<p class="MsoNormal" style="margin: 0mm; text-align: justify; font-size: 10.5pt; font-family: 游明朝, serif;"><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;">The formation and evolution of multiple stars is expected to be partly determined by the fragmentation of parent dense molecular clumps. The formation process of binary and multiple stars remains to be elucidated, particularly for high-mass stars. The hierarchical fragmentation is likely to contribute to the structure formation in molecular clouds and the formation of binary and multiple stars. Toward a full understanding of how binary and multiple stars form in high-mass star formation environment, we analyze the internal structure of high-mass star-forming molecular clumps such as spatial distribution of dense cores. We use ALMA 1.3mm dust continuum data of 30 massive star-forming clumps. The target clumps have masses greater than M </span><span lang="EN-US" style="font-size: 11pt; font-family: "Cambria Math", serif;">?</span><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;"> 100M</span><span lang="EN-US" style="font-size: 11pt; font-family: "Cambria Math", serif;">?</span><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;"> at distances of D </span><span lang="EN-US" style="font-size: 11pt; font-family: "Cambria Math", serif;">?</span><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;"> 1?5 kpc.<o:p></o:p></span></p><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;">In total, we identified 579 cores by dendrogram. Then, we applied the minimum spanning tree (MST) to quantitatively obtain the separations of cores. We found that the distribution of core separation has a peak around 6000 au after correcting the 3D projecting effect. We searched several observational biases such as spatial resolution, mass sensitivity, and mass completeness. Then, we obtained the result that the separation distribution still had a peak around 6000 au. On the other hand, we derived mass completeness limit of 3M</span><span lang="EN-US" style="font-size: 11pt; font-family: "Cambria Math", serif;">?</span><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;">, corresponding to 80% detection rate, and obtained the separation distribution whose identified core mass was restricted to be heavier than 3M</span><span lang="EN-US" style="font-size: 11pt; font-family: "Cambria Math", serif;">?</span><span lang="EN-US" style="font-size: 11pt; font-family: Century, serif;">. The peak was located around 7000 au. We found these separation distributions were well consistent with thermal Jeans length of each clump.</span>