# The brain's energy budget (round textbook figures, see the text).
body_watts = 100          # resting metabolic rate of an adult, about 100 W
brain_share = 0.20        # the brain uses about 20 % of it ...
brain_mass_share = 0.02   # ... while being about 2 % of body mass
task_extra = 0.05         # task-evoked increases: typically under 5 % of baseline

brain_w = body_watts * brain_share
print(f"brain at rest: {brain_w:.0f} W, {brain_w * 86400 / 4184:.0f} kcal per day")
print(f"energy per kg, brain vs body average: {brain_share / brain_mass_share:.0f} ×")
print(f"a demanding task adds at most about {brain_w * task_extra:.1f} W")
print(f"so ongoing 'default' activity is ≥ {100 * (1 - task_extra / (1 + task_extra)):.0f} % "
      "of what the brain spends during a task")
# brain at rest: 20 W, 413 kcal per day
# energy per kg, brain vs body average: 10 ×
# a demanding task adds at most about 1.0 W
# so ongoing 'default' activity is ≥ 95 % of what the brain spends during a task

from collections import deque

# A toy brain network (not real connectome data): five modules joined
# through a few hubs, the posterior cingulate (PCC) among them.
edges = """mPFC-PCC mPFC-AG_L mPFC-AG_R mPFC-HF PCC-AG_L PCC-AG_R PCC-HF AG_L-AG_R
FEF-IPS_L FEF-IPS_R IPS_L-IPS_R dlPFC_L-dlPFC_R dlPFC_L-PPC dlPFC_R-PPC
dACC-AI dACC-dlPFC_L AI-dlPFC_R V1-V2 V2-IPS_R M1-FEF M1-V1
PCC-dlPFC_L PCC-dACC PCC-IPS_L PCC-V2 mPFC-dACC PPC-IPS_L""".split()
G = {}
for e in edges:
    a, b = e.split("-")
    G.setdefault(a, set()).add(b)
    G.setdefault(b, set()).add(a)

def eigen_centrality(G, steps=200):
    x = {v: 1.0 for v in G}
    for _ in range(steps):                      # power iteration on (A + I)
        y = {v: x[v] + sum(x[u] for u in G[v]) for v in G}
        norm = max(y.values())
        x = {v: y[v] / norm for v in G}
    return x

def efficiency(G):
    """Global efficiency: mean of 1/shortest-path length over all pairs."""
    nodes, tot = list(G), 0.0
    for s in nodes:
        dist, q = {s: 0}, deque([s])
        while q:
            v = q.popleft()
            for u in G[v]:
                if u not in dist:
                    dist[u] = dist[v] + 1
                    q.append(u)
        tot += sum(1 / d for t, d in dist.items() if t != s)
    n = len(nodes)
    return tot / (n * (n - 1))

def without(G, node):
    return {v: G[v] - {node} for v in G if v != node}

ec = eigen_centrality(G)
print("top hubs by eigenvector centrality:")
for v in sorted(G, key=ec.get, reverse=True)[:4]:
    print(f"  {v:8s} degree {len(G[v])}, centrality {ec[v]:.2f}")
base = efficiency(G)
print(f"global efficiency, whole network: {base:.3f}")
for v in ("PCC", "dACC", "M1"):
    e = efficiency(without(G, v))
    print(f"  without {v:5s}: {e:.3f} ({100 * (e / base - 1):+.1f} %)")
# top hubs by eigenvector centrality:
#   PCC      degree 8, centrality 1.00
#   mPFC     degree 5, centrality 0.76
#   dACC     degree 4, centrality 0.60
#   AG_L     degree 3, centrality 0.56
# global efficiency, whole network: 0.532
#   without PCC  : 0.428 (-19.6 %)
#   without dACC : 0.517 (-2.8 %)
#   without M1   : 0.548 (+3.0 %)