17. Network graphs — position carries no meaning · Dr. Seonggu Sohn's Data Visualization, First Steps

Fig. 2E draws the gene regulatory network ARACNe found. DDX54 alone regulates 1,105 genes.

A network graph is made of two things — nodes and edges. But only the edges are in the data. The data says “A and B are connected”; it says nothing about where A belongs on screen.

Node positions are decided by a layout algorithm, usually a force-directed one that pretends connected nodes attract and unconnected ones repel. And that algorithm gives a different answer every time you run it.

Re-lay out the same network several times. The shape changes; the connections do not.

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The three look nothing alike. And yet not one connected pair changed. Only the seed did.

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import matplotlib.pyplot as plt
import viz, numpy as np, json

F = json.load(open("viz_facts.json"))
N = F["net"]
n = len(N["nodes"]); E = N["edges"]

def layout(seed, steps=140):
    rng = np.random.default_rng(seed)
    P = rng.normal(0, 1, (n, 2))
    for _ in range(steps):
        F_ = np.zeros((n, 2))
        for i in range(n):                       # nodes push each other apart
            d = P[i] - P
            r = np.linalg.norm(d, axis=1) + 1e-6
            F_[i] += (d / (r**2)[:, None]).sum(axis=0) * .05
        for i, j, w in E:                        # connected nodes pull together
            d = P[j] - P[i]
            F_[i] += d * .02; F_[j] -= d * .02
        P += F_ * .5
    return P

fig, ax = plt.subplots(1, 3, figsize=(11, 3.7))
for a, seed in zip(ax, [1, 2, 3]):
    P = layout(seed)
    for i, j, w in E:
        a.plot(P[[i, j], 0], P[[i, j], 1], lw=.7, color="#bbb", zorder=1)
    a.scatter(P[:, 0], P[:, 1], s=42, color=viz.PAL[0], zorder=2)
    a.set_title("seed = %d" % seed, fontsize=9)
    a.set_xticks([]); a.set_yticks([]); a.set_aspect("equal")
fig.tight_layout()
print("%d nodes - %d edges. The three pictures use exactly the same data." % (n, len(E)))

So is a network graph useless? No. It just answers a different question.

What a network graph answers

how tangled the whole thing is. Roughly how many blobs there are. Whether edges pile onto one node. Fig. 2E is really showing “DDX54 has a lot of edges”

What it cannot answer

how many edges each node has. Which node is more central. That is a bar chart's job

The same data. But now you can read how many. The graph was not bad — the question was different.

Python Runs in your browser

import matplotlib.pyplot as plt
import viz, numpy as np, json

F = json.load(open("viz_facts.json"))
N = F["net"]
deg = np.zeros(len(N["nodes"]), int)
for i, j, w in N["edges"]:
    deg[i] += 1; deg[j] += 1

o = np.argsort(deg)[::-1][:12]
fig, ax = plt.subplots(figsize=(5.6, 3.4))
ax.barh([N["nodes"][i] for i in o][::-1], [deg[i] for i in o][::-1], color=viz.PAL[0])
ax.set_xlabel("number of edges", fontsize=8); viz.bare(ax)
ax.tick_params(labelsize=7)
fig.tight_layout()
print("Count the edges and draw bars, and what you were eyeballing becomes a number.")

🤔 Check yourself

Two nodes sit close together in a network graph. What does that mean?

🤔 Check yourself

You want to show which gene connects to the most others. How?