## Exercise 1

### Connectivity Matrix

```
imagesc(matrix)
```

## Exercise 1

Plotting the correlation distribution:

```
degree = sum(matrix_thresh);
% plot the correlation distribution
figure;
hist(degree,20);
xlabel('Degree')
ylabel('Frequency')
```

## Exercise 1

### Correlation Distribution

## Exercise 1

### Degree Distribution

## Exercise 1

Calculating the mean shortest path length $L$ and the clustering coefficient $C$, for your thresholded, binarized network:

```
C = mean(clustering_coef_bu(matrix_thresh));
L = charpath(distance_bin(matrix_thresh));
% Values for C and L: C = 0.49, L = 2.93
```

## Exercise 2

Generating null networks:

```
randmatrix = cell(1,100);
for ind = 1:100
[R,eff] = randmio_und_connected(matrix_thresh, 10);
randmatrix{1,ind} = R;
end
```

## Exercise 2

Calculating $C_{r}$ and $L_{r}$:

```
for ind = 1:100
C_rand(ind) = mean(clustering_coef_bu(randmatrix{1,ind}));
L_rand(ind) = charpath(distance_bin(randmatrix{1,ind}));
end
mean(C_rand) % = 0.25
mean(L_rand) % = 2.3
```

$\sigma = \frac{0.49/0.25}{2.9/2.3} = 1.6 > 1$

→ We have a small-world network!