An evolution model for regional collaborative innovation under the perspective of complex network

Abstract

This paper proposed a novel method to analyze the regional collaborative innovation evolution under the perspective of complex network. To clearly describe the complex network evolution problem, the concept of 1) “graph with the characteristic of dynamic” and 2) “network evolution” are provided in advance. Afterwards, we illustrate the internal structure of the regional collaborative innovation system, which contains several elements, such as universities, research institutes, enterprises, intermediary organizations, financial institutions, government and so on. Therefore, we can see that the regional collaborative innovation system can be regarded as a complex system. Furthermore, when the elements in the regional collaborative innovation system can coordinate with each other well, it will be in good working order. In our proposed regional collaborative innovation evolution algorithm, to reduce the computation cost, we suppose that each node in the complex network can only connect to less than a specific nunber of neighbors. Particularly, for a given node, the maximum number of its neighbors is determined by node importance. Afterwards, the regional collaborative innovation evolution can be analyzed by the probability desity function which is calculated by the node importance and node connectivity. Finally, a case study is conducted to make performance evaluation, and we collect the raw dataset from five main sources in 2008–2013. Experimetal results demonstrate that the proposed algortihm can effectively analyze the regional collaborative innovation evolution. Moreover, utilizing the experimental results several suggestions are proposed for government.

Keywords

Regional collaborative innovation complex network network evolution statistical yearbook

1 Introduction

As is illustrated in Wikipedia, the concept of complex network refers to a graph with non-trivial topological features. Features belonged to complex network do not occur in simple networks (e.g. lattices or random graphs) but often happen in real graphs. Studying the complex network has attracted more and more attentions, and it is a hot topic in the research of computer networks and social networks [1, 2]. However, although complex network is of great importantce in intelligent computing, researchers have not figured out that the internal structure and properties of it. As is well known that randomness is in line with the major features of the complex networks, and it is easier to obtain a visual understanding of how the complex networks are constructed [3]. Particularly, network evolution model can not only obtain correctly the processes that assembled the networks but also make it clear that how different microscopic processes affect network topology.

Considering complex network may change its internal structure with time varying, hence, it is quite important to study the dynamic behavior of the complex network. However, in the formers studies of complex network evolution models, most of them concentrate main macroscopic properties, e.g., small-world effect and scale-free property [4]. If only considering the macroscopic features, it is difficult to provide the credible review of the different evolution models. Therefore, local structures and execellent evolution model should be deeply studied in the future.

On the other hand, regional collaborative innovation has been studied not only in theory but also practice. In fact, currently, governments attempt to construct regional collaborative innovation system to inspire innovation enthusiasm for different innovative enterprises [5, 6]. Meanwhile, the regional collaborative innovation system can also play an important role for enhancing regional innovation ability and economic development level [7]. In the regional collaborative innovation system, it is of great importance to connect innovations with development of regional economy. Particularly, studying on the laws of network evolution in regional collaborative innovation under the complex network perspective can help government to know rules and characteristics of regional economic development [8]. Furthermore, policy making can benefit from the research in this paper.

This paper proposes a novel method to analyze regional collaborative innovation ability using the technology of complex network evolution. The rest of the paper is structured as follows. Section 2 presented the related works of this paper. In Section 3, we explain the problem of complex network evolution. Section 4 proposes the method to analyze regional collaborative innovation ability using complex network evolution. To demonstrate the effectiveness of the proposed method, Case study is designed conducted in Section 5. Finally, the conclusions are drawn in Section 6.

2 Related works

Complex network systems have been widely used in both the social science and natural science. Particularly, Complex networked systems are made up of a multitude of interacting agents communicating with each other based on a network of complex interconnections. Meanwhile, complex network provides an effective way to describe many application systems and contains the following attributes: 1) topology, 2) dynamics and 3) evolution. In this paper, we focus on the evolution of complex systems, and the related works about complex system evolution are listed as follows.

Alvarez et al. utilized the complex network evolution technology to predict the birth and death ratio. In this paper, master equations for the evolution of complex networks with birth and negative transition probabilities per unit time are analyzed in detail. Particularly, the basic dynamical function for its stationary solution refers to the ratio between drift and diffusion coefficients [8].

Duan et al. concentrated on the problem of network evolution of node importance through the information about cascading failures. A new node importance indicator is presented in this work according to the load turbulence of each node. On the other hand, network evolution of node importance is implemented with the load redistribution rule, node capacity, and network topology [9].

In the field of information processing in smart grid, Pagani et al. studied how different network topologies and growth models facilitate a more efficient and reliable network, and how the power company can facilitate the emergence of a decentralized electricity market. Furthermore, this paper illustrated the importance of network connectivity in enhancing the properties of reliability and path-cost reduction. Finally, experimental results demonstrate that a particular type of evolution balances best the ratio between increased connectivity and the cost of network scale increasing [10].

Kasthurirathna et al. focused on the problem of influence of the topological structure of social systems on the network evolution. In this paper, the authors simulated a coordination game on 4 classes of complex networks which have been commonly utilized to construct social systems. Experimental results show that when time-lags and noise in the information about relative payoffs can greatly influence the emergence of coordination [11].

Anzo et al. studied on the influeces of structural evolution on the stability of synchronized behavior in complex network system. The main innovations of this papers lie in that structural evolution used in this paper is divided into classes, that is, 1) the topology changes with an arbitrary switching law among a set of admissible patterns of connection, and 2) the strength of connection evolves is determined by an adaptive law [12].

In paper [13], the authors focused on the application of network evolution in information science, and proposed a new approach to study the evolution of Linux kernel components based on the complex network theory. Particularly, this paper aimed to make clear how the kernel of Linux operating system evolve in the past years. After investigating node degree distribution, clustering coefficient, and average path length from the linux kernel version 1.0 to version 2.4.35, the conclusions are drawn that, in the development of Linux kernel, graphs of the file system, driver, kernel, memory management, and net components have the characteristics of scale-free and small-world complex networks [13].

Li et al. presented the conception and evaluation indexes of emergency logistics network connecting reliability to construct evaluation index system of complex network reliability, and then illustrated the proposed indexes quantitatively to test the network connecting reliability.

Furthermore, the authors presented a novel network topological model and develop the simulation tools to test the system reliability when the attacking behavior happens [14].

Hadzibeganovic et al. proposed a novel agent-based evolutionary model of tag-mediated altruism, which is suitable to be used in large-scale complex networks. Different to the former theoretical predictions, the authors found that altruistic acts in non-repeated interactions can emerge as a natural consequence of recognition of heritable phenotypic traits such as visual tags. Furthermore, the authors disvovered that topological regimes in which cooperation usually prevails in a short period of time[15].

From the above related works introduction, we can see that complex system evolution has been widely used in many fileds which cover both social science and natural science. However, as far as we know, the technology of complex system evolution has not applied in the research of regional collaborative innovation. Hence, in this paper, we will try to provide an effective method to use the network evolution in the regional collaborative innovation problem under complex system perspective.

3 Explaining the complex network evolution problem

Before providing the algorithm for analyzing regional collaborative innovation through complex network evolution, the problem of complex network evolution should be explained in advance. The complex network evolution problem contains four main parts as follows.

Θ: A set of possible structures in the complex system.

Ψ: A set of operators which are utilized to be used in improving structures in the complex system.

X: A set of input elements from the outside environment.

Γ : X × Θ → Ψ: Adaptive plan.

It is well known that complex network can be represented as a generalized dynamic graph G = (V, E), in which V = { v₁, v₂, ⋯ , v_n } and E = { e_ij } , i, j ∈ { 1, 2, ⋯ , n } represents the node set and edge set respectively. To explain the process of network evolution more clearly, we provide an example in Fig. 1.

As is shown in Fig. 1, we explain how a specific network evolves using three different states. In state 1, an original graph with six nodes and seven edges are included. Particularly, with the network dynamics varying, node importance and edge weight are changed as well. In this figure, the node importance is represented by radius of the node, and the edge weight is denoted as thickness of the line. Particularly, the bigger the node radius is, the more important node is. Meanwhile, the thicker the line is, the bigger the edge weight is. Afterwards, state 1 is transformed to state 2 by modifying the edge weights, and state 2 is converted to state 3 through adding new nodes and new edges. Afterwards, two important concepts in network evolution are defined as follows.

Definition 1. Graph with the characteristic of dynamic

For a given graph with N nodes, and the network structure and operator are represented as μ and ν respectively. Hence, the dynamic graph can be represented as DG = (N, μ, V, E, U, T, ν), in which symbols are defined as follows.

N ={ n₁, n₂, ⋯ , n_m } is the finite set of graph nodes.

μ ={ a₁, a₂, ⋯ , a_n } and a_i ∈ V × V means the finite set of graph edges.

V ={ v₁, v₂, ⋯ , v_m }, among which v_i refers to the set of node state.

E ={ e₁, e₂, ⋯ , e_m }, among which e_i refers to the set of edge state.

U ={ u₁, u₂, ⋯ , u_p }, where u_i is the set of external input.

T means the set of times which is related to network dynamics.

Π : V × E × U × T → V × E denotes the convertion between different node/edge states

Definition 2. Network evolution

Utilizing the graph defined in Definition 1, the process of network evolution can be defined as the collection ϒ = (D, Ψ, Ξ, P), and symbols in ϒ is defined as follows.

D = (d₁, d₂, ⋯ , d_x) represents the set of dynamic graphs.

Ψ ={ η₁, η₂, ⋯ , η_y } denotes the set of structural operators.

Ξ is input from outside environment

P : Ξ × D → Ψ refers to evolution plan which can choose the operators η ∈ Ψ to be utilized when the current structure is converted to a new one.

4 Analyzing regional collaborative innovation through complex network evolution

4.1 Overview of the regional collaborative innovation problem

In this section, will describe the regional collaborative innovation problem, and analyze why the complex network evolution technology can effectively solve it. Firstly, in Fig. 2, structure of the regional collaborative innovation ability model is illustrated, in which the foundation of innovation resources should be supported by hard and soft environment for innovation. Afterwards, the innovation, configuration and application of knowledge can be circulated in the regional collaborative innovation system.

Secondly, as is shown in Fig. 3, architecture of the regional innovation system under the collaborative perspective is described in detail.

The regional innovation system can be regarded as a complex system, in which several elements are included, such as universities, research institutes, enterprises, intermediary organizations, financial institutions, government and so on. Figure 3 shows that regional innovation system can run well only when the collaborative relationships between different elements can be effectively coordinate with each other.

4.2 Algorithm description

To effectively analyze the network evolution of regional collaborative innovation system, in this section, a regional collaborative innovation evolution algorithm is given. Considering that too many edges in the complex network may low down the system performance, in this algorithm, we add some constraint conditions. The main idea of our algorithm lies in that we assume that each node in the complex network can only connect to less than a specific nunber of neighbors. For a given node, the maximum number of its neighbors is determined by node importance. The proposed algorithm is given asfollows.

Algorithm 1: Complex network based regional collaborative innovation evolution algorithm

Step 1: Starting with N initial nodes, and then constructing a fully connected graph.

Step 2: At each time slot, choosing a node with uniform probability and then deleting the edges which connect the nodes with the node importance less than a threshold.

Step 3: For a newly added node, selecting the nodes to which the given new node should connect. For the node i, the probability P_i of it is influenced by the node connectivity (C_i) and node importance (I_i). P_i can be computed as follows. $P_{i} = \frac{f (I, C_{i}) \cdot C_{i}}{\sum_{j \in Neighbors of node i} f (I_{j}, C_{j}) \cdot C_{j}}$ (1) where f (I, C_i) represents the probability of the node i connecting the newly added nodes. That is, when C_i is closer to its max value, node i can not be connected to other new nodes.

Step 4: To calculate the degree distribution p (C), the following equation should be used:

$\frac{\partial (C_{i})}{\partial (t)} = \frac{m \cdot f (I, C_{i}) \cdot C_{i}}{\sum_{j \in Neighbors of node i} f (I_{j}, C_{j}) \cdot C_{j}}$ (2)

In the neighbors of each node, the followsing equation is satisified: $\sum_{j \in Neighbors of node i} f (I_{j}) \cdot C_{j} = R \cdot \hat{I} \cdot AVG (D)$ (3) where R denotes the number of ndoes in the neighbors of the newly added node, $\hat{I}$ refers to the expected value of f (I), and AVG (D) means the average degree of the whole complex network. AVG (D) can be calculated as follows. $AVG (D) = 2 \cdot \frac{q \cdot t + r_{0}}{q_{0} + t}$ (4) where q₀ and r₀ mean number of nodes and number of edges at the initial state respecitvely. Symbol q denotes the number of edges of the newly added node.

Step 5: For the given node i, its node connectivity (C_i) $C_{i} = max (C_{i}) / - 1 + \frac{max (C_{i}) - q}{q} \cdot e^{\frac{I}{R \cdot \hat{I}} \cdot (t_{i} - t)}$ (5)

Step 6: In order to achieve the probability desity function, the following equation should be calculated. $P (C) = \int_{I_{\min}}^{I_{max}} δ \cdot \frac{2 \cdot R \cdot \hat{I}}{q_{0} + t} \cdot \frac{C_{max}}{I_{max}} \cdot \frac{1}{C \cdot max (C_{i}) - C^{2}} dI$ (6) where parameter δ refers to the distribution of node importance I, and C means the continuous random variable to represent node connectivity. I_max and I_min represent the max and min value of node importance.

5 Case study and results analyzing

Data collection is a key part in the process of empirical research, so how to obtain data source is an important problem. The collected dataset must be from the authoritative organizations as far as possible to ensure the authenticity. Hence, the credibility of the empirical findings can be ensured only when the dataset is accurate. This study requires a lot of raw data to construct the regional collaborative innovation complex system. Therefore, we collect the raw dataset from five main sources, which are: 1) comprehensive statistical yearbook of our country, 2) other kinds of professional statistical yearbook, 3) comprehensive statistical yearbook published by local governments, 4) various professional statistical yearbooks, and 5) other kinds ofpublications.

In the process of data collecting, all kinds of statistical yearbooks and related publications are refered, such as “China statistical yearbook”, “China statistical yearbook on science and technology”, “China’s regional economic statistical yearbook”, “China statistics yearbook on high technology industry”, “Almanac of China’s Finance and Banking”, “China’s transportation statistical yearbook”, “Chinese regional innovation capability report”, “The statistical analysis of paper in Chinese science and technology”, “Chinese torch program statistics”, and so on. However, some important data can not be obtained from the published publications. Hence, some source data are directly collected through relevant departments of the government.

As is shown in Fig. 4, the source data used in the regional collaborative innovation analyzing is organized into a hierarchical structure which is made up of three levels. At the first level, five parts are included, which are 1) Innovation resources guaranteeing ability, 2) Knowledge innovation ability, 3) Knowledge configuration ability, 4) Knowledge applying ability, and 5) Innovation environment supporting ability. These five parts can construct a complete regional collaborative innovation system. To study the network evolution of complete regional collaborative innovation system, the data from 2008 to 2013 are collected to make the dataset.

Using the above data, a complex network of regional collaborative innovation is constructed. There are 953 nodes (individuals) in this complex network. Next, the average payoff and individual cooperation rate of the propoed algorithm is given.

Combining the experimental results from Figs. 5 and 6, it can be seen that when the number of iterations is larger than 500, both the average payoff and individual cooperation rate are stable.

Afterwards, in Fig. 7, we test degree distribution of the proposed complex network, and the symbol K denotes the degree. Experimental results show that when the structure of the given complex is evolved, the degree distribution changes as well. Furthermore, the degree distribution of the complex network in the problem of regional collaborative innovation follows the power law distribution. Moreover, the structure of the proposed complex network is more similar to the BA scale-free network.

Next, we will testify the average degree of the complex network when the network evolution happens. Experimental results in Fig. 8 demonstrate that the average degree increases at first, and then decreases. At last, it slowly increases again. The reasons lie that 1) The individuals in the proposed complex network have the relationships with other neighbors, and in the initial stage neighbor increasing play an important role in this system. 2) When edges in this network increase to a specific threshold, some individuals may discover that there are more and more neighbors who can not be matched. 3) Afterwards, in the next stage, because individuals are easier to be matched, the average degree may be come to the steadily increasing state.

On the other hand, in Fig. 9, we will test how the percentage of the number of neighbors without changing influences the distribution of individual neighbor. Figure 9 explains that using the proposed method, with the evolution of the network, the majority neighbors are effectively changed.

Integrating the above experimental results, several suggestions can be obtained by analyzing the evolution of regional collaborative innovation complex network: (1) To continuously enhance the ability of regional collaborative innovation, regional indigenous innovation alliance should develop rapidly. Because we find from the experimental results that regional indigenous innovation alliance can greatly help to improve the internal structure of regional collaborative innovation complex network. (2) To ensure that the path exploited by many regions can be developed effectively, the local government should explore regulated operational mechanism of regional collaborative innovation alliance and let regional collaborative innovation alliance show its superiority.

In the regional collaborative innovation system, local governments play an important role in improving regional collaborative innovation ability. Furthermore, local governments should pay specifical attentions to new ideas, effective policies, and collaboration of various departments.

5 Conclusion

In this paper, we focus on the problem of regional collaborative innovation evolution utilizing the complex network technology. In our proposed regional collaborative innovation system, universities, research institutes, enterprises, intermediary organizations, financial institutions, government are included. In the proposed regional collaborative innovation evolution algorithm, we add a condition that a node can only be connected to a fixed number of neighbors. Futhremore, the regional collaborative innovation evolution can be analyzed by computing the probability desity function. In the experiment, five types of data are collected, such as 1) Innovation resources guaranteeing ability, 2) Knowledge innovation ability, 3) Knowledge configuration ability, 4) Knowledge applying ability, and 5) Innovation environment supporting ability. Finally, experimental results demonstrate the effectiveness of the proposed algorithm. In the futhre, we will expand the proposed works in the following aspects: (1) Try to using other datasets to make the performance evluations, for example, we could collect related data from other countries. (2) We should use the proposed algorithm to compare the regional collaborative innovation evolution in different regions.

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