Bridges in social networks: current status and challenges

Literature search strategy

We performed a systematic search across multiple academic databases, including Google Scholar, Web of Science, and Scopus to identify relevant studies. We used a combination of targeted search queries based on relevant keywords such as “bridge detection in social networks,” “network connectivity bridges,” “functional and structural bridges,” and “bridge nodes in signed networks.” Additionally, we reviewed references from key survey articles to ensure the inclusion of influential studies that are not always identified through keyword searches.

We applied a structured literature review methodology to ensure the reliability of our search process. The study selection process includes the removal of duplicate articles, an initial title and abstract screening, and a full-text review to determine relevance to the research scope. Studies that did not explicitly define or apply bridges in social networks were excluded.

Inclusion and exclusion criteria

To ensure a high standard of relevance and quality, the following inclusion criteria are defined:

• Studies that explicitly examine bridge detection and its structural or functional aspects, or their applications in network analysis.

• Peer-reviewed journal and conference articles, as well as preprints available in recognized repositories, published from 2,000 onward.

• Although the main inclusion window began in 2,000, key foundational studies predating this period were included because they established essential concepts relevant to subsequent research.

• Articles that present empirical analysis, formal definitions, or algorithmic approaches to bridge detection.

• Articles that address bridges in both signed and unsigned networks.

We applied the following exclusion criteria:

• Studies that do not provide an explicit definition or application of bridges in social networks.

• Articles that focus solely on community detection without discussing bridges.

• Duplicates retrieved from multiple databases.

The final selection process involved multiple screening steps, including title and abstract review, full-text examination, and duplicate removal, to ensure the inclusion of the most relevant studies.

Ensuring comprehensive and unbiased coverage

We adopted several strategies to maintain a balanced and unbiased literature review. First, we included studies from multiple domains, such as computational social science, network theory, and applied machine learning, to prevent disciplinary bias. Additionally, we ensured a mix of foundational works (e.g., (Granovetter, 1973; Burt, 2005)) and recent developments in bridge detection. We implemented clearly defined selection rules and cross-validated our study inclusion against existing review articles on social network bridges to enhance objectivity. This approach minimizes the overrepresentation of specific perspectives while maintaining a comprehensive review.

This survey presents a comprehensive and balanced analysis of bridge structures in social networks, incorporating key theoretical and empirical contributions. Furthermore, the categorization framework developed in this study is expected to serve as a valuable reference for future research in bridge detection algorithms and network analysis. This structured review supports the continued advancement of methodologies for identifying and characterizing bridges across different network types.

A total of 24 core studies were included in this review (20 on unsigned networks and four on signed networks). Additionally, 12 application-oriented articles were selected to illustrate practical implementations of bridge concepts in diverse domains, including medicine, health and behavioral sciences, biology, transportation, and energy systems.

Basic concepts in network analysis

Network analysis examines the structural and functional properties of networks, which are typically modeled as graphs consisting of vertices and edges (Newman, 2010; Easley & Kleinberg, 2010). These graphs vary in complexity, featuring directed or undirected edges and weighted or unweighted links, depending on the nature of the relationships (Watts, 2004a). Directed edges represent asymmetric relationships, such as one-way communication or influence, while undirected edges indicate mutual interactions. Weighted edges reflect the strength or importance of connections, whereas unweighted edges assume uniform relationships. Understanding these distinctions is essential for accurately modeling real-world networks and analyzing the roles of bridges across various graph types.

Key concepts in network analysis include: (i) degree, which represents the number of edges connected to a node, with high-degree nodes often functioning as hubs (Newman, 2010; Barabási & Albert, 1999); (ii) paths, sequences of edges that connect nodes, crucial for understanding network efficiency (Newman, 2010); (iii) connected components, groups of nodes that are mutually reachable from each other (Newman, 2010; Erdös & Rényi, 1959); and (iv) centrality measures, such as degree centrality and betweenness centrality, which quantify the importance of nodes within the network (Freeman, 1978; Borgatti & Everett, 2006; Bonacich, 1987).

Unsigned networks

Unsigned networks are characterized by edges that lack a sign, representing relationships without categorizing them as positive or negative. These networks are used when the nature of the relationship is neutral, unknown, or irrelevant to the analysis. Formally, an unsigned network is defined as $G=(V,E)$, where V denotes the set of vertices, and E represents the set of edges. The focus in unsigned networks is primarily on the structural properties rather than the polarity of relationships. Although unsigned networks have primarily been used to study structural properties, they have also served as frameworks for analyzing polarization phenomena (Morales et al., 2015; Garimella et al., 2018).

Unsigned networks are widely applied in fields such as social sciences, biology, and transportation, where connections are essential but do not inherently carry positive or negative attributes. Research in unsigned networks often focuses on understanding the overall structure of the network, detecting communities, predicting links, and analyzing the roles of specific links and nodes, such as bridges. These studies uncover patterns, optimize performance, and reveal hidden structures in complex systems.

Signed networks

Understanding the distinctions between signed and unsigned networks is essential for bridge analysis. Unlike unsigned networks, which indicate connections without additional context, signed networks explicitly represent positive or negative interactions between nodes. Positive interactions signify cooperative or friendly relationships, while negative interactions indicate conflict or antagonism. This distinction provides deeper insight into the structural and functional roles of bridges in networks (Brzozowski, Hogg & Szabo, 2008; Kunegis, Lommatzsch & Bauckhage, 2009; Lampe, Johnston & Resnick, 2007).

Formally, a signed network is defined as G = $(V,E^{+},E^{-})$, where V denotes the set of nodes, $E^{+}$ represents the set of positive edges indicating friendly relationships, and $E^{-}$ represents the set of negative edges indicating antagonistic relationships. Positive edges in $E^{+}$ are assigned values greater than 0. Negative edges in $E^{-}$ are assigned values less than 0.

Modeling both positive and negative interactions offers a comprehensive framework for understanding real-world social networks. Signed networks capture broader social dynamics than unsigned networks by incorporating both cooperative and adversarial relationships. Positive ties reflect trust or alliances, whereas negative ties highlight conflict or rivalry. This dual nature of relationships introduces complexities for algorithms originally designed for unsigned networks, which often struggle with negative links (Girdhar & Bharadwaj, 2017; Kim et al., 2023). Consequently, specialized approaches are required for tasks such as community detection, link prediction, and influence modeling in signed networks to effectively account for both cooperative and adversarial interactions (Yang et al., 2012; Wang et al., 2017).

Global and local bridges

This section categorizes bridges based on the structural impact of each type: (i) global bridges and (ii) local bridges. A global bridge is an edge whose removal results in the disconnection of the networks into separate components (Huang et al., 2019a). As shown in Fig. 1A, the blue edge between $u_1$ and $u_2$ represents a global bridge. Its removal divides the network into two disconnected components. Jensen et al. (2016) used global bridges to identify critical nodes, such as airports, within air transportation networks. Additionally, global bridges have been used to identify interdisciplinary nodes in scientometric networks, highlighting their role in facilitating connectivity across diverse domains.

In contrast, a local bridge is an edge whose removal increases the shortest path distance between its endpoints to a value greater than 2, without disconnecting the network (Granovetter, 1973). For example, in Fig. 1B, the red edges $\{u_4,u_5\}$ and $\{u_2,u_9\}$ are local bridges. Removing these edges increases the distance between their endpoints, but does not split the network into separate components. Papadopoulos et al. (2009) demonstrated the utility of local bridges in community detection, where they are used to identify boundaries between groups within networks. Methods utilizing local bridging values have been applied to delineate community structures in real-world networks, such as user-generated platforms. For simplicity, this article collectively refers to global and local bridges as bridges.

Importance of bridges

Bridges (Bondy & Murty, 2008; Burt, Kilduff & Tasselli, 2013; Burt & Soda, 2021) are critical for understanding the structure and functionality of the network, particularly for analyzing the robustness and resilience of networks. Bridge nodes (or articulation points) are nodes whose removal increases the number of connected components, often linking different subgroups and ensuring network cohesion.

Bridge nodes play a pivotal role in extending the reach of 2-hop connections, particularly when compared to non-bridge nodes. As shown in Fig. 2A, information originating from a non-bridge node remains confined to a single community. In contrast, Fig. 2B illustrates how a bridge node facilitates connections between multiple communities, with blue lines representing bridges. This illustrates the importance of bridge nodes in expanding connectivity and linking disparate parts of the network. Zhang & Li (2017) further underscore the importance of bridge nodes in enabling the diffusion of information and rumors between communities, highlighting their role as critical pathways in social networks.

Structural bridges

Graph representation and partitioning focus on the role of structural bridges in preserving network connectivity and identifying community structures. Structural bridges are crucial to maintaining the overall structure of the network by preserving connections between subcomponents.

Graph partitioning

Graph partitioning, or community detection, involves dividing a graph into smaller subgroups or communities. A common approach is edge-cutting, where edges are removed to reduce connectivity and separate the network. Edge selection is typically based on measures such as centrality or the role of edges in connecting communities. The removal of selected edges highlights the structure of the network by separating densely connected regions. Bridges, which connect distinct communities, are often targeted to identify community boundaries, which makes them essential for community detection. For example, Fig. 3 illustrates the graph partitioning process, with a focus on bridges between different communities. The bridges, highlighted in orange, play a key role in linking the communities, while the blue lines represent weaker connections facilitated by these bridges. The figure demonstrates how bridges contribute to maintaining connectivity between communities.

In unsigned networks, Papadopoulos et al. (2009) introduced the Bridge Bounding method, a localized approach for efficient community discovery. In this approach, bridges are defined as nodes that link densely connected subgroups. The Bridge Bounding algorithm identifies bridges by analyzing local connectivity and structure. It calculates edge betweenness centrality, which measures the number of shortest paths passing through a given edge. Nodes connected by edges with high betweenness are identified as potential bridges. These bridges define the boundaries of communities, reflecting the underlying topology of the network.

Hu & Dong (2019) proposed a cross-social-network interconnection model based on bridge communities. The model focuses on the role of bridges in connecting different social networks. It ranks nodes using centrality measures such as degree, betweenness, and closeness centrality. High-ranking nodes are matched across networks using similarity measures based on user attributes, such as username, gender, and location. Nodes with high similarity form bridge communities that act as bridges between networks. The model strengthens the connections between these nodes to improve interconnectivity. This process facilitates the dissemination of information and maintains network connectivity. The framework employs clustering algorithms that account for the enhanced connectivity provided by bridges. The resulting clusters reflect the true interconnectivity of the networks. Although the primary objective of this approach is to enhance interconnectivity across social networks, the clustering component of the framework also contributes to graph partitioning by identifying community structures reinforced through bridge-based connections.

Hwang et al. (2008) introduced bridging centrality, a novel metric designed to identify nodes and edges that serve as critical bridges between network communities. Bridging centrality combines betweenness centrality with a bridging coefficient, which measures the likelihood of connecting distinct network modules. This combination captures both local and global properties, highlighting key elements that maintain network cohesion and facilitate information flow. The article also presents a graph clustering algorithm that leverages the bridge centrality to define community boundaries. By iteratively removing edges with the highest bridging centrality scores, the algorithm identifies clusters with higher modularity and effectively distinguishes cohesive substructures within the network.

Gao, Musial & Gabrys (2017) proposed a Community Bridge Boosting Prediction Model (CBBPM), which improves link prediction by using community bridges. The model categorizes the nodes as within-community or cross-community, depending on whether they connect different communities. The core idea is to boost the similarity scores of the bridges, defined as nodes connecting different communities. Bridges are identified based on their degree and the proportion of connections to different communities. Nodes with low degrees or those most closely connected to a single community are excluded. Boosting the similarity scores of the selected bridges improves their importance in the prediction model, resulting in improved link prediction accuracy across various social networks. Figure 4 illustrates the crucial role of bridges in the CBBPM model. The red nodes represent bridges that facilitate connections between communities, while the blue lines show the predicted potential links between these communities, demonstrating how bridges enhance link prediction.

In signed networks, Ehsani & Mansouri (2023) introduced the BridgeCut algorithm to partition signed networks into balanced subgraphs. The algorithm ensures a fair and efficient partitioning process. BridgeCut, inspired by the Girvan-Newman (Blondel et al., 2008) community detection method, focuses on negative edges that act as bridges. It calculates edge betweenness centrality to identify negative edges functioning as bridges. These edges are iteratively added to the bridge set to improve the network’s balance index. The process divides the network into two near-balanced partitions, with the remaining nodes assigned based on their connections. BridgeCut was evaluated on multiple datasets, achieving balanced partitions with high internal stability and a low proportion of negative edges.

Functional bridges

Information propagation examines how functional bridges support the flow of information between communities. These bridges improve communication and resource distribution between disconnected regions, ensuring efficient interaction across communities. Table 4 summarizes key studies in these research areas, categorizing them by bridge types (structural or functional) and highlighting their main focus of research.

Medical networks

Bridge symptoms function as critical bridges in psychological networks, facilitating the co-occurrence and interaction of mental disorders by linking distinct clusters of symptoms. These functional bridges maintain connectivity within disorder clusters, enabling interactions that perpetuate comorbid conditions. Groen et al. (2020) explored the comorbidity between depression and anxiety using a dynamic psychological network perspective. The study identified bridge mental states, such as “worrying” and “feeling irritated,” which act as critical links connecting distinct symptom clusters. These bridge symptoms facilitate the persistence of comorbidity and exacerbate both conditions over time, highlighting their potential as targets for therapeutic interventions.

Jones, Ma & McNally (2021) introduced the concept of bridge centrality to quantify the importance of symptoms that connect different mental disorders within symptom networks. Four network metrics—bridge strength, bridge betweenness, bridge closeness, and bridge expected influence—were developed to measure these bridges. Applying these metrics to 18 group-level comorbidity networks demonstrated how bridge symptoms can drive the progression from one disorder to another. Together, these studies underscore the value of identifying bridge symptoms to inform intervention strategies and improve mental health outcomes.

Health and behavioral sciences

Recent studies have used network analysis to identify bridge symptoms and traits that connect diverse psychological and behavioral conditions. Zhao et al. (2023) modeled relationships between internet addiction (IA) and depression, identifying bridge symptoms such as “guilty” and “escape” that link symptom clusters across both conditions. Qu et al. (2024) applied cross-lagged panel network analysis to examine associations between short video addiction and depressive symptoms, highlighting “conflict” and “sad mood” as key bridges connecting these domains.

Blasco-Belled (2023) analyzed the interplay between character strengths and mental health indicators, identifying traits like “love”, “hope”, and “gratitude” as bridge nodes connecting positive and negative aspects of mental health. Jurado-González et al. (2024) investigated comorbidity among anxiety, depression, and somatic symptoms, showing how bridge symptoms such as “low energy” and “sad mood” sustain co-occurring conditions. These insights emphasize that targeting bridge symptoms and traits can disrupt maladaptive interactions and support more effective interventions.

Biological networks

In unsigned networks, Cheng, Huang & Sun (2008) defined bridge motifs as weak links connecting distinct modules in biological systems. Their detection method uncovers global statistical properties and local connection structures that are functionally significant. Applied to gene regulation networks, bridge motifs were shown to highlight topological patterns distinguishing species.

Panni & Rombo (2015) proposed strategies for identifying disease modules composed of interconnected genes or proteins linked to specific diseases. These disease modules act as functional bridges between different disease pathways, aiding the understanding of comorbidities and revealing therapeutic targets. For example, bridges linking drug-target modules to disease clusters can inform repositioning efforts by identifying shared molecular mechanisms underlying multiple conditions. Together, these studies illustrate how bridge structures can uncover complex relationships among biological entities.

Transportation networks

In transportation networks, bridges play a critical role in maintaining connectivity and mitigating cascading failures. Xiao, Huang & Tang (2023) proposed a quantitative framework to assess the importance and correlation of urban bridges and roads for evaluating road network vulnerability. The study introduced measurement indicators such as node degree, proximity centrality, intermediary centrality, and interrupt centrality to capture the structural significance of bridges. By modeling road networks using dual representations and applying grey correlation analysis, the authors demonstrated that bridge nodes often exhibit the highest correlation with overall network performance, underscoring their pivotal role in sustaining system resilience.

Qiang, Wancheng & Xinzhi (2021) focused on seismic vulnerability and retrofit prioritization of bridge networks under budget constraints. They developed multiple bridge importance ranking methods combining topological and fragility considerations and formulated the selection of retrofit strategies as a 0–1 knapsack optimization problem. Simulation results revealed that retrofitting strategies prioritizing both network topology and structural fragility achieved superior improvements in post-seismic reliability compared to methods relying solely on individual criteria. These findings highlight that the strategic reinforcement of critical bridges is essential for enhancing the resilience and reliability of transportation networks in seismic regions.

Energy networks and power systems

In energy networks, bridges play an essential role in improving stability and preventing cascading failures. Lan & Zocca (2021) proposed a bridge-block decomposition refinement framework that partitions power grids into smaller sub-networks by selectively switching off transmission lines. This process increases the number of bridge-blocks, which act as barriers to failure propagation, thereby improving robustness against cascading line failures. The authors introduced a novel Mixed-Integer Linear Programming (MILP)-based optimization approach using DC power flow models, as well as an efficient AC recursive tree partitioning method, demonstrating that these strategies can significantly enhance failure localization while minimizing line congestion.

Ódor et al. (2024) analyzed European high-voltage power grids using large-scale Kuramoto swing equation simulations to study how adding or removing bridges affects network synchronization and cascade dynamics. Their results show that well-placed bridges improve synchronization and reduce cascade sizes near the synchronization transition region, where self-organization drives power grid behavior. Conversely, bridge removals or poorly placed additions can exacerbate failures due to Braess’s paradox. The study emphasizes that bridge placement must consider both topological and dynamical factors to achieve optimal resilience and prevent large-scale blackouts.

Unsigned networks

In unsigned networks, which lack edge signs but may still include edge weights, local bridges are defined as edges whose removal increases the shortest path between two nodes by at least two (Granovetter, 1973). However, this definition implicitly assumes unweighted graphs, treating all connections as equally important regardless of their strength. In practice, bridges causing larger increases in effective distance or occupying more central structural positions can contribute more significantly to network connectivity and information flow. This oversimplification reduces the ability to effectively evaluate the diverse roles of bridges that strengthen community cohesion and facilitate information propagation.

This issue is not limited to local bridges but applies to broader bridge definitions. Equal treatment of all bridges overlooks differences in their contributions to network functionality, which depend on factors such as network position and the relative significance of the connections. Incorporating metrics that reflect these varying contributions could improve the assessment of community cohesion, information dissemination, and network resilience (Opsahl, Agneessens & Skvoretz, 2010).

Beyond the foundational definition by Granovetter (1973), recent studies have extended the analysis of network connectivity and robustness by incorporating weighted metrics and meso-scale structures. Opsahl, Agneessens & Skvoretz (2010) introduced measures accounting for both edge weights and connectivity patterns, while Rombach et al. (2017) proposed a framework for detecting core-periphery structures, which can reveal cohesive cores critical for maintaining overall connectivity. However, despite these advances, there remains a need to integrate bridge-centric and core-periphery perspectives to develop unified metrics that can better quantify the role of critical connections in supporting resilience, information diffusion, and structural cohesion in complex networks.

Building upon applications described in prior sections (Xiao, Huang & Tang, 2023; Qiang, Wancheng & Xinzhi, 2021), recent studies have demonstrated the importance of identifying critical bridges to improve resilience in transportation networks. However, most existing approaches remain static and do not consider temporal fluctuations in traffic loads or network topology. Future research could develop predictive models that integrate structural indicators with real-time flow data to dynamically assess bridge vulnerability and support proactive intervention strategies under disruptions.

Signed networks

Signed networks reflect dual relationships with positive and negative edges (Tang et al., 2016; Leskovec, Huttenlocher & Kleinberg, 2010; Yang et al., 2012). Structural bridges in signed networks influence inter-community dynamics by facilitating cooperation through positive connections or highlighting conflicts through negative connections. These characteristics distinguish signed networks from unsigned networks and highlight the need to reconsider how key structural elements are defined (Yang, Cheung & Liu, 2007; Derr, Ma & Tang, 2018).

The definition of bridges in unsigned networks, which focuses solely on maintaining connectivity, cannot be directly applied to signed networks due to the duality of positive and negative edges. Algorithms designed for unsigned networks do not capture the unique complexities of signed relationships (Kunegis et al., 2010). The duality of edges complicates the identification of structural elements, such as bridges. Table 3 illustrates the absence of a widely accepted definition of bridges in signed networks. Balance Theory (Heider, 1946) and Status Theory (Leskovec, Huttenlocher & Kleinberg, 2010) offer foundations for analyzing signed relationships but lack integration into bridge definitions.

Recent advances have proposed signed graph neural networks and embedding methods (Derr, Ma & Tang, 2018; Huang et al., 2019b; Liu, 2022; Zhou & Yan, 2025), which aim to capture the dual nature of positive and negative relationships. However, these approaches primarily focus on node classification and link prediction, with limited attention to the identification and characterization of structural bridges. Developing a comprehensive framework that integrates sign-aware embedding with structural metrics could improve the quantification of bridge importance and enable tracking of their temporal evolution. This refined perspective may support practical applications such as polarization mitigation, conflict prediction, and resilience assessment in online social platforms.

General considerations for bridge analysis

In addition to the specific challenges in unsigned and signed networks, several general considerations apply to both types of networks. Bridges in directed networks require an analysis of edge directionality, as their removal may impact flows in one direction while preserving the opposite flow (Malliaros & Vazirgiannis, 2013). In weighted networks, the importance of bridges depends on edge weights, where high-weight bridges often play more significant roles in information diffusion (Opsahl, Agneessens & Skvoretz, 2010; Riascos & Mateos, 2021). Bridge detection in large-scale networks requires algorithms that remain computationally efficient while processing large datasets (Perozzi, Al-Rfou & Skiena, 2014; Harenberg et al., 2014; Tang et al., 2015). Furthermore, time-varying networks introduce additional complexity, which requires adaptive algorithms that can efficiently handle real-time updates at nodes and edges (Xue et al., 2022; Rossetti & Cazabet, 2018).

Recent advances in dynamic graph learning (Pareja et al., 2020; Chen et al., 2024) have introduced frameworks capable of modeling evolving topologies and time-dependent interactions, which could be adapted to improve bridge detection in temporal networks. Future research may explore the integration of dynamic embedding techniques with bridge importance metrics to support applications such as early warning systems in infrastructure networks and adaptive content moderation in online platforms.