The emergence of an animal’s personality is the result of interactions between genetics, environment and experience. It is known that individuals are able to modulate their behaviour according to the context or the social environment. Many studies have shown for example, that familiarity among conspecifics diminishes aggressiveness, although little is known about the underlying processes. Nevertheless, personality traits have long been determined while ignoring the social context, especially in lower vertebrates such as fish. In the present experiment, we hypothesize that group connections (network density) may be positively correlated to consistency of aggressiveness by avoiding over-aggressive acts in further encounters. To test this hypothesis, we used eels (Anguilla anguilla) as a model species and monitored both aggressiveness and sociability in 64 individuals over their first 7 months of growth from the glass eel stage. As expected, social fish were less aggressive than their non-social counterparts at all times, highlighting the existence of a behavioural syndrome in eels. Additionally, rank-order consistency of aggressiveness was higher in groups of fish with high social connectivity, compared to those in less-connected fish groups. While aggressiveness must be consistent to be considered a personality trait, our results suggest that both aggressiveness and its consistency are influenced by initial social context