We study the effect of the choice of embedding geometry on the entropy of random geometric graph ensembles with soft connection functions. First we show that when the connection range is small, the entropy is dependent only on the dimension of the geometry and not the shape, but for large connection ranges the boundaries of the domain matter. Next, we formulate the problem of estimating entropy as a problem of estimating the average degree of a graph with the binary entropy function as its connection function. We use this formulation to study the effect of boundaries on the entropy, and to estimate the entropy of soft random geometric graphs in complicated geometries where a closed form pair distance density is not available.

翻译：我们研究了嵌入几何选择对具有软连接函数的随机几何图系综熵的影响。首先，我们证明当连接范围较小时，熵仅取决于几何的维度而不取决于其形状，但对于较大的连接范围，区域的边界则变得重要。接着，我们将估计熵的问题表述为估计以二元熵函数作为连接函数的图的平均度的问题。利用这一表述，我们研究了边界对熵的影响，并估计了在复杂几何中（其中闭合形式的点对距离密度不可用）软随机几何图的熵。