Louvain算法
一種基于模塊度的圖算法模型，與普通的基于模塊度和模塊度增益不同的是，該算法速度很快，而且對一些點多邊少的圖，進行聚類效果特別明顯。
算法流程：
1、初始時將每個頂點當作一個社區，社區個數與頂點個數相同。
2、依次將每個頂點與之相鄰頂點合并在一起，計算它們的模塊度增益是否大于0，如果大于0，就將該結點放入該相鄰結點所在社區。
3、迭代第二步，直至算法穩定，即所有頂點所屬社區不再變化。
4、將各個社區所有節點壓縮成為一個結點，社區內點的權重轉化為新結點環的權重，社區間權重轉化為新結點邊的權重。
5、重復步驟1-3，直至算法穩定。

# coding=utf-8 import collections import randomdef load_graph(path):G = collections.defaultdict(dict)with open(path) as text:for line in text:vertices = line.strip().split()v_i = int(vertices[0])v_j = int(vertices[1])w = float(vertices[2])G[v_i][v_j] = wG[v_j][v_i] = wreturn Gclass Vertex():def __init__(self, vid, cid, nodes, k_in=0):self._vid = vidself._cid = cidself._nodes = nodesself._kin = k_in ?# 結點內部的邊的權重class Louvain():def __init__(self, G):self._G = Gself._m = 0 ?# 邊數量self._cid_vertices = {} ?# 需維護的關于社區的信息(社區編號,其中包含的結點編號的集合)self._vid_vertex = {} ?# 需維護的關于結點的信息(結點編號，相應的Vertex實例)for vid in self._G.keys():self._cid_vertices[vid] = set([vid])self._vid_vertex[vid] = Vertex(vid, vid, set([vid]))self._m += sum([1 for neighbor in self._G[vid].keys() if neighbor > vid])def first_stage(self):mod_inc = False ?# 用于判斷算法是否可終止visit_sequence = self._G.keys()random.shuffle(list(visit_sequence))while True:can_stop = True ?# 第一階段是否可終止for v_vid in visit_sequence:v_cid = self._vid_vertex[v_vid]._cidk_v = sum(self._G[v_vid].values()) + self._vid_vertex[v_vid]._kincid_Q = {}for w_vid in self._G[v_vid].keys():w_cid = self._vid_vertex[w_vid]._cidif w_cid in cid_Q:continueelse:tot = sum([sum(self._G[k].values()) + self._vid_vertex[k]._kin for k in self._cid_vertices[w_cid]])if w_cid == v_cid:tot -= k_vk_v_in = sum([v for k, v in self._G[v_vid].items() if k in self._cid_vertices[w_cid]])delta_Q = k_v_in - k_v * tot / self._m ?# 由于只需要知道delta_Q的正負，所以少乘了1/(2*self._m)cid_Q[w_cid] = delta_Qcid, max_delta_Q = sorted(cid_Q.items(), key=lambda item: item[1], reverse=True)[0]if max_delta_Q > 0.0 and cid != v_cid:self._vid_vertex[v_vid]._cid = cidself._cid_vertices[cid].add(v_vid)self._cid_vertices[v_cid].remove(v_vid)can_stop = Falsemod_inc = Trueif can_stop:breakreturn mod_incdef second_stage(self):cid_vertices = {}vid_vertex = {}for cid, vertices in self._cid_vertices.items():if len(vertices) == 0:continuenew_vertex = Vertex(cid, cid, set())for vid in vertices:new_vertex._nodes.update(self._vid_vertex[vid]._nodes)new_vertex._kin += self._vid_vertex[vid]._kinfor k, v in self._G[vid].items():if k in vertices:new_vertex._kin += v / 2.0cid_vertices[cid] = set([cid])vid_vertex[cid] = new_vertexG = collections.defaultdict(dict)for cid1, vertices1 in self._cid_vertices.items():if len(vertices1) == 0:continuefor cid2, vertices2 in self._cid_vertices.items():if cid2 <= cid1 or len(vertices2) == 0:continueedge_weight = 0.0for vid in vertices1:for k, v in self._G[vid].items():if k in vertices2:edge_weight += vif edge_weight != 0:G[cid1][cid2] = edge_weightG[cid2][cid1] = edge_weightself._cid_vertices = cid_verticesself._vid_vertex = vid_vertexself._G = Gdef get_communities(self):communities = []for vertices in self._cid_vertices.values():if len(vertices) != 0:c = set()for vid in vertices:c.update(self._vid_vertex[vid]._nodes)communities.append(c)return communitiesdef execute(self):iter_time = 1while True:iter_time += 1mod_inc = self.first_stage()if mod_inc:self.second_stage()else:breakreturn self.get_communities()if __name__ == '__main__':G = load_graph(r'C:\\Users\\程勇\\Desktop\\similarity.txt')algorithm = Louvain(G)communities = algorithm.execute()# 按照社區大小從大到小排序輸出communities = sorted(communities, key=lambda b: -len(b)) # 按社區大小排序count = 0for communitie in communities:count += 1print("社區", count, " ", communitie)

測試用例文件如圖：

這是部分測試用例的截圖，一行的前兩個數是頂點編號，第三個數是權重。按照每個社區大小順序從大到小打印：

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