Measuring social mobility in temporal networks

2025-02-04

AI Summary

Quantifying social mobility in temporal networks remains challenging due to the dynamic interplay between node-level and neighborhood-level positional evolution. Method: We propose “hierarchical mobility,” defined as the cross-temporal evolution and coupling of node and neighborhood centrality (proxied by degree), and develop a novel triadic statistical framework—comprising mobility, altruism, and community metrics—grounded in temporal modeling, dynamic correlation analysis, and synthetic network generation incorporating preferential attachment and reset mechanisms. We validate the framework across 26 real-world temporal networks. Contribution/Results: Our approach enables conditional identification of the reverse “rich-get-richer” effect—requiring degree inequality as a prerequisite—and establishes an interpretable, discriminative metric system for network structural dynamics. Empirical results reveal strong temporal stability in hierarchical positions, low correlation between individual and neighborhood mobility, and robust cross-domain discriminability of network architectures.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In complex networks, the rich-get-richer effect (nodes with high degree at one point in time gain more degree in their future) is commonly observed. In practice this is often studied on a static network snapshot, for example, a preferential attachment model assumed to explain the more highly connected nodes or a rich-club}effect that analyses the most highly connected nodes. In this paper, we consider temporal measures of how success (measured here as node degree) propagates across time. By analogy with social mobility (a measure people moving within a social hierarchy through their life) we define hierarchical mobility to measure how a node's propensity to gain degree changes over time. We introduce an associated taxonomy of temporal correlation statistics including mobility, philanthropy and community. Mobility measures the extent to which a node's degree gain in one time period predicts its degree gain in the next. Philanthropy and community measure similar properties related to node neighbourhood. We apply these statistics both to artificial models and to 26 real temporal networks. We find that most of our networks show a tendency for individual nodes and their neighbourhoods to remain in similar hierarchical positions over time, while most networks show low correlative effects between individuals and their neighbourhoods. Moreover, we show that the mobility taxonomy can discriminate between networks from different fields. We also generate artificial network models to gain intuition about the behaviour and expected range of the statistics. The artificial models show that the opposite of the"rich-get-richer"effect requires the existence of inequality of degree in a network. Overall, we show that measuring the hierarchical mobility of a temporal network is an invaluable resource for discovering its underlying structural dynamics.

Problem

• Measure social mobility in temporal networks.
• Analyze node degree propagation over time.
• Define hierarchical mobility for network dynamics.

Innovation

• Temporal network hierarchical mobility analysis
• Taxonomy of temporal correlation statistics
• Artificial network models validation