<p>Community search is currently attracting a lot of attention. The problem of a community search in a node-attributed graph is to locate a meaningful community that satisfies certain query parameters. It has piqued the interest of both industry and academia. Most research on finding communities in graphs focuses on either the link weight or the node attributes. This can be inefficient when you need to find communities that are both weighted and share similar characteristics. To address this, this paper proposes two approaches: <i>Bottom-Up and Top-Down</i>. Both approaches use link weight and node attributes to identify the top-r-weighted and attributed k-core communities, where r denotes the number of top-ranked communities. The <i>Bottom-Up approach</i> utilizes the global search paradigm to find communities, while <i>Top-Down method</i> utilizes a local search to efficiently find the top-weighted and attributed communities. To achieve this efficient local search, the <i>Top-Down method</i> leverages two special indexes: <i>a simple index and a matrix-based index</i>. The study compared all methods with several real-world data sets and found that <i>Top-Down method</i> that leverages <i>matrix-based index</i> was the most effective and efficient.</p>