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Core periphery structures exist naturally in many complex networks in the realworld like social,
economic, biological and metabolic networks. Most of the existing research efforts focus on the
identification of a meso scale structure called community structure. Core periphery structures are another
equally important meso scale property in a graph that can help to gain deeper insights about the
relationships between different nodes. In this paper, we provide a definition of core periphery structures
suitable for weighted graphs. We further score and categorize these relationships into different types based
upon the density difference between the core and periphery nodes. Next, we propose an algorithm called
CPMKNN (Core PeripheryMutual K Nearest Neighbors) to extract core periphery structures from
weighted graphs using a heuristic node affinity measure called Mutual Knearest neighbors (MKNN).
Using synthetic and realworld social and biological networks, we illustrate the effectiveness of developed
core periphery structures.
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