Validating network growth models via the confusion matrix.

Column headings show the model and parameters used to grow the random graph forward. Row labels show the model used in the reversal (assuming optimal parameters). For the node degree reconstruction ( row), we removed nodes in increasing order of their degree in the extant network (nodes with the same degree were ordered randomly). For the centrality reconstruction ( row), we removed nodes in decreasing order of their closeness centrality in the extant network. Each cell contains Anchor/Footrule scores (PA, node degree, and centrality do not generate Anchor scores). Performance was averaged over 1000 runs. Bolded cells indicate best performance. For example, for DMC random graphs with , reversing with FF produces a 33.1% Footrule score compared to a 45.5% score when the graph is reversed with DMC itself. The non-model-based heuristics produce good age-estimates when applied to models where degree is known to be correlated with age (FF and PA) as is expected; however, the downside to these approaches is that they do not produce a likelihood estimate for ancestral graphs, nor do they predict node anchors. For identifying anchors and for DMC age estimates, reversing with the model used to grow the graph forward resulted in the best performance.列标题标注了用于正向生成随机图（Random Graph）的模型与参数设置。行标签则标注了逆向重建过程中使用的模型（假设采用最优参数配置）。针对节点度重建任务，我们按照现存网络中节点度（Node Degree）的升序移除节点（度值相同的节点将按随机顺序排列）；针对中心性重建任务，则按照现存网络中节点接近中心性（Closeness Centrality）的降序移除节点。每个单元格包含Anchor得分（Anchor Score）与Footrule得分（Footrule Score）（优先连接（Preferential Attachment，PA）、节点度与中心性方法均无法生成Anchor得分）。实验性能取1000次独立运行的平均值。加粗单元格代表该指标下的最优性能。例如，针对某参数下的DMC随机图，使用FF进行逆向重建可得到33.1%的Footrule得分，而使用DMC自身进行逆向重建时的得分则为45.5%。非基于模型的启发式方法在应用于节点度与年龄已知存在相关性的模型（如FF与PA）时，可得到较好的年龄估计结果，这与预期相符；但这类方法的缺陷在于，既无法为祖先图生成似然估计，也无法预测节点锚点。在锚点识别与DMC年龄估计任务中，使用与正向生成图所用模型一致的方法进行逆向重建，可取得最优性能。