:))

docs/Notes/Miscellaneous/erdos-renyl-model.md

@@ -0,0 +1,22 @@
+---
+title: "Erdos Renyl Model"
+tags:
+    - Graphs
+---
+
+# Erdos Renyl Model : Generating Random Graphs
+
+## 1. Overview
+
+- There are two variants of Erdos Renyl Model:
+    - G(n, p) : n nodes, each edge is present with probability p
+    - G(n, m) : n nodes, m edges are chosen uniformly at random from the set of all possible edges
+
+- Equivalently, all graphs with n nodes and M edges have equal probability of $p^M (1-p)^{\binom{n}{2}-M}$
+- The parameter p in this model can be thought of as a weighting function; as p increases from 0 to 1, the model becomes more and more likely to include graphs with more edges and less and less likely to include graphs with fewer edges.
+-  A graph in G(n, p) has on average ${\binom{n}{2}}p$ edges. 
+-  The distribution of the degree of any particular vertex is binomial: $P(deg(v)=k)=\binom{n-1}{k}{p^k}(1-p)^{n-1-k}$ 
+
+## 2. References
+
+- https://www.geeksforgeeks.org/erdos-renyl-model-generating-random-graphs/

docs/Notes/Miscellaneous/index.md

@@ -22,3 +22,4 @@ Following are the tags which were used in this section:
 
 - Basics
 - ICL
+- Graphs