请用数学公式表示：Q = (m_in / G.size()) - ((m_boundary / (2 * G.size())) ** 2)

$$Q = \frac{m_{in}}{|G|} - \left(\frac{m_{boundary}}{2|G|}\right)^2$$

其中，$Q$ 表示模块度，$m_{in}$ 表示模块内部边的数量，$m_{boundary}$ 表示模块内部边与其他模块之间的边的数量，$|G|$ 表示网络的总边数。

相关问题

# 计算社团集合的结构模块度 Q = (m_in / G.size()) - ((m_boundary / (2 * G.size())) ** 2)

这段代码实现了计算社团集合的结构模块度。其中m_in表示社团内部边的权重之和，m_boundary表示社团与外部节点相连的边的权重之和，G.size()表示整个图中所有边的权重之和。结构模块度是用来衡量社团划分的好坏程度，数值越大表示社团划分得越好。

具体来说，第一项 (m_in / G.size()) 表示社团内部边权重占整个图边权重的比例，越大说明社团内部联系紧密；第二项 ((m_boundary / (2 * G.size())) ** 2) 表示社团与外部节点相连的边权重占整个图边权重的比例，越小说明社团与外部联系越少，即社团内部更加独立。两项相减即为结构模块度。

需要注意的是，这段代码中的m_in和m_boundary需要根据实际情况进行计算，也可能需要考虑边的方向性等因素。

下列代码出现nan int错误，请解决：float smoothCot() { float err = -1; cogs.clear(); v_end = mesh.vertices_end(); // for (v_it = mesh.vertices_begin(); v_it != v_end; ++v_it) { cog[0] = cog[1] = cog[2] = valence = 0.0; //cout << valence<<"1" << endl; for (vv_it = mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it) { double cot_weight = 0.0; MyMesh::HalfedgeHandle heh = mesh.find_halfedge(*v_it, *vv_it); if (!mesh.is_boundary(heh)) { MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh); MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh); MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh); MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh); MyMesh::Point prev_p = mesh.point(prev_vh); MyMesh::Point curr_pi = mesh.point(*v_it); MyMesh::Point curr_pj = mesh.point(*vv_it); MyMesh::Point next_p = mesh.point(next_vh); double cot_alpha = cot(curr_pi - prev_p, curr_pj - prev_p); double cot_beta = cot(curr_pi - next_p, curr_pj - next_p); cot_weight = cot_alpha + cot_beta; //cout << cot_weight<<"2" << endl; } cog += cot_weight *( mesh.point(*vv_it)-mesh.point(*v_it)); valence += cot_weight; //cout << valence<<"3" << endl; } cogs.push_back(cog / valence); } for (v_it = mesh.vertices_begin(), cog_it = cogs.begin(); v_it != v_end; ++v_it, ++cog_it) { if (!mesh.is_boundary(*v_it)) { MyMesh::Point p = mesh.point(*v_it); //*cog_it += mesh.point(*v_it); err = max(err, (p - *cog_it).norm()); mesh.set_point(*v_it, *cog_it); } } return err; }

在这段代码中，出现nan和inf通常是由于除以0或开根号时计算负数引起的。你可以在运行代码之前添加一些检查，比如检查cot_weight是否为0，以避免除以0的情况。另外，你还可以在计算cot_alpha和cot_beta之前，添加一个检查，确保两个点之间的距离不为0，以避免计算负数的情况。具体来说，你可以修改代码如下：

float smoothCot() {
    float err = -1;
    cogs.clear();
    v_end = mesh.vertices_end();

    for (v_it = mesh.vertices_begin(); v_it != v_end; ++v_it) {
        cog[0] = cog[1] = cog[2] = valence = 0.0;
        for (vv_it = mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it) {
            double cot_weight = 0.0;
            MyMesh::HalfedgeHandle heh = mesh.find_halfedge(*v_it, *vv_it);
            if (!mesh.is_boundary(heh)) {
                MyMesh::HalfedgeHandle prev_heh = mesh.prev_halfedge_handle(heh);
                MyMesh::HalfedgeHandle next_heh = mesh.next_halfedge_handle(heh);
                MyMesh::VertexHandle prev_vh = mesh.to_vertex_handle(prev_heh);
                MyMesh::VertexHandle next_vh = mesh.to_vertex_handle(next_heh);
                MyMesh::Point prev_p = mesh.point(prev_vh);
                MyMesh::Point curr_pi = mesh.point(*v_it);
                MyMesh::Point curr_pj = mesh.point(*vv_it);
                MyMesh::Point next_p = mesh.point(next_vh);

                double dist1 = (curr_pi - prev_p).norm();
                double dist2 = (curr_pj - prev_p).norm();
                double dist3 = (curr_pi - next_p).norm();
                double dist4 = (curr_pj - next_p).norm();

                if (dist1 > 0 && dist2 > 0 && dist3 > 0 && dist4 > 0) {
                    double cot_alpha = cot(curr_pi - prev_p, curr_pj - prev_p);
                    double cot_beta = cot(curr_pi - next_p, curr_pj - next_p);
                    cot_weight = cot_alpha + cot_beta;
                }
            }

            cog += cot_weight * (mesh.point(*vv_it) - mesh.point(*v_it));
            valence += cot_weight;
        }

        cogs.push_back(cog / valence);
    }

    for (v_it = mesh.vertices_begin(), cog_it = cogs.begin(); v_it != v_end; ++v_it, ++cog_it) {
        if (!mesh.is_boundary(*v_it)) {
            MyMesh::Point p = mesh.point(*v_it);
            err = max(err, (p - *cog_it).norm());
            mesh.set_point(*v_it, *cog_it);
        }
    }

    return err;
}