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Emergence and evolution of social networks through exploration of the Adjacent Possible space

Social Work

Emergence and evolution of social networks through exploration of the Adjacent Possible space

E. Ubaldi, R. Burioni, et al.

Discover a groundbreaking microscopic model for social network growth by Enrico Ubaldi, Raffaella Burioni, Vittorio Loreto, and Francesca Tria! This research vividly illustrates the dynamics of acquiring acquaintances and interactions, validating its findings against real-world networks like Twitter and co-authorship in APS.

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Playback language: English
Introduction
Human interaction forms the foundation of societies, and the structure of these interactions—social networks—offers valuable insights into social organization and evolution. Understanding how individuals form new connections and distribute their social interactions is crucial for comprehending social dynamics. Previous research has highlighted the heterogeneous propensity of individuals to engage in social interactions, leading to heavy-tailed distributions of activity and degrees. Individuals tend to interact with similar others (triadic closure) but also seek novel connections (focal closure) based on shared interests or experiences. Social networks are dynamic, with links continuously created and destroyed, significantly affecting their topological properties and the processes unfolding within them. Existing models often suffer from limitations. Many are solely growth models, neglecting network dynamics. Others require pre-defined heterogeneous distributions to reproduce real-world heterogeneity, failing to capture the underlying mechanisms. This study aims to address these shortcomings by applying the concept of the Adjacent Possible space.
Literature Review
Prior research on social network evolution has explored various mechanisms. Models focusing on growth often simulate the addition of nodes and edges based on copying neighbors (copying models), rewiring existing connections (rewiring models), or preferential attachment based on topological, information-based, or hierarchical factors. These models predominantly deal with binary networks, lacking weighted edges to represent interaction strength. Existing dynamic models, which account for repeated interactions, often require data-driven heterogeneous distributions to match real-world heterogeneity in node fitness or interaction propensity. Other models concentrate on specific aspects, like activation patterns or partner selection strategies, but lack a comprehensive account of network evolution. The Adjacent Possible framework, initially used in biology and later adapted to model innovation processes, provides a promising approach for this research. This framework posits that the space of possibilities an agent explores is partitioned into the actual (already explored), the adjacent possible (one step away), and the non-adjacent possible (potentially accessible in the future). Recent mathematical formalizations of this framework allow for quantitative predictions on innovation dynamics, making it a suitable foundation for modeling social network dynamics.
Methodology
This research proposes a novel model based on the Adjacent Possible framework, using a minimal set of microscopic rules defined at the individual level. The model conceptualizes social network growth as an exploratory process, where individuals expand their potential contacts (their Adjacent Possible space) with each new connection. The core of the model is a multi-agent adaptation of a modified Pólya urn model. Each agent (urn) represents an individual, and balls within the urn represent connections to other agents. The dynamics involve drawing balls (selecting contacts), reinforcement (increasing the likelihood of repeated interactions by adding copies of the drawn ball), and novelty (expanding the Adjacent Possible space by adding new balls when a novel connection is made). Three key aspects of the model are (1) the multi-agent Pólya urn representation, (2) the mechanism for adjacent possible space expansion, and (3) the exploration strategy. The exploration strategy dictates how an agent selects new contacts (memory buffer) when a novel connection is formed. The study explores three strategies: Weighted Sample with Withdrawal (WSW), Symmetric Sliding Window (SSW), and Asymmetric Sliding Window (ASW). The model parameters are the reinforcement parameter (p), the number of novelties shared (v), and the chosen exploration strategy (s). The relative importance of reinforcement and exploration is determined by the ratio R = p/v. The model's predictions are tested against three real-world social networks: the American Physical Society (APS) co-authorship network, the Twitter mention network (TMN), and a mobile phone network (MPN). The model's parameters are optimized using a cost function that compares eight key observables (strengthening exponent, average degree growth exponent, edge growth exponent, clustering coefficient, and fractions of old/new open/closed links) between the model and the empirical data. A subsampling technique is applied to the APS data to address the presence of cliques, ensuring a fairer comparison with the model.
Key Findings
The model successfully reproduces numerous features of the three real-world social networks across different scales. It accurately captures the heavy-tailed distributions of activity and degree, the sub-linear growth of average degree, the functional form of the strengthening probability (the probability of forming a new connection given existing connections), and the temporal growth of the total number of edges (Heaps' law). The model also reproduces Taylor's law, showing a linear relationship between the mean and standard deviation of the number of links created by individuals, indicating complex, correlated dynamics. Furthermore, the model accurately predicts the distribution of link weights, demonstrating adherence to the Granovetter's weak and strong ties principle. The model captures the network's community structure (modularity) and core-periphery organization, accurately predicting community size distributions and the fraction of core nodes within communities. The temporal evolution of link formation (old/new open/closed links) is also correctly reproduced, with discrepancies in the APS dataset resolved after subsampling. The optimal parameter values provide insights into the interplay of exploration and reinforcement processes in the different networks. For the TMN, exploration and reinforcement are equally important, while in the MPN, reinforcement dominates, and in the APS, exploration prevails. The optimal exploration strategies show preference for most frequent contacts in TMN, recent contacts in MPN, and recent contacts symmetrically in APS (with asymmetry when considering subsampled data).
Discussion
The findings demonstrate that a simple model based on the Adjacent Possible framework and minimal microscopic rules can reproduce a wide range of complex features observed in real-world social networks. The model successfully captures both the static and dynamic properties of these networks, without relying on pre-defined heterogeneous distributions or specific rules for partner selection. The model provides insights into how the interplay of exploration and reinforcement shapes the evolution of social networks, with different networks exhibiting varying balance between these processes. This explains a variety of social network features which had previously been modelled independently. The exploration strategies reveal preferences for selecting new connections based on either the most frequent (TMN) or the most recent (MPN and APS) past interactions, reflecting the diverse nature of social interactions in each network. The model also shows a good qualitative agreement with more detailed, but less easily measurable metrics, like the temporal correlations in link formation.
Conclusion
This research provides a unified model for social network growth and dynamics, based on the principles of the Adjacent Possible space and minimal microscopic rules. The model successfully reproduces a wide range of structural and dynamic features in real-world social networks without making strong assumptions. Future work could extend the model to incorporate factors like semantics, homophily, and more sophisticated memory buffer exchange strategies. Testing the model's predictive power on forecasting future connections would also be a valuable extension. The model presented here establishes a strong link between network theory and urn models, suggesting promising avenues for future research in understanding social interactions and informing policies addressing collective phenomena in social networks.
Limitations
The model does not currently account for factors such as semantic similarity between individuals, homophily (a tendency to connect with similar individuals), or the influence of external factors on network formation. The model's accuracy in reproducing the distribution of the strengthening constant (c) shows some limitations, primarily due to the inherent constraints of the urn model, which limits the variability of c. The analysis was performed on a subset of the MPN dataset due to computational limitations. The subsampling performed for the APS dataset, while improving the fit, alters the original data structure. Finally, only a limited number of exploration strategies have been investigated.
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