Update README.md for assignment 1

Author: stef4k

assignment-1/README.md

@@ -1,6 +1,58 @@
 # Degeneracy - Graph Theory
 
-This assignment was asking to detect the [k-cores](https://en.wikipedia.org/wiki/Degeneracy_(graph_theory)) of a graph. Implement the following algorithm to find the core number of each node of any given graph:
+This assignment required to detect the [k-cores](https://en.wikipedia.org/wiki/Degeneracy_(graph_theory)) of a graph. Implement the following algorithm to find the core number of each node of any given graph:
 
-The greek version of the assignment description is found [here](https://github.com/dmst-algorithms-course/assignment-2019-1/blob/master/assignment_2019_1.ipynb)
+
+<img src="https://github.com/stef4k/Algorithms-and-data-structures-assignments/blob/main/assignment-1/images/kcores%20algorithm.png" width="500" height="600" />
+
+## Running the script
+Use the command line to run the script:  
+
+`python k_cores.py <input_file>`  
+
+where `input_file` is the name of the file that contains the graph we wish to analyze. The graph files have the following form:
+
+0 1  
+0 2  
+1 3  
+2 3  
+2 6  
+2 7  
+3 6  
+3 7  
+3 8  
+4 5  
+5 6  
+5 10  
+6 7  
+7 8  
+7 11  
+8 9  
+
+In other words, each line of the file describes one edge between two nodes. In fact, all graphs are undirected.
+
+## Example
+The script is runned for the text file [example_graph.txt](https://github.com/stef4k/Algorithms-and-data-structures-assignments/blob/main/assignment-1/graphs/example_graph.txt):  
+
+`python k_cores.py example_graph.txt`  
+
+The exit of the script should be the following:  
+
+0 2  
+1 2  
+2 3  
+3 3  
+4 1  
+5 1  
+6 3  
+7 3  
+8 2  
+9 1  
+10 1  
+11 1  
+
+Also, run the script for the graph [human brain functional activations](https://github.com/stef4k/Algorithms-and-data-structures-assignments/blob/main/assignment-1/graphs/human_brain_functional_activations.txt) and verify the [solutions](https://github.com/stef4k/Algorithms-and-data-structures-assignments/blob/main/assignment-1/solutions/human_brain_solutions.txt).
+
+## 
+[Complete Greek version of the assignment description](https://github.com/dmst-algorithms-course/assignment-2019-1/blob/master/assignment_2019_1.ipynb)