= Solution
The diagram has all possible undirected <edges> except $AB$: it is a <complete graph> on five <vertices> with one <edge> removed. Therefore $A$ and $B$ each have three neighbours, while $C,D,E$ each have four.
The neighbours of $A$ and $B$ form a triangle, so their <clustering coefficients> equal one. Each of $C,D,E$ has five of the six possible neighbour–neighbour <edges>, giving $5/6$. The nodal <average shortest path length> is $\ell_i=\frac14\sum_{j\ne i}d(i,j)$. All <graph distances> equal one except $d(A,B)=d(B,A)=2$, hence
$$
\boxed{\begin{array}{c|ccccc}
i&A&B&C&D&E\\\hline
k_i&3&3&4&4&4\\
C_i&1&1&5/6&5/6&5/6\\
\ell_i&5/4&5/4&1&1&1
\end{array}}.
$$
Averaging the nodal quantities gives
$$
\boxed{\bar C=\frac9{10}=0.9,\qquad L=\frac{11}{10}=1.1}.
$$
The ordered-pair distance sum is $22$, and the <graph diameter> is two.
If the intended unnormalized “small-worldness” is the ratio of clustering to path length, the computed quantities give
$$
\boxed{\frac{\bar C}{L}=\frac9{11}\approx0.818}.
$$
That ratio has no universal threshold for identifying a <small-world network>. The standard reference-normalized <small-worldness>, $\sigma=(\bar C/C_{\rm ref})/(L/L_{\rm ref})$, cannot receive a numerical value when no reference is specified and the question forbids using a <network null model>.<Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence by Mark D. Humphries and others>[New measures of small-world-ness, Definitions 1–2]{ref}
\b[The graph has high clustering and short paths in the descriptive sense.] With nine of ten possible <edges>, however, those properties follow directly from its near completeness; they do not by themselves establish <small-world network> structure relative to a reference. This distinguishes the metrics that can be computed directly from the stronger classification that requires a stated convention.
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