diff --git a/webapp/path_navigator.html b/webapp/path_navigator.html
index efa25d5..20cd2d6 100644
--- a/webapp/path_navigator.html
+++ b/webapp/path_navigator.html
@@ -419,6 +419,33 @@
             return label;
         }
         
+        // Calculate edge opacity based on harmonic distance: normalized 0→0.5, 1→1
+        function calcEdgeOpacity(ratio) {
+            const parts = ratio.split('/');
+            if (parts.length === 2) {
+                const n = parseInt(parts[0]);
+                const d = parseInt(parts[1]);
+                const product = n * d;
+                if (product <= 1) return 1;  // handle 1/1 edge case
+                const rawOpacity = 1 / Math.log2(product);
+                return 0.5 + (rawOpacity / 2);  // normalize: 0→0.5, 1→1
+            }
+            return 1;
+        }
+        
+        // Calculate edge width: inverse of harmonic distance (2-5px range)
+        function calcEdgeWidth(ratio) {
+            const parts = ratio.split('/');
+            if (parts.length === 2) {
+                const n = parseInt(parts[0]);
+                const d = parseInt(parts[1]);
+                const product = n * d;
+                if (product <= 1) return 5;  // handle 1/1 edge case
+                return (1 / Math.log2(product) * 3) + 2;
+            }
+            return 3.5;
+        }
+        
         // Multiply two fractions and return as string
         function multiplyFractions(frac1, frac2) {
             const f1 = parseFraction(frac1);
@@ -659,15 +686,17 @@
                     {
                         selector: 'edge',
                         style: {
-                            'width': 2.5,
+                            'width': function(ele) { return calcEdgeWidth(ele.data('ratio')); },
                             'line-color': '#ffffff',
                             'curve-style': 'straight',
                             'target-arrow-shape': 'none',
+                            'line-opacity': function(ele) { return calcEdgeOpacity(ele.data('ratio')); },
                             'label': 'data(ratio)',
                             'font-size': '12px',
                             'color': '#ffffff',
                             'text-rotation': '0deg',
                             'text-margin-y': 0,
+                            'text-opacity': 1,
                             'text-background-color': '#000000',
                             'text-background-opacity': 0.8,
                             'text-background-padding': '2px',
@@ -681,6 +710,7 @@
                             'line-style': 'dashed',
                             'curve-style': 'straight',
                             'target-arrow-shape': 'none',
+                            'line-opacity': 1,
                             'label': '',
                         }
                     },