```ts
export function nameKinTie(links: Array<Record<string, unknown>>, one: string, other: string): string {
    if (!Array.isArray(links)) {
        throw new Error("Links must be an array");
    }

    const parentMap: Record<string, Set<string>> = {};
    const childMap: Record<string, Set<string>> = {};

    const validateName = (name: string) => {
        if (typeof name !== "string" || name.trim() === "") {
            throw new Error("Invalid name");
        }
    };

    links.forEach(link => {
        if (typeof link !== "object" || !link) {
            throw new Error("Link must be an object");
        }

        const child = link.child as string;
        const parent = link.parent as string;

        validateName(child);
        validateName(parent);

        if (child === parent) {
            throw new Error("A person cannot be their own parent");
        }

        if (!parentMap[child]) {
            parentMap[child] = new Set();
        }
        if (!childMap[parent]) {
            childMap[parent] = new Set();
        }

        if (parentMap[child].size >= 2) {
            throw new Error("A person cannot have more than two parents");
        }

        parentMap[child].add(parent);
        childMap[parent].add(child);
    });

    const detectCycle = (name: string, path: Set<string>): boolean => {
        if (path.has(name)) {
            return true;
        }
        path.add(name);

        const parents = parentMap[name];
        if (!parents) {
            return false;
        }

        for (const parent of parents) {
            if (detectCycle(parent, new Set(path))) {
                return true;
            }
        }

        return false;
    };

    for (const link of links) {
        const child = link.child as string;
        const parent = link.parent as string;

        if (detectCycle(child, new Set()) || detectCycle(parent, new Set())) {
            throw new Error("Links close a loop");
        }
    }

    if (!parentMap[one] || !parentMap[other]) {
        throw new Error("Either person is named nowhere in the links");
    }

    const findDistance = (start: string, target: string): number => {
        let queue = [start];
        let distance = 0;
        const visited = new Set<string>(queue);

        while (queue.length > 0) {
            if (visited.has(target)) {
                return distance;
            }

            const nextQueue: string[] = [];
            for (const name of queue) {
                const parents = parentMap[name];
                if (parents) {
                    for (const parent of parents) {
                        if (!visited.has(parent)) {
                            nextQueue.push(parent);
                            visited.add(parent);
                        }
                    }
                }
            }

            queue = nextQueue;
            distance++;
        }

        return -1; // No path found
    };

    const oneAncestors: Record<string, number> = {};
    const otherAncestors: Record<string, number> = {};

    const findAncestors = (name: string, ancestors: Record<string, number>, depth: number) => {
        if (ancestors[name] !== undefined) {
            return;
        }
        ancestors[name] = depth;

        const parents = parentMap[name];
        if (parents) {
            for (const parent of parents) {
                findAncestors(parent, ancestors, depth + 1);
            }
        }
    };

    findAncestors(one, oneAncestors, 0);
    findAncestors(other, otherAncestors, 0);

    let minU = Infinity;
    let minV = Infinity;
    let result: string = "unrelated";

    for (const [ancestor, u] of Object.entries(oneAncestors)) {
        if (otherAncestors[ancestor] !== undefined) {
            const v = otherAncestors[ancestor];

            if (u < minU || (u === minU && v < minV)) {
                minU = u;
                minV = v;

                if (u === 0 && v === 0) {
                    result = "self";
                } else if (v === 0) {
                    switch (u) {
                        case 1: result = "parent"; break;
                        case 2: result = "grandparent"; break;
                        default: result = `great-grandparent`.padStart(u + 8, 'g'); break;
                    }
                } else if (u === 0) {
                    switch (v) {
                        case 1: result = "child"; break;
                        case 2: result = "grandchild"; break;
                        default: result = `great-grandchild`.padStart(v + 8, 'g'); break;
                    }
                } else if (u === 1 && v >= 2) {
                    switch (v - u) {
                        case 1: result = "aunt-or-uncle"; break;
                        default: result = `great-aunt-or-uncle`.padStart(v + 8, 'g'); break;
                    }
                } else if (u >= 2 && v === 1) {
                    switch (u - v) {
                        case 1: result = "niece-or-nephew"; break;
                        default: result = `great-niece-or-nephew`.padStart(u + 8, 'g'); break;
                    }
                } else if (u >= 2 && v >= 2) {
                    const degree = Math.min(u, v) - 1;
                    const removal = Math.abs(u - v);
                    result = `${degree === 0 ? "" : degree + " "}cousin${removal === 0 ? "" : " " + removal + " times removed"}`;
                }
            }
        }
    }

    return result;
}
```