Abstract: The maximum clique problem (MCP) is a significant problem in computer science field because of its complexity, challenging and the extensive applications in data mining and other fields. This paper puts forward a new degree-based approach to finding the maximum clique in a given graph G. According to the characteristic that the degree of the vertexes in a maximum clique is relatively larger, the new approach solves the maximum clique by starting from the first vertex which degree is the largest in the graph G. In order to further improve the efficiency of the algorithm, this paper presents three improvement and pruning strategies based on the characteristics of the graph and the maximum clique. This paper proves that the new approach is correct and complete, the time complexity is[O(1.442n)], and the space cost is [O(n2)]. Finally, an empirical study verifies the effectiveness and efficiency of the new approach.

Key words: maximum clique problem (MCP), the degree of vertexes, NP complete problem

摘要： 由于最大团问题（maximum clique problem，MCP）的复杂性、挑战性，以及在数据挖掘等领域的广泛应用，使得求解MCP问题具有非常重要的意义。根据最大团顶点度数较大的特点，提出了从图中第一个度数最大的顶点出发递归求解最大团的算法（简称度数法）。为了进一步提高算法的效率，根据图的特点和最大团的特点提出了三个改进的剪枝策略。从理论上证明了算法的正确性和完整性，其时间复杂度为[O(1.442n)]，空间为[O(n2)]。通过实验验证了度数法及其改进剪枝策略的效果和效率。

关键词: 最大团问题（MCP）, 顶点度数, NP完全问题