Updated assessment of regional business networks

UDC 330
Publication date: 03.05.2019
International Journal of Professional Science №5-2019

Updated assessment of regional business networks

Losev A.S.
research associate, Candidate of Physics and Mathematics
Institute of Applied Mathematics FEB RAS, Vladivostok, Russia
Abstract: In the real work indicators of regional enterprise networks are considered. By means of modern mathematical methods of processing of network structures, the specified estimates of the offered indicators in limit cases are received. More detailed study and assessment, allowed to unite these indicators and to pass from the dot analysis of separate characteristics of network to the system analysis, forming an overall picture about structure and functioning of the studied network.
Keywords: business network, regional structure, assessments network, indicators network

Rapid development of information and network technologies is reflected in all fields of activity of the modern person. In the context of so aggressive implementation of information technologies there is a natural modernization of the enterprises and aspiration to correspond, keep up to date. The most interesting emergence of networks of various nature social, political, enterprise, production, etc. is considered. As a result of transition to network representation, the approach of the same name by means of which the analysis of various indicators and processes which are taking place in the studied networks is carried out was widely used. The tasks arising in enterprise networks have special relevance. The relevance of a research of enterprise networks is proved by the fact that market perception changes, therefore, there are new laws of development and methods of work on it. The market in this concept – not just the sphere of exchange of the benefits or flexible structure which cells are filled with separate firms. First of all, it is the difficult alarm mechanism which helps firms to choose and equip under itself certain market niches in the form of network communications with suppliers and consumers, and these niches do not exist in finished form [1].

Unlike the enterprise organizations, networks are steadier and competitively capable in the corresponding information and technological space of the modern market. Direct contacts allow participants of networks to communicate, carry out mutually control and to quickly resolve conflict situations. Long knowledge of each other helps to form the social capital in the form of the saved-up mutual obligations, to form trust and business reputations.

In the real work indicators of the enterprise networks developed in work [2] are considered. By means of modern mathematical methods of processing of networks, the specified estimates of the offered indicators in limit cases are received and also intermediate conditions of networks of the regional level are considered.

Let’s enter into consideration enterprise network which represents coalition education, not always uniform in a configuration, structure or properties, but which is engaged in economic activity in the corresponding segment of the market. It can be presented as the coherent focused count which knots are agents, and arches – existence of communication between them. Between agents we will mean not only economic transaction, but also information transfer by communication, instructions and orders. Respectively, feedback will be characterized as the report on the done work or an opportunity to contact directly the higher agent. Consideration of enterprise network through focused the count differs from traditional representation [3]. However, observations of work of enterprise networks show that the nondirectional count is not able to transfer all complexity of production communications and is convenient only when modeling the social networks founded on a parity basis without establishment of subordination.

We will be limited to consideration of the networks of small dimension which are not exceeding the regional level that is dictated by the considered indicators.

The dimension of network (n) – the indicator characterizing number of agents of which consists network. At first sight, purely this indicator is not of interest. However, its value directly is reflected in all subsequent indicators that does not reduce its importance and demands its separate consideration. In addition, if to speak about modern information technologies which are widely applied and adopted, in the enterprise sphere then this indicator can be defining in their analysis. Namely, the fact that at the organization of communication in network the Internet is used leads to the fact that this network can carry not only corporate, but regional and global character.

Density of communication of network (p) – the relation of the actual communications in network ( ) to the greatest possible number of communications between all its elements ( ). In general idea the enterprise network cannot consist less than of two agents, also in it there cannot be isolated agents, otherwise connectivity condition is violated. Therefore, it is possible to claim that the network with the minimum number of edges of n1 is rigidly centralized treelike or radial [4].

From here we receive that density of communication of network belongs to an interval [1/n; 1]. In a case  it is about direct submission of each agent higher, without feedback. In a case  it is about the full-coherent network consisting of agents of one level. Such network can be compared to some democratic community in which decision is made by vote or the coalition from universal agents where everyone can carry out any role from the performer to the chief. An example of such network are various social networks, but not networks of enterprise type since they it is formed on the basis of material benefit which is in most cases distributed according to the hierarchy which is absent on the social networks founded by adherents on a parity basis.

Separately it is necessary to consider a case when  what to speak about rather high level of the organization of network with existence of feedback and does network of more flexible. On an equal basis with it at  in network groups of agents managing directors at various levels of the network building a power vertical which existence generally does not contradict uniform centralization of network are formed.

Extent of centralization of network one of sizes which determination causes the difficulties connected with disagreements in the understanding of this characteristic. Interpretation of this size consists in definition of a measure of grouping of agents around the uniform center [5]. For definition of this measure use rather difficult formulas based, as a rule, on use of indicators of centrality of the actor taking into account rationing of number of communications [6.7]. In work [2] authors managed to receive simpler formula which is not assuming rationing of number of communications and calculations of indicators of centrality of actors. However this simplification reduced value of extent of centralization of network to the probabilistic size characterizing existence or lack of the center in general idea. Use of this size in such representation does not allow to characterize network as supporting one center or a set.

Centralization is a concentration of the rights of decision-making, concentration of powers of authority at the top level of the management of the organization [8]. Therefore, extent of centralization of network has to be defined not only existence or lack of the operating top, but its number, concentration and a possibility of transfer of decisions on all levels of network, i.e. remoteness of the lowest level of network from the center.

Calculation of this indicator is rather difficult and labor-consuming task, however the developed methods in work [9] for a complex research of the focused networks, allow to reduce labor input in comparison with the known estimates of extent of centralization of network [5]-[7] and to receive more exact assessment of characteristic of network in comparison with the simplified methods [2]. The algorithm of «transfer of the minimum controlling sets of tops in an orgraf» received in work [9] allows to break network into clusters which elements form connectivity components in the focused count generated by initial network.

Therefore, it is possible to claim that each cluster received in enterprise network forms set of agents of network of one level. In addition, in an algorithm from work [9] on a set of clusters the relation of a partial order which unambiguously defines hierarchy between them is defined. In a case with enterprise network, the hierarchy forms a power vertical and strict submission of agents in network.

Thus, use of fast and compact modern mathematical algorithms [9], allows to transform initial network to the network consisting of various associations of agents of one level of the power. The dimension of the transformed network can be treated as the number of levels of hierarchy in initial network. The clusters consisting of one agent are new elements of network which did not acquire communications yet. The cluster is most than others on the relation of a partial order, unambiguously is defined as the operating top having only outgoing communications and not being in submission, and the number of the coming-out communications of this cluster can be considered literally how extent of centralization of network.

Heterogeneity of network – an indicator of heterogeneity of elements of network. To naturally assume that the functioning enterprise network should not consist only of agents of the economic sphere. Therefore, this indicator defines degree of the agents connected with business activity, but not engaged in it directly. It is about auxiliary tasks which need to be solved for maintenance of functioning of any network and not only enterprise. For example, work with public organizations, political, public authorities.

As characteristic of heterogeneity of network in work [2] the following size is offered:  i.e. unit minus the relation of number of businessmen in network to the total number of agents of network. This indicator defines percent of heterogeneity of network, but informs us on arrangement not of enterprise agents in network a little. It should be noted, position of agents in network plays a huge role on assessment of activity of network in general. For example, the network may support one agent not of the field of activity, but if he is located at the beginning of hierarchy, then it is one situation, and if at the end, then it perfect another. Depending on it is possible not only to say about legality and legitimacy of activity of enterprise network, but also to assume its main objectives and the prospects of development.

For specification of arrangement of the agents who are carrying out auxiliary tasks of network it is offered to consider their arrangement in the network received as a result of a clustering by an algorithm of «transfer of the minimum controlling sets of tops in an orgraf». It is logical to assume that the agents working on auxiliary tasks in this network will be presented in the form of the clusters containing one element, closing on itself communications, performing as binding elements of various departments with the outside world or other networks. It is also lawful to assume that agents not of the enterprise nature should not form separate clusters at the top and average levels of hierarchy of network, otherwise, there is a serious suspicion about the legality given networks.

Therefore, use of the combined assessment of heterogeneity of network by means of assessment of a share of agents not of the enterprise nature and their arrangement in the clustered representation to network, allows to characterize more precisely the nature of activity of network, to assume about legality and certain resistance to stress to impacts on it from the outside.

Thus, the indicators of assessment of enterprise networks developed earlier and specified due to use of modern mathematical methods allow to pass from descriptive result to the system analysis that speaks about the better analysis of the device and functioning of the studied network.


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