A weighted network graph displays relationships between entities using edge thickness to represent connection strength or weight. Unlike basic network graphs where edges are uniform, the varying line widths immediately communicate the relative importance of each relationship. This visualization makes it easy to identify strong vs weak connections, central hubs with many heavy links, and structural patterns in weighted relational data.
""" anyplot.ai
network-weighted: Weighted Network Graph with Edge Thickness
Library: letsplot 4.9.0 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-17
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
LetsPlot.setup_html()
np.random.seed(42)
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
BRAND = "#009E73" # Okabe-Ito position 1
# Create trade network: 15 countries with weighted trade relationships
countries = [
"USA",
"China",
"Germany",
"Japan",
"UK",
"France",
"Canada",
"Mexico",
"Brazil",
"India",
"S.Korea",
"Italy",
"Australia",
"Spain",
"Netherlands",
]
n_nodes = len(countries)
# Generate edges with weights (bilateral trade in billions USD)
edges_data = []
edge_pairs = [
(0, 1, 550),
(0, 2, 180),
(0, 3, 220),
(0, 4, 140),
(0, 6, 380),
(0, 7, 420),
(0, 9, 95),
(0, 10, 130),
(1, 2, 200),
(1, 3, 340),
(1, 4, 85),
(1, 10, 290),
(1, 12, 160),
(2, 3, 55),
(2, 4, 150),
(2, 5, 180),
(2, 8, 45),
(2, 13, 65),
(2, 14, 220),
(3, 4, 35),
(3, 10, 85),
(3, 12, 70),
(4, 5, 95),
(4, 11, 55),
(4, 14, 80),
(5, 11, 85),
(5, 13, 95),
(6, 7, 75),
(7, 8, 40),
(8, 9, 30),
(9, 12, 25),
(11, 13, 45),
(12, 14, 35),
]
for src, tgt, weight in edge_pairs:
edges_data.append({"source": src, "target": tgt, "weight": weight})
# Calculate positions using spring layout (simple force-directed simulation)
pos = np.zeros((n_nodes, 2))
# Initial positions in a circle
angles = np.linspace(0, 2 * np.pi, n_nodes, endpoint=False)
pos[:, 0] = np.cos(angles)
pos[:, 1] = np.sin(angles)
# Force-directed iterations with weight-aware attraction
for _ in range(150):
forces = np.zeros_like(pos)
# Repulsion between all nodes
for i in range(n_nodes):
for j in range(i + 1, n_nodes):
diff = pos[i] - pos[j]
dist = max(np.linalg.norm(diff), 0.1)
force = diff / (dist**2) * 0.5
forces[i] += force
forces[j] -= force
# Attraction along edges (weighted)
for edge in edges_data:
i, j = edge["source"], edge["target"]
diff = pos[j] - pos[i]
dist = max(np.linalg.norm(diff), 0.01)
# Weight influences attraction strength more strongly
weight_factor = (np.log1p(edge["weight"]) ** 1.2) * 0.002
force = diff / dist * weight_factor
forces[i] += force
forces[j] -= force
# Apply forces with damping
pos += forces * 0.08
# Center
pos -= pos.mean(axis=0)
# Scale positions with margin for labels
pos = pos / np.abs(pos).max() * 3.2
# Calculate weighted degree for node sizing
weighted_degree = np.zeros(n_nodes)
for edge in edges_data:
weighted_degree[edge["source"]] += edge["weight"]
weighted_degree[edge["target"]] += edge["weight"]
# Create node dataframe
nodes_df = pd.DataFrame({"x": pos[:, 0], "y": pos[:, 1], "label": countries, "weighted_degree": weighted_degree})
# Create edges dataframe with line segments
edges_list = []
for edge in edges_data:
src, tgt = edge["source"], edge["target"]
edges_list.append(
{"x": pos[src, 0], "y": pos[src, 1], "xend": pos[tgt, 0], "yend": pos[tgt, 1], "weight": edge["weight"]}
)
edges_df = pd.DataFrame(edges_list)
# Normalize edge weights for line width (1 to 8 range)
min_w, max_w = edges_df["weight"].min(), edges_df["weight"].max()
edges_df["line_width"] = 1 + (edges_df["weight"] - min_w) / (max_w - min_w) * 7
# Normalize node sizes (6 to 18 range for better visibility)
min_d, max_d = nodes_df["weighted_degree"].min(), nodes_df["weighted_degree"].max()
nodes_df["node_size"] = 6 + (nodes_df["weighted_degree"] - min_d) / (max_d - min_d) * 12
# Create the plot
anyplot_theme = theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid=element_blank(),
axis_title=element_blank(),
axis_text=element_blank(),
axis_ticks=element_blank(),
plot_title=element_text(size=28, color=INK),
plot_subtitle=element_text(size=18, color=INK_SOFT),
legend_title=element_text(size=16, color=INK),
legend_text=element_text(size=14, color=INK_SOFT),
legend_background=element_rect(fill=PAGE_BG, color=INK_SOFT),
legend_position=[0.95, 0.25],
legend_justification=[1, 0.5],
)
plot = (
ggplot()
# Edges as segments with varying width based on weight
+ geom_segment(aes(x="x", y="y", xend="xend", yend="yend", size="weight"), data=edges_df, color=INK_SOFT, alpha=0.5)
# Scale for edge thickness - use Okabe-Ito color for legend
+ scale_size(range=[1, 10], name="Trade Volume\n(Billions USD)")
# Nodes as points sized by weighted degree
+ geom_point(aes(x="x", y="y", size="node_size"), data=nodes_df, color=BRAND, alpha=0.9, show_legend=False)
# Node labels
+ geom_text(aes(x="x", y="y", label="label"), data=nodes_df, size=14, color=INK, nudge_y=0.4, fontface="bold")
# Styling
+ labs(
title="network-weighted · letsplot · anyplot.ai",
subtitle="International Trade Network (Edge Thickness = Trade Volume)",
)
# Explicit axis limits to prevent label clipping
+ scale_x_continuous(limits=[-5, 5])
+ scale_y_continuous(limits=[-5, 5])
+ theme_minimal()
+ anyplot_theme
+ ggsize(1600, 900)
)
# Save PNG (scaled 3x for 4800 × 2700 px)
ggsave(plot, f"plot-{THEME}.png", path=".", scale=3)
# Save HTML for interactive version
ggsave(plot, f"plot-{THEME}.html", path=".")
Part of Weighted Network Graph with Edge Thickness on anyplot.ai.