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This study aims to review the literature on graph-theoretic mining methods for node importance in both static and dynamic world city networks, which is correspondingly categorised by graph-theoretic node importance mining on network topologies and transmission mechanisms.

The authors overview the graph-theoretic indicators of node importance: centrality and power. Then, the methods of graph-theoretic node importance mining on network topologies are assessed with node relevance, centrality- and power-based measurements, heterogeneous fusion and other miscellaneous approaches. The latest progress in transmission mechanisms is also reviewed in this study involving network evolution, node immunisation and robustness in dynamics. Finally, the findings are analysed and future directions in this field are suggested.

The method development of node importance mining is driven by complex application-based problems within a transmission mechanism. Fusion measurements, based on centrality and power, are extended by other graph mining techniques in which power has a significant role. In conclusion, the trends of node importance mining focus on power-embedded fusion measurements in the transmission mechanism-based complex applications.

This is the first systematic literature review of node importance from the view of graph-theoretic mining.

Complex mechanical 3D computer-aided design (CAD) model embodies rich implicit design knowledge. Through discovering the key function parts and key function module in 3D CAD assembly model in advance, it can promote the designers’ understanding and reuse efficiency of 3D assembly model in design reuse.

An approach for discovering key function module in complex mechanical 3D CAD assembly model is proposed. First, assembly network for 3D CAD assembly model is constructed, where the topology structure characteristics of 3D assembly model are analyzed based on complex network centrality. The degree centrality, closeness centrality, betweenness centrality and mutual information of node are used to evaluate the importance of the parts in 3D assembly model. Then, a multi-attribute decision model for part-node importance is established, and the comprehensive evaluation for key function parts in 3D assembly model is accomplished by combining Analytic Hierarchy Process and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). Subsequently, a community discovery of function module in assembly model-based Clauset–Newman–Moore (CNM)-Centrality is given in details. Finally, 3D CAD assembly model of worm gear reducer is taken as an example to verify the effectiveness and feasibility of proposed method.

The key function part in CAD assembly model is evaluated comprehensively considering assembly topology more objectively. In addition, the key function module containing key function part is discovered from CAD assembly model by using CNM-Centrality-based community discovery.

The approach can be used for discovering important design knowledge from complex CAD assembly model when reusing the assembly model. It can help designers capture and understand the design thinking and intent, improve the reuse efficiency and quality.

The paper first proposes an approach for discovering key function module in complex mechanical 3D CAD assembly model taking advantage of complex network theory, where the key function part is evaluated using node centrality and TOPSIS, and the key function module is identified based on community discovery.

Currently, China’s manufacturing industry chain still faces the danger of chain breakage due to the persistent “lack of technology” issue. The definition and detection of key nodes in the industry chain are significant to the enhancement of the stability of the industry chain. Therefore, detecting the key nodes in the manufacturing industry chain is necessary.

A complex network based on the links amongst listed manufacturing enterprises is built, and the authors analyse the network’s basic characteristics and vulnerability, taking into account the impact of scientific and technological innovation on the stability of the industry chain.

It is found that the high structural characteristic of midstream nodes in the naval architecture and marine engineering equipment industry chain determines their importance to stability, and the key status of upstream nodes is reflected in the weakness of technological innovation. The upstream nodes should focus on improving their independent innovation and R&D capability, whilst the midstream nodes should maintain a close supply–demand cooperation relationship.

The key node detection model for industry chain stability is constructed by considering various factors from the perspective of network and technological innovation. Empirical study is conducted to verify effectiveness of proposed method.

The manufacturing industry and the producer service industry have a high degree of industrial correlation, and their integration will cause changes in the complex industrial network topology, which is an important reason for the synergistic effect. This paper describes the topology of industrial systems using complex network theory; further, it discusses how to identify the criticality and importance of industrial nodes, and whether node characteristics cause synergistic effects.

Based on the input-output data of China in 2007, 2012 and 2017, this paper constructs the industrial complex network of 30 Chinese provinces and cities, and measures the regional network characteristics of the manufacturing industry. The fixed-effect panel regression model is adopted to test the influence of agglomeration degree and centrality on synergies, and its adjustment mechanism is explored.

The degree of network agglomeration in the manufacturing industry exerts a negative impact on the synergistic effect, while the centrality of the network exerts a significant promoting effect on the synergistic effect. The results of adjustment mechanism test show that enhancing the autonomous controllable ability of the regional industrial chain in the manufacturing industry can effectively reduce the effect of network characteristics on the synergistic effect.

Based on input-output technology, this paper constructs a complex industrial network model, however, only basic flow data are used. Considerable in-depth and detailed research on the economic and technological connections within the industry should be conducted in the future. The selection of the evaluation index of the importance of industrial nodes also needs to be further considered. For historical reasons, it is also difficult to obtain and process data when carrying out quantitative analysis; therefore, it is necessary to make further attempts from the data source and the expression form of evaluation indicators.

In a practical sense this has certain reference value for the formulation of manufacturing industrial policies the optimization of regional industrial layout and the improvement of the industrial development level. It is necessary to formulate targeted and specialized industrial development strategies according to the characteristics of the manufacturing industry appropriately regulate the autonomous controllable ability of the industrial chain and avoid to limit the development of industries which is in turn limited by regional resources. Industry competition and market congestion need to be reduced industry exchanges outside the region encouraged the industrial layout optimized and the construction of a modern industrial system accelerated.

The above research results hold certain reference importance for policy formulation related to the manufacturing industry, regional industrial layout optimization and industrial development level improvement. Targeted specialized industrial development strategies need to be formulated according to the characteristics of the manufacturing industry; the autonomous controllability of the industrial chain needs to be appropriately regulated; limitation of regional resources needs to be avoided as this restricts industrial development; and industry competition and market congestion need to be reduced. Agglomeration of production factors and optimization of resource allocation is an important part of a beneficial regional economic development strategy, and it is also an inevitable choice for industrialization to develop to a certain stage under the condition of a market economy. In alignment with the research conclusions, effective suggestions can be put forward for the current major industrial policies. In the process of promoting the development of the manufacturing industry, it is necessary for regional governments to carry out unified planning and guidance on the spatial layout of each manufacturing subsector. Regional governments need to effectively allocate inter-industry resources, better share economies of scale, constantly enhance the competitive advantages and competitiveness of development zones and new districts and promote the coordinated agglomeration and development of related industries with input industries. Industrial exchanges outside the region should be encouraged, the industrial layout should be optimized and the construction of a modern industrial system should be accelerated.

Complex network theory is introduced to study the industrial synergy effect. A complex industrial network of China's 30 regions is built and key network nodes are measured. Based on the dimensionality of the “industrial node – industrial chain – industrial complex network”, the research path of industrial complex networks is improved.

The need for stakeholder theory has been widely highlighted in the literature to develop solid strategies for a large organization. However, there is still a lack of user-friendly visualization tools and no unique approach exists to identify and engage stakeholders. This paper aims to propose a general methodology to co-design the sustainability ecosystem at the local scale, to explore it and to assess the impact of a large organization within the identified ecosystem.

The methodology consists of two main processes: identifying an ontological map of the sustainability topics network and designing the local sustainability stakeholders ecosystem. Both processes are based on a nodes identification phase and a nodes prioritization phase. The identification phase was achieved by engaging 160 citizens, for the topics network and nearly 40 relevant stakeholders, for the stakeholders’ ecosystem, with a collaborative participatory mapping process. The prioritization phase was conducted because of three indicators, i.e. the closeness, the betweenness and the eigenvector centrality.

Betweenness centrality results to be the best indicator to assess the importance of a stakeholder with respect to the whole network, while eigenvector centrality highlights the quality of the already engaged stakeholders of an organization, as it mainly depends on the number of links of the first order neighbors. On the contrary, the closeness centrality, when applied to a small network, seems to be not appropriate to assess the centrality of a stakeholder.

This approach revealed some criticalities in the mapping process, as in the weighting link procedure. Further investigations are needed to generalize the approach to a dynamic one, to allow real-time mapping and to develop a robust interconnection among centrality degrees and the power, interest and legitimacy concept of stakeholder theory.

Obtained results for a case study, i.e. the position of the University of Turin Green Office within the City of Turin sustainability ecosystem, are discussed showing how social network analysis centrality degrees can be used to quantitatively assess the role of an organization within a stakeholders’ ecosystem.

Centrality analysis allows identifying emergent topics/stakeholders within a network of words/actors that, at a first sight, should not be considered by decision-makers and managers.

A new methodology for stakeholder identification and prioritization is proposed exploiting online data visualization tools, participatory mapping and social network analysis.

In online social network analysis, the problem of identification and ranking of influential nodes based on their prominence has attracted immense attention from researchers and practitioners. Identification and ranking of influential nodes is a challenging problem using Twitter, as data contains heterogeneous features such as tweets, likes, mentions and retweets. The purpose of this paper is to perform correlation between various features, evaluation metrics, approaches and results to validate selection of features as well as results. In addition, the paper uses well-known techniques to find topical authority and sentiments of influential nodes that help smart city governance and to make importance decisions while understanding the various perceptions of relevant influential nodes.

The tweets fetched using Twitter API are stored in Neo4j to generate graph-based relationships between various features of Twitter data such as followers, mentions and retweets. In this paper, consensus approach based on Twitter data using heterogeneous features has been proposed based on various features such as like, mentions and retweets to generate individual list of top-k influential nodes based on each features.

The heterogeneous features are meant for integrating to accomplish identification and ranking tasks with low computational complexity, i.e. O(n), which is suitable for large-scale online social network with better accuracy than baselines.

Identified influential nodes can act as source in making public decisions and their opinion give insights to urban governance bodies such as municipal corporation as well as similar organization responsible for smart urban governance and smart city development.

Based on the perspective of technology supply chain, this study explores the effect of macroeconomic uncertainty regarding the spatiotemporal evolution of urban innovation networks to establish causality.

It collects patent trading data for 283 cities in China (2005–2017) and employs the spatial econometric model to investigate the causal relationship.

The regional transfer of advanced technology in China is rising sharply, and the innovation network based on patent trading is typically high-density, multi-direction and wide-spreading. Further, macroeconomic uncertainty has a negative effect on the scale of innovation flows and the absorptive capacity in eastern cities. However, it has no significant impact on the innovation network characteristics in developed cities. In contrast, macroeconomic uncertainty is detrimental for the absorptive capacity and node importance in inland and undeveloped cities.

As macroeconomic uncertainty increases, it is important to improve the quality of the urban innovation network with a better understanding of heterogeneity to promote further suitability innovation at the region-level.

This study highlights a clear and distinctive view that macroeconomic uncertainty not only directly affects the evolution of the urban innovation network but also indirectly affects the characteristics of other city nodes via the spatial spillover mechanism.

This paper presents a critical review of the economic network analysis methods and their applications to maritime transport. A network can be presented in terms of its structure, topology, characteristics as well as the connectivity with different measures such as density, degree distribution, centrality (degree, betweenness, closeness, eigenvector and strength), clustering coefficient, average shortest path length and assortative. Various models such as the random graph model, block model, and ERGM can be used to analyse and explore the formation of a network and interaction between nodes. The review of the existing theories and models has found that, while these models are rather computationally intensive, they are based on some rather restrictive assumption on network formation and relationship between ports in the network at the local and global levels that require further investigation. Based on the review, a conceptual framework for maritime transport network research is developed, and the applications for future research are also discussed.

This paper presents a critical review of the economic network analysis methods and their applications to maritime transport. A network can be presented in terms of its structure, topology, characteristics as well as the connectivity with different measures such as density, degree distribution, centrality (degree, betweenness, closeness, eigenvector and strength), clustering coefficient, average shortest path length and assortative. Various models such as the random graph model, block model, and ERGM can be used to analyse and explore the formation of a network and interaction between nodes. The review of the existing theories and models has found that, while these models are rather computationally intensive, they are based on some rather restrictive assumption on network formation and relationship between ports in the network at the local and global levels that require further investigation. Based on the review, a conceptual framework for maritime transport network research is developed, and the applications for future research are also discussed.

This study explores the characteristics of high-speed rail (HSR) and air transportation networks in China based on the weighted complex network approach. Previous related studies have largely implemented unweighted (binary) network analysis, or have constructed a weighted network, limited by unweighted centrality measures. This study applies weighted centrality measures (mean association [MA], triangle betweenness centrality [TBC], and weighted harmonic centrality [WHC]) to represent traffic dynamics in HSR and air transportation weighted networks, where nodes represent cities and links represent passenger traffic. The spatial distribution of centrality results is visualized by using ArcGIS 10.2. Moreover, we analyze the network robustness of HSR, air transportation, and multimodal networks by measuring weighted efficiency (WE) subjected to the highest weighted centrality node attacks. In the HSR network, centrality results show that cities with a higher MA are concentrated in the Yangtze River Delta and the Pearl River Delta; cities with a higher TBC are mostly provincial capitals or regional centers; and cities with a higher WHC are grouped in eastern and central regions. Furthermore, spatial differentiation of centrality results is found between HSR and air transportation networks. There is a little bit of difference in eastern cities; cities in the central region have complementary roles in HSR and air transportation networks, but air transport is still dominant in western cities. The robustness analysis results show that the multimodal network, which includes both airports and high-speed rail stations, has the best connectivity and shows robustness.