c语言实现模块度算法

模块度（Modularity）是衡量网络社区结构划分质量的一个指标，用于评估将网络划分成多个社区（或模块）的优劣。高模块度意味着网络内的边大多数集中在社区内部，而社区间的边相对较少。以下是使用C语言实现基本模块度计算的一个简化示例。

请注意，由于模块度算法通常涉及复杂的图结构和社区划分算法，这里仅展示模块度计算的核心概念，而不涉及特定的社区检测算法。

#include <stdio.h>
#include <stdlib.h>#define V 4 // 假设图中有4个顶点// 定义图的结构
typedef struct {int numVertices; // 顶点数int **adjMatrix; // 邻接矩阵
} Graph;// 创建图并初始化邻接矩阵
Graph* createGraph(int vertices) {Graph *graph = (Graph*)malloc(sizeof(Graph));graph->numVertices = vertices;graph->adjMatrix = (int**)malloc(vertices * sizeof(int*));for (int i = 0; i < vertices; i++) {graph->adjMatrix[i] = (int*)malloc(vertices * sizeof(int));for (int j = 0; j < vertices; j++) {graph->adjMatrix[i][j] = 0; // 初始化邻接矩阵为0}}return graph;
}// 添加边
void addEdge(Graph *graph, int src, int dest) {// 无向图graph->adjMatrix[src][dest] = 1;graph->adjMatrix[dest][src] = 1;
}// 计算模块度
double modularity(Graph *graph, int communities[], int numCommunities) {double Q = 0.0;int m = 0; // 边的总数int *degrees = (int*)calloc(graph->numVertices, sizeof(int)); // 每个顶点的度数// 计算总边数和每个顶点的度数for (int i = 0; i < graph->numVertices; i++) {for (int j = 0; j < graph->numVertices; j++) {m += graph->adjMatrix[i][j];degrees[i] += graph->adjMatrix[i][j];}}m /= 2; // 每条边被计算了两次// 计算模块度for (int i = 0; i < graph->numVertices; i++) {for (int j = 0; j < graph->numVertices; j++) {if (communities[i] == communities[j]) { // 如果i和j属于同一个社区Q += (graph->adjMatrix[i][j] - (degrees[i] * degrees[j]) / (2.0 * m));}}}Q = Q / (2.0 * m);free(degrees);return Q;
}int main() {Graph *graph = createGraph(V);addEdge(graph, 0, 1);addEdge(graph, 1, 2);addEdge(graph, 2, 3);addEdge(graph, 3, 0);// 假设社区划分，例如：顶点0和1在社区1，顶点2和3在社区2int communities[V] = {1, 1, 2, 2};double Q = modularity(graph, communities, 2);printf("Modularity: %f\n", Q);// 释放资源...return 0;
}