  The detection of community structure is probably one of the hottest trends in
complex network research as it reveals the internal organization of people,
molecules or processes behind social, biological or computer networks\dots The
issue is to provide a network partition representative of this organization so
that each community presumably gathers nodes sharing a common mission, purpose
or property. Usually the identification is based on the difference between the
connectivity density of the interior and the boundary of a community. Indeed,
nodes sharing a common purpose or property are expected to interact closely.
Although this rule appears mostly relevant, some fundamental scientific
problems like disease module detection highlight the inability to determine
significantly the communities under this connectivity rule. The main reason is
that the connectivity density is not correlated to a shared property or
purpose. Therefore, another paradigm is required for properly formalize this
issue in order to meaningfully detect these communities. In this article we
study the community formation from this new principle. Considering colors
formally figures the shared properties, the issue is thus to maximize group of
nodes with the same color within communities.. We study this novel community
framework by introducing new measurement called \emph{chromarity} assessing the
quality of the community structure regarding this constraint. Next we propose
an algorithm solving the community structure detection based on this new
community formation paradigm.
