title: Same values for PCA Loadings results
body: <p>I've recently performed a Principle component analysis for my masters thesis where I have 25 network datasets, formatted into graphs and applied 5 measurements to each graph. The measurements were formatted into a table where the rows are datasets and the columns are the results, as shown below:</p>
  
  <p><a href="https://i.stack.imgur.com/Bn9ek.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Bn9ek.png" alt="enter image description here"></a></p>
  
  <p>I then scaled the results to ensure that they are centered to have mean zero (according to An Introduction to Statisical learning, G. James, 2013), with this function: </p>
  
  <pre><code>dat &lt;- data.frame(lapply(measures, function(x) scale(x, center = FALSE, scale = max(x, na.rm = TRUE)/100)))
  </code></pre>
  
  <p>This scale function is applied by each measure's standard deviation. I then applied PCA using the princomp function in R, <code>princomp(dat, cor = T, scores = T)</code> which returned these loading results:</p>
  
  <pre><code>Loadings:
                  Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
  Transitivity    0.585  0.412  0.246  0.136  0.640
  Reciprocity     0.540 -0.145 -0.336 -0.750 -0.111
  centralization -0.600  0.280        -0.582  0.469
  density                0.327 -0.893  0.261  0.146
  assortativity          0.790  0.159 -0.111 -0.581
  
                  Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
  SS loadings       1.0    1.0    1.0    1.0    1.0
  Proportion Var    0.2    0.2    0.2    0.2    0.2
  Cumulative Var    0.2    0.4    0.6    0.8    1.0
  </code></pre>
  
  <p>I would like to ask what would cause the SS loadings and Proportion Variables to have exactly the same results? I'm not sure if this is a discrepancy in my data, the scaling methods I'm using or if this is even something I should worry about. I see that someone had similar results in this <a href="https://stackoverflow.com/questions/48610260/the-result-loadings-of-pca-in-r">query</a>, but did not discuss it, so perhaps it's normal? Any explanation for the impact this has will be much appreciated. </p>
  
  <p>Biplot:</p>
  
  <p><a href="https://i.stack.imgur.com/uaLBm.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/uaLBm.png" alt="enter image description here"></a></p>
  
  <p>The Screeplot is also doesn't make much sense, since I expected a exponential drop-off, I assume this is a reflection of the loadings results. 
  Screeplot:</p>
  
  <p><a href="https://i.stack.imgur.com/wXYkt.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/wXYkt.png" alt="enter image description here"></a></p>