Social and economic in our life are tightly interconnected and interrelated. Any social system cannot exist without material economic basis, and along with formal economic relations social informal relations, as the rule of thumb, are formed. One can distinguish two type networks: formed by social relations and relations of economic type. This study was conceived to compare structures of social and economic systems in order to find out their structural peculiarities. Better understanding of structural characteristics can result in better system control. The focus was made on structural characteristics providing system sustainability. It was revealed that cyclic contour set could be proposed as a sustainable structural pattern for an economic system, but it is not true for a social one. For a social system, analysis of triad census on the theoretical basis of structural balance models delivers valuable results for predicting this system sustainability, but for an economic system, this concept was not proved to be the truth. For information support of the research, program was coded that calculates main network parameters and reveals all the cyclic structures in the input network.
Social and economic in our life are tightly interconnected and interrelated. A social
system cannot exist without material economic basis, and along with formal economic
relations social informal relations of friendship, fellow feeling, and etc., are usually
formed. For economic relations interconnected with social ones, new term
“embedded” was introduced. This idea of structurally embedded ties was discussed in details
by M. Granovetter in his famous paper [
On the other hand, during the last decade the issue of “social capital” becomes a
really challenging concept in the social theory. This view of social sounds as a real
economic term: “Social capital can be defined as resources embedded in a social
structure which are accessed and/or mobilized in purposive actions” [
Moreover, social and economic systems may be considered as communication
networks. Luhmann in [
These materials propose a piece of consideration on the topic of economic and social network topological peculiarities from the standpoint of their sustainability.
In many economic theories cycle is proposed to be a structural pattern delivering
economic system sustainability. In the field of social system theory there are special
theories and models of sustainability known as the “structural balance” concepts.
They are detailed in [
In this research social and economic networks were engineered. All techniques used for data collection and network reconstruction are discussed in the next section. Special software product was coded to calculate network parameters and to detect all the cyclic structures in a network. 2
A questionnaire is considered to be the most common source of social communication
data [
It is common knowledge that it is very difficult to receive real economic data. That
is why, economic communication networks were developed with the experimental
economics [
Participants were collected among representatives of the local entrepreneurial
community. Each experiment lasted for two hours: during the first hour participants
were acquainted with the rules and regulations, the second hour was spent for
communications of participants and network formation activity. One of the main
requirements of the experiment was exchange of goods and services produced by participants
in the real life conditions. Intensification of exchange and network formation was
reached by the negative interest rate [
The main network parameters are collected in Table 1. Economic networks, as was discussed above, are the results of the business games in Ufa (column Ufa), Ekaterinburg (column Ekaterinburg), and Moscow (column Moscow). Two of social networks were built based on data stored in “KOMPAS TQM” system and reflect communications between students from two different groups (Gr.34 and Gr.35) from the fourth year of education. The third social network is the result of special survey where students were asked to choose their friends from the list, and the friendship network was engineered based on the received data (Fr.201 network). The first task was to find cyclic structures of different dimensions in economic and social networks. In order to understand how these structures are common for these type networks, this procedure was fulfilled also for the corresponding random networks (of the same size and density). Several random networks were built and investigated for every real network, and mean numbers of revealed cyclic structures were calculated.
In general, the task to detect cyclic structures in a network in the graph theory sounds as to find simple cyclic subgraphaphs in a graph. In our research we had to analyze oriented graphs (orgraphs) and, consequently, had to take arc direction into consideration.
The program was coded for network analysis. This program visualizes network as a graph, calculates network main parameters, and finds all cyclic structures in it.
In Fig. 1 program window is shown. In the center of the window network graph is visualized. In the right side panels, network parameters (the upper panel) and the chosen node parameters (the lower panel) are listed.
In order to reveal all cyclic structures, DFS-algorithm (DFS – depth-first search) with some improvements was implemented. This recurrent algorithm supposes a graph vertices bypass with “deeper“ motion into the graph while it is possible.
The algorithm for cyclic structures search consists of the following steps: 1. Choose a vertex in the graph in a random way; 2. This vertex is marked as a “visited” one; 3. Look for neighbours of this vertex (the vertex’s neighbour is a vertex in the opposite end of an arc starting with this vertex); 4. For every revealed neighbour, the same actions for their neighbour revealing are done. All found neighbours are stored in the special stack; 5. This search is interrupted when the current vertex has been already marked as a “visited” one or when all vertices have been bypassed; 6. If the current vertex has been already visited (is marked as a “visited” one), the stack is analyzed to determine this vertex first position in it (thus, a cycle is detected): ─ for the detected cycle hash function is calculated; ─ if this cycle is a new one (with a new hash function value), then this cycle is inserted in the special program collection, and this vertex is deleted from the stack; ─ a new search starts for the preceding vertex from the stack.
Cyclic structures were revealed in economic networks and in corresponding
random networks. Random networks were built with the help of Pajek [
Cyclic structure distributions are demonstrated for two economic networks in Fig.2. It is evident, that for economic networks these structures are really intrinsic, as if they are more frequent for every dimension in distribution than for random networks. b) 3 4 5 6 7 8 9 10 11 12 13
Quite opposite results were received for social networks. This is quite clear from the diagrams demonstrated in Fig. 3. One can infer that a cyclic contour of any size in a social network is not its inherent structure. 4
There are several structural balance theories. They are described in details in [
According to the first (Basic, in Pajek - Balance) model a group presented by a balanced directed graph can be partitioned into two antagonistic subgroups (one of these subgroups can be empty), every subgroup has only mutual ties within its subgraph, and there are only null ties between the two subgraphs. b) 12 10 8 6 4 2 0
The second (Clusterability) model extends Balance model to more sociologically reasonable notion of clusterability, which allows existence of more than two subgroups (subgraphs). But the rules are the same: mutual links in a subgroup (subgraph), and null links between the subgroups (subgraphs).
The third (Ranked Clusters) model assumes that any group is a subgroup hierarchy where every hierarchical level has at least one subgroup. This model extends clustering introducing directed (asymmetric) ties between subgroups, with orientation of this ties consistent with hierarchical ordering in which ties are directed from ”lower” to “higher” levels (any lower level subgroup member prefers those who are members of the higher level subgroups).
The fourth (Transitivity) model is the most general model of all discussed and subsumes the other models as special cases. The main rule in this model is as follows: if there are 3 members named A, B, C in a group, and A has a tie with B, B has a tie with C, then A must have a tie with C.
To reveal whether a network graph corresponds to the discussed models,
SNAmethodology proposes to analyze the triad census characteristic of a network graph.
This procedure is realized by Pajek framework [
It was proved with χ2 criteria usage that: ─ there is a statistically significant difference between a social network triad census (column “Revealed”) and the census of corresponding random networks (column Expected); ─ difference existence/absence for an economic network and corresponding random networks cannot be proved because the portion of expected values less than 5% is more than 20%, and χ2 criteria cannot approve or disapprove the hypothesis of difference existence/absence in this case.
On the base of results in Table 2 (this table in the research report contains censuses for all discussed networks and some more networks which were not mentioned in this paper), one can conclude that social networks meet the balance model requirements, and there are no reasons to make the same decision for economic networks. For example, Gr.34 network is well conformed with Basic model, Clusterability model, and Ranked Clusters model, and do not corresponds to Transitivity model, but it includes the less number of forbidden triads that the corresponding random networks (55 against 97.58). For the Moscow game economic network, numbers of forbidden triads in this network and in corresponding random networks are almost equal. 5
Although social and economic networks are tightly intertwined and make influence on each other, they have their own structural peculiarities that might be taken into consideration to propose effective system control. Cyclic contours can be considered to be inherent for an economic system and form structural basis of its sustainability, but this structural pattern is rather seldom in a social network. As for social systems, for the theoretical basis of their sustainability structural balance concepts can be adopted, but this idea was not proved for economic systems.