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Area of Science:

  • Network Science
  • Social Psychology
  • Graph Theory

Background:

  • Traditional balance theory focuses on undirected networks and triadic motifs.
  • Frustration in signed networks is less understood, especially for directed connections.
  • Reciprocity in signed networks, particularly directed ones, remains poorly understood.

Purpose of the Study:

  • To explore the concept of frustration in signed, directed networks.
  • To develop a principled approach for studying reciprocity in these networks.
  • To test the applicability of balance theory to directed, signed networks.

Main Methods:

  • Extended the exponential random graph framework to binary, directed, signed networks.
  • Incorporated global and local constraints into network models.
  • Quantified and compared empirical patterns of mutualistic and antagonistic cycles of length 2.

Main Results:

  • Existing balance theory, even when extended, fails to consistently explain patterns in directed, signed networks.
  • A coarser definition of balance partially resolves ambiguities but is insufficient.
  • Empirical signed networks exhibit high reciprocity, indicating the importance of bidirectional dyads.

Conclusions:

  • A new theoretical framework is required to account for edge directionality in signed networks.
  • Bidirectional dyads play a crucial role in determining frustration at higher network levels.
  • Future research should focus on developing theories that integrate directionality and reciprocity.