## 1 Introduction
The developed algorithm does not include a training phase, so computationally-efficient solutions could be reached to segment the region-of-interest [11]. [PERSON] _et al._ developed a new methodology, called data cloud geometry-tree, which derived from the empirical similarity measurements a hierarchy of clustering configurations that captures the geometric structure of the data, and had a built-in mechanism for self-correcting clustering membership to multi-scale clustering, which provided a better quantification of the multi-scale geometric structures of the data [12]. [PERSON] _et al._ created a parameter-free kernel spectral clustering model and exploited the structure of the projections in the eigenspace to automatically identify the number of clusters, which showed the efficiency for large-scale complex networks [13]. [PERSON] _et al._ introduced a self-tuning scaling parameter for the Gaussian kernel function, and on that basis, [PERSON] _et al._ introduced a parameter for the shared nearest neighbors self-tuning Gaussian kernel function and proposed an adaptive spectral clustering algorithm based on the shared nearest neighbors. This algorithm exploited the information about local density embedded in the shared nearest neighbors, thereby learning the implicit information of the cluster's structure and improving the algorithm's performance [14, 15]. Due to the non-homogeneous of the network topology, each node in the network is of different importance. The similarity of two vertices relates not only to the number of neighbors shared, but also closely to the importance of the shared neighbor vertices. In a graph, the importance of a vertex is related to the vertex's out-degree, in-degree and neighboring vertexes' importance. The greater the importance of the shared neighbors between two vertexes, the more possible it is that these two vertexes belong to the same cluster. [PERSON] _et al._ introduced hubs and authorities based on the idea of characterizing the most important vertices in a graph representing the connections between vertices [16]. From an implicit relation, an \"authority score\" and a \"hub score\" to each vertex of a given graph can be obtained as the limit of a converging iterative process, which can be used to represent the importance of the vertices [17]. In this paper, we propose the importance of a shared nearest neighbors-based similarity measure for constructing the similarity matrix, originating from the idea of \"authority score\" and \"hub score\". In this measure, we first find the importance of every vertex through the limitation of a converging iterative process and then look for the maximal importance in shared nearest neighbors between each of two vertices. The greater the maximal importance, the more similar the two vertices are. Therefore, we can get structure information between every two vertices and then utilize this information to self-tune the Gaussian kernel function. Finally, we get the similarity measure based on the importance of shared nearest neighbors. The rest of this paper is organized as follows. In Section 2, we give a brief outline of similarity graphs. In Section 3, we propose a new similarity measure and apply it to the construction of the similarity matrix. In Section 4, we present the experiment results for the proposed algorithm on some datasets, followed by the concluding remarks given in Section 5.