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Previous network models have imagined that connections change to promotestructural balance, or to reflect hierarchies. We propose a model where agentsadjust their connections to appear credible to an external observer. Inparticular, we envision a signed, directed network where positive edgesrepresent endorsements or trust and negative edges represent accusations ordoubt, and consider both the strategies an external observer might use toidentify credible nodes and the strategies nodes might use to then appearcredible by changing their outgoing edges. First, we establish that an externalobserver may be able to exactly identify a set of 'honest' nodes from anadversarial set of 'cheater' nodes regardless of the 'cheater' nodes'connections. However, while these results show that an external observer's taskis not hopeless, some of these theorems involve network structures that areNP-hard to find. Instead, we suggest a simple heuristic that an externalobserver might use to identify which nodes are not credible based upon theirinvolvement with particular implicating edge motifs. Building on these notions,and analogously to some models of structural balance, we develop a discretetime dynamical system where nodes engage in implication avoiding dynamics,where inconsistent arrangements of edges that cause a node to look 'suspicious'exert pressure for that node to change edges. We demonstrate that thesedynamics provide a new way to understand group fracture when nodes are worriedabout appearing consistent to an external observer.

Implication Avoiding Dynamics for Externally Observed Networks