Calculating h index of a citation in JavaScript

The h-index is a metric used to measure both the productivity and citation impact of a researcher. In JavaScript, we can calculate it by analyzing an array of citation counts for a researcher's papers.

What is H-Index?

A researcher has h-index of value h if they have h papers with at least h citations each, and the remaining papers have no more than h citations each. For example, if a researcher has papers with citations [1, 6, 3, 0, 5], they have 3 papers with at least 3 citations (papers with 6, 3, and 5 citations), so the h-index is 3.

Algorithm Approach

We use a counting approach where we track how many papers have each citation count, then work backwards to find the maximum h-index value.

Implementation

const arr = [1, 6, 3, 0, 5];

const findHIndex = (arr = []) => {
    let possible = [];
    let { length: len } = arr;
    
    if (len === 0) {
        return 0;
    }
    
    // Initialize counting array
    possible.length = len + 2;
    possible = possible.join('-').split('').map(() => 0);
    
    // Count papers by citation count
    for (let i = 0; i < len; i++) {
        let val = arr[i];
        let ind = val > len ? len : val;
        possible[ind] += 1;
    }
    
    // Find h-index by working backwards
    let result = 0;
    for (let k = len; k >= 0; k--) {
        result += possible[k];
        if (result >= k) {
            return k;
        }
    }
};

console.log("Citations array:", arr);
console.log("H-index:", findHIndex(arr));

Citations array: [ 1, 6, 3, 0, 5 ]
H-index: 3

Alternative Simpler Approach

Here's a more intuitive solution using sorting:

const findHIndexSimple = (citations) => {
    // Sort in descending order
    citations.sort((a, b) => b - a);
    
    let hIndex = 0;
    for (let i = 0; i < citations.length; i++) {
        // Check if current paper and previous papers have enough citations
        if (citations[i] >= i + 1) {
            hIndex = i + 1;
        } else {
            break;
        }
    }
    
    return hIndex;
};

// Test with multiple examples
const testCases = [
    [1, 6, 3, 0, 5],
    [3, 0, 6, 1, 5],
    [100],
    [0, 0, 0, 0],
    [1, 1, 1]
];

testCases.forEach(citations => {
    console.log(`Citations: [${citations.join(', ')}] ? H-index: ${findHIndexSimple(citations)}`);
});

Citations: [1, 6, 3, 0, 5] ? H-index: 3
Citations: [3, 0, 6, 1, 5] ? H-index: 3
Citations: [100] ? H-index: 1
Citations: [0, 0, 0, 0] ? H-index: 0
Citations: [1, 1, 1] ? H-index: 1

How It Works

The sorting approach works by:

• Sorting citations in descending order
• For each position i, checking if the citation count is ? (i+1)
• The largest valid i+1 value becomes the h-index

Comparison

Conclusion

The h-index calculation involves finding the maximum number h where a researcher has h papers with at least h citations each. The sorting approach is more intuitive, while the counting approach offers better time complexity for large datasets.