Introduction

Architectural culture is a specific type of culture [1]. The unique architectural culture of a region is the material and spiritual wealth accumulated and created in the course of its social and historical development, and it is often formed in a unique historical context and historical stage. With the development of society and the acceleration of urbanization, the study of regional architectural cultural heritage has received increasing attention in recent years.

Scholars’ research on architectural culture in different regions has gone through both vertical and horizontal development processes. Horizontally, it focuses on the study of architecture and urban ontology, including the functional, spatial, material and technical forms of architecture or cities. While vertically, it emphasizes the analysis of cultural phenomena such as the dissemination [2], exchange [3], evolution [4] and change [5] of architectural culture in different regions. Although previous studies have been quite comprehensive, they have focused mostly on the qualitative interpretation of the ontological and environmental-cultural attributes of a particular architectural heritage building or architectural heritage community [6]. At present, quantitative and comprehensive analyses of the interpretation of the characteristics of urban architectural heritage groups and the spatial and temporal evolution of urban architectural culture are still lacking. This study adopts a computational approach to explore the patterns of distribution and evolution of architectural culture in different historical areas in the city. We contend that a comprehensive exploration of the architectural and cultural landscape is essential for a nuanced comprehension of the city’s architectural culture.

With the continuous development of digital technology, the expression of cultural characteristics of architectural heritage has also entered the digital era, which is no longer difficult for the collection of multiple types of architectural and cultural information. The visualization of architectural heritage through digital means allows for a better visual understanding of a region's unique architecture and urban culture. Owing to the greater diversity of information obtained, the data in our study also tend to incorporate multifaceted data from text, images, and audio-visuals, which ensures and supports the effective quantification of architectural culture. Cultural computing is the field of application of computers and computing technologies for cultural preservation, recovery, storage, modelling, reproduction, presentation and dissemination [7]. Japanese researcher Tosa formalized the concept of cultural computing in 2005 [8, 9]. He noted that an important aspect of cultural computing is to reveal the evolutionary characteristics and explore the laws of cultural change, development, etc., which is the key issue of cultural quantification, and additionally indicated that the digital construction of culture requires the construction of a complete set of cultural computing methodology systems [10]. However, the system is still in its infancy. The methodology used in this study can be considered a partial exploration and attempt to develop a methodological system for cultural computing.

In recent years, scholars have tried to perform quantitative analyses of culture with new perspectives and methods, but a more nuanced perspective is still lacking. British evolutionary biologist Richard Dawkins, in his 1976 book The Selfish Gene, defined a meme as “the smallest unit of cultural transmission, analogous to a gene in biology, which is naturally selected for by virtue of the effect of its expression on its own survival and reproduction in a cultural environment” [11, 12]. At the same time, the host of the meme tends to reorganise or mutate the representation of the message when replicating and transmitting the meme [13]. The concept of memes provides a unit of culture that can be shared and transmitted across time, allowing cultural quantification to take place in a fine-grained manner.

With the development of computational technology, researchers have begun to use more quantitative methods to analyse and calculate cultural memes to reduce the effects of the highly subjective and workload-intensive nature of traditional research. Li HF used cultural modifiers as the smallest unit of a dynasty and extracted cultural memes on the basis of the names of cultural artefacts to quantify the degree of similarity and differences in the cultural characteristics of Chinese dynasties [14]. Yang SM took the core cultural elements of traditional Chinese settlements as cultural memes and proposed a meme-based approach to mining, organizing and presenting the cultural knowledge of traditional Chinese settlements from the perspective of knowledge management [15]. These studies have made it possible to use memes as an entry point for cultural computing. Different computational methods are used to study cultural memes with different emphases. Compared with previous qualitative studies on urban architectural culture, this study adopts social network computing method to quantitatively explore the correlation of cultural memes in urban architectural heritage groups and deduce the evolution law of urban architectural culture. This method is innovative in the study of urban development.

The concept of social networks originated with English anthropologist Radcliffe-Brown’s focus on social structure [16]. Initially, this concept aimed to elucidate the corresponding behavior of actors through analysis of traditional small-group relationships (e.g., kinships, neighborhoods, classmates), and has subsequently garnered endorsement and progressive refinement by sociologists in related fields [17, 18]. Graph theory is an important theoretical source for exploring the structure of social network systems. Its focus is on exploring the connectivity between nodes without considering their shape, size, distance and orientation. Graph theory has been widely used in the field of architecture, such as the spatial syntax method, which is based on graph theory and is used to calculate the configurational spatial relationships between streets in the built environment [19]. In the study of urban architectural and cultural spaces, the cultural memes of architectural heritage are considered points, the channels connecting these memes are considered lines, and the points and lines form the spatial topology. Owing to the strong spatial resolution capability of graph theory, objects of spatial studies can be formed into abstracted spatial organizations through topological relations [20]. With the development of computer technology, various social network analysis tools based on graph theory have emerged, such as Gephi, Ucinet0020 [21], and Pajek [22]. The scope of the application of social network analysis methods in the field of architectural disciplines has also expanded in recent years. Zhu et al. assessed the network connection strength and spatial structure characteristics of the Beijing‒Tianjin‒Hebei (BTH) city cluster as an example and provided practical suggestions for the optimization of the BTH city cluster [23]. Xiang et al. conducted a comprehensive study of the architectural, spiritual and clan networks of the Tunpu community, which has a history of multiple migrations and a special cultural background, located in Guizhou Province, southwestern China [24]. Currently, the development and application of digital technologies, such as social networks, provide new methods for multidimensional analyses of urban architectural heritage and new possibilities for efficiently calculating the architectural culture of cities.

Relevant concepts and theories

Relevant concepts

Architectural memes

American architectural theorist Nikos A. Salingeros introduced meme theory into the field of architecture in 2002, proposing that an architectural meme is “a visual element of a particular architectural style, a reproduction of architectural form, geometric configurations, surfaces, and other elements,” and that it is “a cluster of freely reproducing fragments of information in a building, an informational entity after the pattern has been greatly simplified” [25]. The expression of an architectural meme is the architectural representation that preserves its core content in a building, which contains a number of architectural information obtained by human beings from the organs of perception, including both explicit basic architectural information, such as the building’s volume, material, colour, structural system, and style, as well as information of greater complexity, such as architectural groups, spatial composition [26], and component forms, and implicit information, such as the emotions and identities of the building’s stakeholders.

Evolution of architectural memes

A meme is intrinsic, and “the way it presents itself to the world as a manifestation of its influence on what surrounds it” and the multiple physical representations that act as modal vehicles constitute “the material shell of culture”, with this way of cultural evolution being termed Lamarckian evolution by meme theory [27]. This theory provides a new direction for us to study the theory of architectural memes; that is, we can directly observe and confirm the changes in modalities through the physical representations of the modality carriers that can be perceived by human beings [28] in order to judge the direction of cultural evolution. From this point of view, the evolution of architectural culture is Lamarckian, and it is through the continuous exploration of the representations of all kinds of buildings (including ruins) and their environments from ancient to modern times that mankind has been searching for the development of their cultures from the surface to the interior.

Types of architectural memes

Any building is comprised of three composite levels: the architectural technology, architectural function and architectural art, which corresponds to the architectural form meme; spatial memes and thinking memes constitute the complete expression of the building [29] and the formation of differences in architectural culture. Susan Blackmore, a British meme scholar, adopted the concept of memeplexes to describe the phenomenon of composite cultures, i.e., cultures are made up of different parts that are individual memes of varying origins, but they also propagate as a combination, and this combination is a memeplex [30]. Architecture can also be viewed as a memeplex, and similar to cultural memes in general, there exists a single meme that drives a particular expression of architecture, which is referred to in this paper as the architectural meme monolith. In contrast to general cultural memes, certain architectural expressions are influenced by the collaborative interaction of clusters comprising multiple modifiers, referred to as architectural memeplexes in this study. These memeplexes encompass various modal groups such as style and affective categories.

Social network analysis

With the increasing depth of theories, methods and techniques of network analyses, social network analyses have also been widely used as an important sociological computational method. In this work, the computational method of social network analysis is used to analyse the interactions between the elements (architectural meme) of the urban network nodes (architectural heritage). The network-based perspective analysis has the following characteristics. First, the interactions between nodes are more important for macroanalysis results than are the characteristics and attributes of the nodes themselves. Second, analysing the nodes in the complex network can completely interpret the pattern characteristics of the whole network [31]. Finally, focusing on the overall structural characteristics of the network at a given time is critical to the future survival and development of the network as a whole. The focus of this study is to analyse the evolution of architectural culture in Harbin during a specific historical period using social network analysis on the basis of previous survey data.

Centrality algorithms

Centrality algorithms can help us to identify important nodes in a network and to deeply analyse their impact on the network structure and functions [32, 33]. Centrality algorithms include degree centrality, betweenness centrality and closeness centrality. To express the extent to which the cultural characteristics of a particular architectural heritage node are exchanged with those of other buildings, degree centrality is used in this study as a measure of the importance of the network nodes in the cultural meme network, i.e., it indicates the number of other buildings that are associated with a particular building. In an architectural meme network, the greater the centrality of a particular architectural node is, the more connections there are to that architectural heritage node, and the greater the similarity to other architectural heritage. The degree of centrality can be calculated using Eq. (1):

$$ D\left( {\text{i}} \right) = \mathop \sum \limits_{j} a_{i,j} $$
(1)

where D(i) is the degree of centrality of node i, ai, j is the adjacency matrix of the nodes in the network, and the same type of architectural meme network establishes the connectivity between the architectural heritage nodes by choosing the appropriate threshold size.

The average degree is the average of the degree, reflecting the strength of the network’s overall cooperative ties [34]. It can be calculated using Eq. (2):

$$ \overline{{D{\text{egree}}}} = \frac{{\sum D{\text{egree}}_{i} }}{n} $$
(2)

Community detection algorithm

Community detection algorithms are used to discover the structure of communities in a network [35], reveal the aggregation behaviour of network nodes, and discover the structural relationships of the overall network, which can also be viewed as a clustering algorithm [36]. The clustering coefficient is the main indicator of the degree of closeness of the neighbouring nodes of a node in a network [37]. It can be calculated using Eq. (3):

$$ C_{i} = \frac{2Ei}{{ki\left( {ki - {1}} \right)}} $$
(3)

where ki is the set of neighbours of node i and Ei is the number of edges that exist between these ki nodes.

The clustering coefficient takes values between 0 and 1. The clustering coefficient is 0 when and only when all network nodes are unrelated to each other; when the network is globally coupled, i.e., when any two nodes in the network can be directly connected, the clustering coefficient is 1; the closer the clustering coefficient is to 1, the higher the degree of agglomeration between the nodes of the network is. More precisely, the clustering coefficient reflects the closeness of neighbouring nodes in the network. The clustering coefficient of a node is the ratio of the number of connection points present at this node to the maximum possible number of connection points, and the clustering coefficient of a network as a whole is the average of the clustering coefficients of the individual nodes. It can be calculated using Eq. (4):

$$ C = \frac{1}{n}\mathop \sum \limits_{i} Ci $$
(4)

where n is the number of network nodes. Thus, having both a small mean path and a high clustering coefficient creates a small-world effect [38].

Computing framework

The data processing in this study consists of three steps: data screening, data integration, and data calculation, based on the aforementioned concepts and methods. The data processing methodological framework is shown in Fig. 1. ArcGIS software was used in the data integration process, and Gephi software was used in the data calculation process, which provided for the visualization of the process and results of the study.

Fig. 1
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Methodological framework

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Data and methods

Study area

As a hub city connecting the Chinese Eastern Railway with the Trans-Siberian Railway, Harbin’s modern urban pattern began with the construction of the Chinese Eastern Railway in 1898 and matured at the end of China’s War of Resistance Against Japanese Aggression (1945) [39]. Within the timeframe of nearly half a century, Harbin has developed rapidly in terms of its urban scale, with a distinctive urban cultural identity. The main manifestation is that Harbin is the earliest and one of the only cities in modern China that was built according to the master plan of a modern city, and its urban planning and architectural design adopted the world’s more advanced design ideas and techniques at that time. Chinese cities such as Qingdao and Dalian are also well-developed cities in the modern era, but in contrast, Harbin’s urban construction is on a larger scale, the implementation of the city’s masterplan is more complete, and the city’s modern architectural features are more obvious. Therefore, the regular interpretation of the architectural culture of modern Chinese cities in Harbin is highly representative.

The study area of this paper is located in Harbin city in the southern part of Heilongjiang Province, China (Fig. 2), at latitudes 44° 03′ to 46° 40′ N and longitudes 125° 41′ to 130° 13′ E [40]. Its main urban areas are divided according to the direction of the railway: Daoli District, Daowai District, and Nangang District. Research on the temporal dimension of the modern city of Harbin since the opening of the port of urban construction and the dissemination of architectural culture has been strongly influenced not only by the time period but also by the large number of modern architectural heritages in Harbin, which were completed during the time period, i.e., from 1898–1945. According to historical data, this period can be divided into a modern city foundation period (1898–1903) [43], an expansion period (1904–1917), a prosperity period (1918–1931) and a supplementary update period (1932–1945). As the central station city of the Chinese Eastern Railway, Harbin’s modern architectural heritage in the main urban area is characterized by buildings that serve railway functions and, in terms of functional dimensions, include almost all the functions that modern people need to live (Table 1) [41]. In the spatial dimension, these architectural heritages are widely distributed in the main urban areas of the city and form a number of historical districts with distinctive cultural characteristics.

Fig. 2
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Study area

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Table 1 Function classification of modern architectural heritage in Harbin
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Data sources

The data for this study are derived from an extensive survey conducted by the author’s team over several years, which comprehensively explores the ontology and environmental aspects of architectural heritage in Harbin, China. The research team created a database of the city’s architectural heritage consisting of basic data on 425 architectural heritage buildings that have existed in the city in recent history. Data were collected via historical information collection, mapping and interviews. The data include the material, structure, district, style, age, point cloud, mapping information, historical information and other related information of each building. The data are in the form of text, images and audio-visuals. As a carrier of urban architectural culture, these detailed basic data have restored the cultural landscape of the city in different periods since modern times and have also enabled workers in the field of urban architectural design to have a direction and basis for thinking about the design of the cultural pattern of the contemporary city.

However, owing to the limited documentation and collection capacity, as well as the impact on the original information of the architectural heritage arising from the renovation activities of historic buildings that may have taken place in recent years, the accuracy and authenticity of the data may be subject to certain errors but will not affect the actual physical significance of the data analysis.

Data processing

Harbin modern architectural memes specifically refer to the basic information elements obtained from the investigated buildings that can visually represent a certain trait of the building. By organizing the basic information of the sample buildings and filtering out the types of architectural modes that can characterize the architectural and cultural qualities of each sample building for generalization, such as material memes (C), structural system memes (G), stylistic memes (F), etc., a cultural meme matrix of Harbin's modern public architecture is established (Table 2), which is conducive to the further correct identification and categorization of architectural and cultural memes. The abbreviations in Appendix have been used for the names of the architectural memes covered in this paper.

Table 2 Cultural meme matrix of Harbin’s modern public architecture
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The information underlying the building have been classified into different cultural modifier types in the obtained cultural meme matrix of Harbin’s modern public architecture. Among all the basic information, the facade material, structural system, and architectural style can most intuitively express the cultural characteristics of the architecture heritage. Therefore, on the basis of the definitions of architectural meme monoliths and architectural memeplexes, this paper focuses on the impact of these three modal types on urban architectural culture.

Study design

Social network analysis performs well in measuring the strength of relationships and connections between different nodes in a network but has some limitations in reflecting the spatial attributes of network nodes. To overcome these limitations, this study uses ArcGIS software to map the geographical coordinates of buildings, emphasize the spatial attributes of buildings [42, 43], construct relationships between multiple architectural heritages, and express the spatial characteristics of the regional architectural culture. Unlike previous studies that focused only on spatiotemporal characteristics or a single research object, this study fully considers the diversity of architectural and cultural characteristics from the perspective of cultural modelling and provides a new approach to the study of regional architectural culture. This study takes the cultural models extracted from Harbin's architectural heritage as the research object, combines quantitative methods with social network analysis, discusses the similarities and differences of the city’s architectural cultural heritage in different periods, and discovers the evolutionary characteristics of the city's architectural culture from a more detailed perspective. The research process was divided into two parts, data processing and data analysis, and Fig. 3 shows the specific framework of this study.

Fig. 3
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Overview of Research

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Results and discussion

Analysis of the qualities of Harbin’s architectural memes

Facade material memes

The facade materials reflect the different textures of the architectural surface. The façade materials of Harbin’s modern public architectural heritage mainly consist of five forms: brick wall + paint, brick wall, cement plaster, stone veneer and timber (Fig. 4). From the spatial and temporal distribution of material memes (Fig. 5), in the foundation period (1898–1903), owing to the tight schedule, to ensure the speed of the construction of the facade of the brick wall as the foundation, representative buildings needed to have a certain artistic effects on the facade of a variety of warm-coloured paintings. During the expansion period (1904–1917) and prosperity period (1918–1931), the city of Harbin saw the migration of expatriates from many countries and the emergence of multicultural architectural coexistence and competition, with cement as the perfect material to easily shape a variety of styles of architectural symbols, which was more expressive. The supplementary update period (1932–1945), to a certain extent, limited the free expression of the artistic layer of the architecture, and this period of modernist architecture mostly focused on functionality with the use of brick as the primary facade material.

Fig. 4
figure 4

Classification of Material Meme of Architecture facade. a Brick wall + paint, b brick wall, c cement plaster, d stone veneer, e Timber

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Fig. 5
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Spatio-temporal distribution of the evolution of the material memes of the façade. a Foundation period (1898–1903), b expansion period (1904–1917), c prosperity period (1918–1931), d supplementary updates period (1932–1945)

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Based on the cultural patterns of the material memes of the architectural façades, cement, as a new high-strength material, is favoured in Harbin’s modern architecture, and is the facade material of most of the medium- and high-grade architectures in Daoli District, Daowai District and Nangang District, and light, ethereal and dignified architectural expressions are portrayed through a variety of clay moulding techniques. The low-grade architectures are mostly brick walls, and the architectural image is rustic and heavy, with a strong sense of sculpture and the majority being in Daowai District. Because stone veneers are not easy to obtain, they are only used in Nangang District, particularly in high-grade architectures, to highlight the heavy and magnificent temperaments of this district, although their numbers are very small.

Structural system memes

The development of advanced structural technology is a technical guarantee for the full continuation of architectural culture [44]. There are various types of structural systems of the modern architecture in Harbin. Brick-wood structures, brick-stone structures, brick-concrete structures, and wooden structures constitute the major of structural systems.

In terms of the temporal and spatial distributions of structural systems (Fig. 6), these structural forms emerged simultaneously during the period of the city’s opening and construction. The brick-wood structures were characterized by a simple construction process, a single material, easy access to materials, a short construction time and the existence of policy advantages at the time. Therefore, the early modern architectures in Harbin mostly adopted this structural system, which was used in all grades of architectures and occupied a large proportion. However, owing to the limitations of the mechanical strength of the structure, the architectures using this structural system generally have a lower number of floors and a smaller volume. In the middle and late development process, the brick–concrete structural system was gradually popularized in Harbin, and its structural freedom and mechanical properties were greatly improved as a result, especially in Nangang District and Daoli District, where it was widely used.

Fig. 6
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Spatio-temporal distribution and share of structural system memes. a Foundation period (1898–1903), b expansion period (1904–1917), c prosperity period (1918–1931), d supplementary updates period (1932–1945)

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Architectural style memes

The architectural style is a group of memes fixed to include one or more architectural attribute memes, architectural spatial memes and architectural vocabulary memes. It shows the most subtle and nuanced differences in how mankind has distinguished the art of architecture at a certain time in history and is the basis for recognizing a certain growth, expansion, and enrichment of the art of architecture [45]. The vocabulary of Western architecture has evolved as it has been introduced to Harbin, a city in China, resulting in numerous instances of cultural collision and fusion. In the modern architecture of Harbin, there appeared a lot of complex collectivism and eclecticism architecture, which were different from the pure classical and Renaissance architecture in the West. This study refers to these styles as imitations of the Renaissance and so on.

From the spatial and temporal distribution of modern architectural style memeplexes in Harbin (Fig. 7), the foundation period (1898–1903) was mainly concentrated in Nangang District, dominated by the Russian architectural style and the budding of the Art Nouveau architectural style. In the expansion period (1904–1917) and prosperity period (1918–1931), Nangang District and Daoli District presented many instances of imitation of the Renaissance, Classical, Baroque and other eclectic architecture style, including the large number of modern Harbin public buildings during this period of time, and these two periods present the most varied forms of architectures. At the same time, Art Nouveau architecture also reached its construction climax during this period and had far-reaching impacts [46]. Although Daowai District was characterised by a wave of Chinese Baroque-style buildings, it has an architectural and cultural style that is very different from that of Daoli District and Nangang District. The supplementary update period saw the emergence of the Modernist and Art Deco movement styles, which represented a sense of minimalism.

Fig. 7
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Spatio-temporal distribution of architectural styles of modern buildings in Harbin. a Foundation period (1898–1903), b expansion period (1904–1917), c prosperity period (1918–1931), d supplementary updates period (1932–1945)

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In terms of the final architectural style patterns (Fig. 8), Daoli District and Nangang District do not form clear boundaries in the distribution of architectural styles, nor do they present a clear style memeplex as in the evolutionary process; rather, they eventually formed a pluralistic coexistence, with eclectic general characteristics. Daowai District has a sizable group of neighbourhoods represented by the Chinese Baroque style, which is quite distinctive from Daoli District and Nangang District.

Fig. 8
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Distribution of modern architectural style memes in Harbin. a Shows the finalized architectural style pattern. b Shows the percentage of architectural styles

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Analysis of the structure of Harbin’s architectural memes

Cluster analysis of architectural memes

This paper uses a community detection algorithm to analyse the cultural community groups in Harbin’s architectural meme network to analyse the cultural characteristics of the city’s architecture during each period of development. On the basis of the organization of the modal system of Harbin’s modern architectural heritage and the types of architectural meme analysed in this paper, a co-occurrence map of the evolution of Harbin’s modern architectural meme network was obtained using the Gephi software platform (Fig. 9). The nodes in the network represent the architectural heritage that emerged in different periods, whereas the lines represent the likelihood of the cultural modalities between two buildings. The size of a node is determined by the node degree; the larger the node is, the more connections the node has with surrounding nodes.

Fig. 9
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Co-occurrence maps illustrating the evolution of modern architectural meme networks. A Foundation period (1898–1903), b expansion period (1904–1917), c prosperity period (1918–1931), d) supplementary updates period (1932–1945)

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As shown in Fig. 10, during the foundation period (1898–1903), each area’s architectural heritage cultural identity was isolated from each other, with Nangang District being the first to complete a concentration of construction activities in a short period of time. The clustering coefficient of the architectural network in this area increased rapidly to 0.63, initially forming a coupled network system. In the expansion period, with the influx of expatriates from various countries and the increase in demand for construction, diversified architectural cultures were disseminated and exchanged in the construction of the city so that the nodes of the network began to produce a certain degree of contact, and the beginning of the community clusters were formed in Daoli District and Nangang District. From the prosperity period (1918–1931) to the supplementary update period (1932–1945), the network clusters were more mature in size. Overall, the continuity characteristics of Harbin’s architectural meme network in all periods were obvious, and the clustering coefficients for all stages were greater than 0.5 in the range of 0.575–0.676 (Fig. 10). This indicates that the overall network has a relatively stable degree of agglomeration with strong genetic characteristics, forming a highly coupled network system.

Fig. 10
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Changes of the clustering coefficient of the architectural meme network over time

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A localised analysis of the interior of the final architectural meme network revealed that the buildings in the Nangang and Daoli districts formed “network clusters [47]” with no clear boundaries. The similarity decreased sequentially from inside the cluster to outside the cluster, indicating that the propagation of Harbin’s modern architectural meme in space becomes more obvious in the modal variation. For example, the architectural meme of Harbin Zhongyang Street, which is located in the centre of this cluster, has high similarity with the architectural meme of Hongjun Street but low similarity with the architectural meme of Huayuan Street, which is located at the periphery of the cluster. This shows that different types of architectural memes will occur in different ways due to the cross-reorganization of regional relations so that the architectural entity produces a new phenotype, develops regional cultural characteristics, and ultimately presents a “core–edge” mode of cultural pattern, showing an obvious “small-world effect”.

Centrality analysis of architectural memes

The centrality of a network measures the density and complexity of the network as a whole, which is influenced mainly by the average degree and scale of the network [48]. The average degree of the network and the scale of the network are mutual constraints; an increase in the average degree increases the network complexity and strengthens the coupling of the network, whereas an increase in the network scale worsens the synchronization state of the network and decreases the complexity of the network [49]. As shown in Fig. 11, the rate (slope) of increase in the network scale (the number of architectural heritages) of the Harbin Public Architecture Meme Network in the foundation period, expansion period and prosperity period is greater than the growth rate of the average degree of the network in the corresponding period. This indicates that the urban architectural cultural structure of the scale expansion speed was too fast in this period, resulting in the degree of coupling not keeping up with the corresponding scale trend, leading to the low centrality of the network. This shows that the input of architectural culture over time is greater than its transmission and integration. The average degree rate of the network is reversed in the replenishment phase, making the final architectural meme network a complex system with strong coupling, a stable nature and strong centrality. The constituent elements (architectural meme) within the system constitute the system as a whole in the form of nonlinear interactions and form a holistic character that transcends the simple superposition of architectural meme monoliths and architectural memeplexes. In the development and evolution of modern architectural culture in Harbin, the complex system constantly emerges from the overall level of complex and diverse regional cultural characteristics, from humanities, nature, the economy and other external systems of quality and energy exchanges, and from each other for a long period of time in a dynamic state of adaptation [50].

Fig. 11
figure 11

Scale and average degree of the network over time

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Conclusions and prospect

Taking modern public buildings in Harbin as an example, this paper extracted the architectural memes of architectural heritage, constructed a cultural meme matrix, and analysed its cultural characteristics. The social network analysis method was used to construct the Harbin architectural meme network and analyse its structural characteristics, and the main conclusions are as follows:

  1. 1.

    By extracting the cultural moduli of Harbin's modern architectural heritage and horizontally comparing its architecture with similar meme elements (material memes, structural system memes, stylistic memes, etc.) from different periods of the modern era, the propagation direction of Harbin's modern architectural culture and the cultural qualities of the city's architectural heritage can be objectively reproduced to a certain extent.

  2. 2.

    A community detection algorithm was used to obtain the cultural similarity of architectural heritage clusters in Harbin's architectural culture meme network. This study revealed that in the modern architectural culture pattern in Harbin, the “Nangang–Daoli architectural culture cluster”, which is characterized by a “core–edge”, and the “Daowai architectural culture cluster”, which is characterized by linear characteristics, formed. The cultural similarities between these two clusters are characterized by continuous inheritance.

  3. 3.

    Through centrality analysis of the architectural meme network, we found that the modern architectural culture of Harbin has formed a holistic cultural identity beyond the simple superposition of architectural meme monoliths and architectural memeplexes in the process of its development and evolution and has also formed a highly coupled and complex architectural cultural system.

Analysing historical information on architectural heritage by qualitative and quantitative methods and establishing an architectural meme network could help reproduce the overall cultural characteristics of regional urban architectural heritage to some extent. In the contemporary urban design of historical and cultural cities, a qualitative approach to weighing the cultural patterns embodied in urban areas is often biased. The data-supported methodology of exploring regional architectural and cultural patterns through a network of urban historical and cultural memes allows us to obtain the clustering and centrality characteristics of architectural heritage cultures in historical urban areas and to provide methodological lessons for the design of architectural and cultural patterns in cities. Practitioners can use the findings of this analysis to quantify the architectural and cultural patterns of different districts in the urban design of historic districts and to harmonize the spatial relationships between contemporary and historic buildings.

We hope to continue this study and focus on the level of integration between different architectural cultures in future studies to provide a more comprehensive analysis of the different architectural and cultural characteristics of cities and to discuss the reasons for the cultural differences.