{
  "analytic": "graph-smoothing",
  "kind": "declared_analytical_or_constructed_example",
  "experimental_model_result": false,
  "panels": [
    {
      "kind": "line",
      "x": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30
      ],
      "series": [
        {
          "label": "Population variance",
          "y": [
            0.3333333333333333,
            0.12037037037037036,
            0.08770576131687241,
            0.06707961819844536,
            0.05284799223949601,
            0.041587619718722296,
            0.03279653297713393,
            0.025857510981478024,
            0.020390358505460143,
            0.016078655488912404,
            0.012678903794115438,
            0.009997978345941448,
            0.007883940406713082,
            0.0062169062057960125,
            0.004902361798447947,
            0.003865773344497866,
            0.0030483681884103803,
            0.0024038006754116266,
            0.0018955248636572778,
            0.0014947223137558418,
            0.001178668155908624,
            0.0009294426188157902,
            0.0007329150086489239,
            0.0005779425206315636,
            0.0004557384597296121,
            0.0003593740489100423,
            0.00028338557844478847,
            0.00022346462220644851,
            0.00017621375671945274,
            0.00013895393262068807,
            0.0001095725767965723
          ]
        }
      ],
      "xlabel": "Repeated averaging steps",
      "ylabel": "Variance in constructed signal",
      "logx": false,
      "logy": false
    }
  ],
  "title": "A fixed path-graph averaging operator smooths this signal",
  "assumptions": "Six-node undirected path, self-loops, row normalization, initial signal[1,0,0,0,0,-1]. Not a trained GCN or universal theorem.",
  "worked": "初始总体方差为0.333333，10次该算子传播后约0.012679。非线性、残差和训练权重会改变行为，不能由此推断实际分类质量。",
  "source_ids": [
    "arxiv-1609.02907",
    "arxiv-1810.00826",
    "arxiv-1706.02216"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "图与特征来源",
    "可见边及划分边界",
    "邻域采样与归一化",
    "共享聚合 / 消息传播",
    "可辨性与信息瓶颈",
    "独立图或时间泛化"
  ]
}