  Recently, the core-periphery (CP) structure of networks as one type of
meso-scale structure has received attention. The CP structure is composed of a
dense core and a sparse connected periphery. In this paper, we propose an
algorithm to detect the CP structure based on the 3-tuple motif, which is
inspired by the idea of motif. In this algorithm, we first define a 3-tuple
motif by considering the property of nodes, and then a motif adjacency matrix
is formed based on the defined motif, finally, the detection of the CP
structure is converted to find a cluster that minimizes the smallest motif
conductance. Our algorithm can detect different CP structures: including single
or multiple CP structure; and local or global CP structures. Results in the
synthetic and the empirical networks indicate that the method is efficient and
can apply to large-scale networks. More importantly, our algorithm is parameter
free, where the core and periphery are detected without the need for any
predefined parameters.
