this below.

First, we assume the “information enclosure probability” of member *x _{i}* comprising a memory channel CN to be ,

*u*and then formulate the relationship of the information “enclosure matrix

_{i}**(= unit matrix),” “nonenclosure matrix**

*E***,” allocation percentage vector for advanced information $d=({d}_{i}),$ and post-event information vector $y=({y}_{j})$ as in formula (6). However, information non-enclosure matrix**

*B***is a square matrix in graph theory in which ${b}_{ij}(=(1-{u}_{i})\cdot {g}_{ij})$ is an element that applies information non-enclosure probability $(1-{u}_{i})$ to an element**

*B**g*of an adjacency matrix $G=({g}_{ij}).$ This element

_{ij}*g*of an adjacency matrix

_{ij}**is a dummy variable that takes the value 1 when a member**

*G**x*can transmit information to a member

_{i}*x*(an arc is present between

_{j}*x*and

_{i}*x*) and 0 when it is not.

_{j}

Next, based on formula (6), we find the allocation percentage for advanced information *d _{i}* such that ① it enlarges the amount of post-event information as much as possible, and ② it equalizes the advanced information allocation percentage as much as possible. Hence, according to a one-factor information channel model (Kunisawa, 1975) approach, we ascertain ① according to the weighted mean

*L*of the inverse (1/

*r*) of the total per

_{i}*i*of elements

*r*in the information transfer matrix $R(=E+B)$ (formula (7)), and formulate ② as a maximization problem of

_{ij}*H*/

*L*as in formula (9) by ascertaining it according to the allocation entropy

*H*of advanced information (formula (8)). However,

*λ*is a Lagrange multiplier. One method according to a one-factor information channel model is to reach a conclusion based upon inference (expanded inference) (Klir and Folger, 1988) from given information (insufficient evidence) when people or organizations are making decisions, such as when a conclusion is not reached. In particular, the above expanded inference is formulated as a maximization problem of Shannon entropy (Shannon, 1948) from the perspective that evidence ought to be fully recognized as being insufficient, while at the same time people or organizations are maximizing the same use of insufficient evidence, and then the choice probability in decision making is estimated (Arizono and Ohta, 1986; Herniter, 1973; Kapur

*et al*., 1984; Yamashita, 2014).

where, *φ* is convex relative to *d _{i}*, so when

*φ*is partially derived by

*d*and denotes 0, formula (10) is obtained.

_{i}

Next, we apply *d _{i}* to both sides of formula (10), which if summed up by

*i*becomes(11)

Thus, Lagrange multiplier *λ* becomes *λ* = 1/*L*. Therefore, when we substitute 1/*L* for *λ* in formula (10),(12)

as a result, the following is obtained. (Kunisawa, 1975)(13)

where, if $exp\{-H/L\}=W,$, then the following simple formula is derived.

Furthermore, using the fact that the sum of *d _{i}* is 1 to numerically determine

*W*, and substituting this

*W*in formula (14), a solution is found for

*d*, maximizing formula (9) (Kunisawa, 1975).

_{i}In this manner, by expanding the model from one for memoryless channels to one for memory channels, it becomes possible to more realistically describe the exchange of information between people. As in the above, it becomes possible to describe actual events in which the sender of information in an organization encloses the information, and thereby the applicability of the model is further widened in scope.

## 7. PROPOSED MODEL IN THIS STUDY

STUDY In this chapter, we will propose a model incorporating consideration of information security measures into the model in the preceding section. This may also be considered an example of applying a memory channel-based model. Here, information security will involve the handling of information such as that for new product development or that should only be handled intra-organizationally; in other words, information that should not be given to outer members. We will refer to such information as confidential information. Confidential information such as that for new product development should be carefully handled by intra-organizational members for the development of competitively advantageous products and enacting sales strategy. When such confidential information is shared with outer members of an organization, it may lead to a corporation losing competitive advantage to other companies. Confidential information should be shared as much as possible within an organization; however, it needs to be blocked to outside of the organization (Tan *et al*., 2016; Zhang *et al*., 2011). Here, we shall consider a communication network in which an outer member of an organization is represented by *x*_{6} as in Figure 2.

The exchange of information between *x*_{1} to *x*_{5} and *x*_{6} in Figure 2 is between the inner and outer members of an organization. Furthermore, in addition to the probability of information enclosure *u _{i}* of members ${x}_{i}(i=1,\hspace{0.17em}\mathrm{...},\hspace{0.17em}5)$ comprising the CN, members ${x}_{i}(i=1,\hspace{0.17em}\mathrm{...},\hspace{0.17em}5)$ newly provide the probability of blocking information ${v}_{i}(i=1,\hspace{0.17em}\mathrm{...},\hspace{0.17em}5)$ from an outer member 6x . In order to discuss only the outflow of information to outer member

*x*

_{6}, the information outflow will be one-way only in this section. Consequently, the information transfer matrix $R(=E+B)$ will consist of five rows and six columns (

**and**

*E***are both five rows and six columns). The elements ${r}_{ij}(i=1,\hspace{0.17em}\mathrm{...},\hspace{0.17em}5,j=1,\hspace{0.17em}\mathrm{...},\hspace{0.17em}6)$ are, for example, represented as follows in a Y type CN. The elements in the sixth column of this matrix are minus the probability of blocking information**

*B**υ*from 1, and represent the information flowing to outside of an organization.

_{i}

In this study, the focus is upon information security in a communication network. Here, using the previously explained memory channel CN analytical model as a basis, we shall prepare a model focusing upon information sharing and information security measures. Therefore, first, we shall assume that the probability of information enclosure *u _{i}* and the probability of blocking information

*v*are each already known, and furthermore, shall consider the problems of ① enlarging the amount of postevent information within an organization minus information outflow as much as possible, and ② estimating the percentage of information allocated in advance

_{i}*d*in order to equalize it as much as possible. Inner members of an organization should share information as much as possible, while there should be as little transmission as possible of confidential information from inner members to outer members. Such an organization is one in which both information sharing and information security measures have been established. This situation will be modeled according to a one-factor information channel model (Kunisawa, 1975; Yamashita, 2014) approach, as in prior research (Yamashita, 1996; Yamashita and Kwon, 2015). Now, we may ascertain ① according to the weighted mean

_{i}*L*of the inverse of the value of subtracting $(1-{v}_{i}),$, which represents the outflowing information, from the total per

*i*of elements

*r*in the information transfer matrix $R(=E+B)$ (formula (16)), and if ② may be ascertained according to the advanced information allocation entropy

_{ij}*H*(formula (15)), then information security problems in an organization may be formulated as in formula (17) as a maximization problem of

*H*/

*L*. Here, enlarging the amount of information that may be transmitted by inner members of an organization, and reducing the amount of information transmitted by inner members to outer members as much as possible, is the same as enlarging the denominator within the parentheses in formula (16).

where, *φ* is convex relative to , *d _{i}* so when

*φ*is partially derived by

*d*and denotes 0, formula (18) is obtained.

_{i}

Next, we apply *d _{i}* to both sides of formula (18), which if summed up by

*i*becomes(19)

Thus, Lagrange multiplier *λ* becomes *λ*=1/*L*. Therefore, when we substitute 1/*L* for *λ* in formula (18),(20)

as a result, the following is obtained.(21)

Here, if $exp[-H/L]=W,$

where the sum of *d _{i}* is 1; therefore, it is possible to numerically determine one

*W*such that the sum from putting

*i*into formula (22) is 1. Furthermore, by substituting this

*W*into formula (22), it is possible to determine a solution for

*d*that maximizes formula (17).

_{i}## 8. EMPIRICAL ANALYSIS OF PROPOSED MODEL ACCORDING TO SIMPLE NUMERICAL EXAMPLES

Using the proposed model in this study, we shall perform an empirical analysis according to simple numerical examples. We establish numerical examples as in Tables 1 and 2 for a memory channel CN comprised of a total of six organizational members: five inner members and one outer member as shown in Figure 2. Thus, when we estimated the advanced information allocation probability , *d _{i}* we obtained the results in Tables 3 to 10. The greyedout sections of the tables indicated the largest of the five ${d}_{i}({d}_{1},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{d}_{5})$ in a column. Tables 4, 5, 6, 7, 8, 9

**＜numerical examples＞**

(M. is an abbreviation for Measure.)

According to the results in Tables 3 to 10, we found that members with a small probability of information enclosure *u _{i}* for information but a large probability of blocking information

*v*had a large advanced information allocation probability

_{i}*d*. Here, we provide a circle type with the lowest centrality, which is little affected by the type of CN, for explanation (Tables 3 and 4). Case-1 and Case-2 in Table 3 are entirely the same in the results of estimating advanced information allocation

_{i}*d*. In Table 1, the enclosure probability for information enclosure

_{i}*u*according to the inner members is entirely the same. Furthermore, in Table 2, the probability of blocking information

_{i}*v*according to the inner members is the same. This means that if the inner members consciously take the same action against closuring and the blocking for information, it can be understand as representing that they are able to get the information allocation with same probability. Next we discuss Case-3 to 6, then almost all of the greyed-out sections correspond to places where the probability of information enclosure

_{i}*u*was the smallest value of 0.1. Above all, places where the font is Gothic correspond to places where the probability of information enclosure

_{i}*u*was the smallest value of 0.1, and the probability of blocking information

_{i}*v*was the largest value of 0.9. This indicates that while information was being actively shared between members within an organization, advanced information should most often be allocated to exemplary members capable of strictly blocking confidential information to outside of the organization. In an actual organization, a state in which both information sharing and information security measures have been firmly established is an ideal one. However, it was felt that the analytical results from our models were valid and in conformance with reality.

_{i}Next, when we focus upon the type of CN, we find that CN structures with high centrality (Y type and wheel type) tend to be more scattered in the advanced information allocation percentage *d _{i}* among members than CN types with low centrality (circle type and chain type). As examples, let us explain focusing upon Case-4 and Measure 6 for each CN (places circled with a large border in Tables 4, 6, 8 and 10). In these places, the difference between the largest value and smallest value in the five

*d*$({d}_{1},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{d}_{5})$ in the column was 0.293 (circle type), 0.350 (chain type), 0.434 (Y type) and 0.529 (wheel type). The size of the difference depended upon whether a CN structure had high centrality. In addition, when we calculate the entropy for the five

_{i}*d*in these places, it is 1.934 (circle type), 1.889 (chain type), 1.749 (Y type) and 1.723 (wheel type). Thus entropy was smaller the higher the centrality. This means that the concentration on specific members is higher, the more allocation of advanced information. In other words, the allocation percentage

_{i}*d*for advanced information ought to be differentiated in as much as a network has significant differences in the amount size of communication between members. It is felt that these results conform to reality.

_{i}Furthermore, when we focus upon the greyed-out sections in Tables 3 to 10, in Tables 3 to 6 (circle type and chain type), there is a large amount of scattering of the greyed-out sections. However, in Tables 7 to 10 (Y type and wheel type), except for Case-6, the greyed-out sections are largely concentrated on *x*_{3}. This indicates that in CN structures with high centrality, except for Case-6, advanced information allocation mostly went to 3x . In this case, the probability of information enclosure *u _{i}* for information of

*x*

_{3}is large, and the probability of information enclosure

*u*for information of those on the periphery $({x}_{1},\hspace{0.17em}\hspace{0.17em}{x}_{2},\hspace{0.17em}\hspace{0.17em}{x}_{4},\hspace{0.17em}\hspace{0.17em}{x}_{5})$ is small. When this happens, in many cases, advanced information allocation mostly goes to those on the periphery. In an actual organization, it is felt that allocating a lot of information among members who will share it without enclosure will result in active intra-organizational communication, so it is felt that the results here conform to reality. On the other hand, in cases such as Case-6, if the probability

_{i}*v*of those on the periphery blocking information is small (Case-6 in Tables 8 and 10, Measure 6), then more information will be allocated to

_{i}*x*

_{3}than to those on the periphery. This may be said to be the result of measures for members in order to prevent information leakage affecting the advanced information allocation probability

*d*.

_{i}## 9. CONCLUSION

In this study, we proposed a CN model capable of describing information security problems, based upon research into memory channel CN in which a memory of information is left with its sender and advancements in the field, and past quantitative CN research using memoryless channels. We established two types of members comprising CN: inner members and outer members of an organization. We then estimated the advanced information allocation percentage of each member, so that information would be equally passed on between inner members as much as possible, while minimizing the outflow of confidential information from inner members to outer members. Thus, we used the proposed model in this study to conduct an empirical analysis using simple numerical examples, and as a result, obtained estimated values for advanced information allocation percentages in close conformance with reality. This is considered to be indicative of the validity of the proposed model. We hope that the results of this study may provide some suggestions for intra-organizational information sharing and information security measures.