let nodes = {
    A: {
        bind: [
            ['B', 2],
            ['C', 10]
        ],
        weight: 0, // Вес самой ноды
        nearest: '', // Близжайшая нода
    },

    B: {
        bind: [
            ['A', 2],
            ['D', 20]
        ],
        weight: Infinity,
        nearest: ''
    },

    C: {
        bind: [
            ['A', 10],
            ['D', 2]
        ],
        weight: Infinity,
        nearest: ''
    },

    D: {
        bind: [
            ['B', 20],
            ['C', 2],
            ['E', 1]
        ],
        weight: Infinity,
        nearest: ''
    },

    E: {
        bind: [
            ['D', 1]
        ],
        weight: Infinity,
        nearest: ''
    }
}

let keys = Object.keys(nodes);

keys.forEach(index => {
    nodes[index].bind.forEach(bind => {
        let name = bind[0];
        let weight = bind[1];

        if(nodes[name].weight > nodes[index].weight + weight) {
            nodes[name].weight = nodes[index].weight + weight;
            nodes[name].nearest = index;
        }
    });
});

keys.forEach(key => console.log(`P: ${key}:${nodes[key].nearest} W: ${nodes[key].weight}`));