  Previous network models have imagined that connections change to promote
structural balance, or to reflect hierarchies. We propose a model where agents
adjust their connections to appear credible to an external observer. In
particular, we envision a signed, directed network where positive edges
represent endorsements or trust and negative edges represent accusations or
doubt, and consider both the strategies an external observer might use to
identify credible nodes and the strategies nodes might use to then appear
credible by changing their outgoing edges. First, we establish that an external
observer may be able to exactly identify a set of 'honest' nodes from an
adversarial set of 'cheater' nodes regardless of the 'cheater' nodes'
connections. However, while these results show that an external observer's task
is not hopeless, some of these theorems involve network structures that are
NP-hard to find. Instead, we suggest a simple heuristic that an external
observer might use to identify which nodes are not credible based upon their
involvement with particular implicating edge motifs. Building on these notions,
and analogously to some models of structural balance, we develop a discrete
time 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 these
dynamics provide a new way to understand group fracture when nodes are worried
about appearing consistent to an external observer.
