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    "# Problem 4.3: Statistics of random genetic circuits\n",
    "\n",
    "<hr>"
   ]
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    "*This problem is still a draft.*\n",
    "\n",
    "In the chapter, we discussed in words an algorithm for generating random directed graphs representing interactions among genes. Starting from a set of nodes and directed edges (arrows), we enforce that each node has the same number of incoming and outgoing arrows. It is a fun (and challenging!) problem to implement such an algorithm, which is what you will do in this problem.\n",
    "\n",
    "We showed that the directed graph can be pictorially represented as a set of nodes with arrows, or as an asymmetric matrix of ones and zeros. Alternatively, and more compactly, it may be represented as an array of 2-tuples, with each 2-tuple representing an arrow connecting two numbered nodes. As an example `(8, 2)` represents an arrow going from node 8 to node 2, and `(10, 11)` represents an arrow going from node 10 to node 11.\n",
    "\n",
    "**a)** Write a function that takes as input an array of 2-tuples representing the regulatory connections of numbered genes and returns an array of 2-tuples representing a random directed graph in which each node (gene) has the same number of incoming and outgoing arrows as in that input network.\n",
    "\n",
    "**b)** Write another function that takes as input an array of 2-tuples representing a network and an array of 2-tuples representing a specific regulatory architecture and then returns the number of instances of that architecture in the input network. Here are some example architectures.\n",
    "\n",
    "- Simple regulation: `[(1, 2)]`\n",
    "- Mutual regulation (as in a toggle circuit): `[(1, 2), (2, 1)]`.\n",
    "- FFL: `[(1, 2), (1, 3), (2, 3)]`\n",
    "\n",
    "**c)** Play with your functions with sample circuits. For starters, you can use the example circuit of [Milo, et al.](https://doi.org/10.1126/science.1089167), shown below,\n",
    "\n",
    "<div style=\"width: 200px; margin: auto;\">\n",
    "\n",
    "![Milo network](milo_network.png)\n",
    "\n",
    "</div>\n",
    "\n",
    "which can be represented as\n",
    "\n",
    "```python\n",
    "milo_example_network = [\n",
    "    (1, 16),\n",
    "    (2, 1),\n",
    "    (3, 12),\n",
    "    (3, 13),\n",
    "    (4, 10),\n",
    "    (4, 11),\n",
    "    (5, 6),\n",
    "    (5, 10),\n",
    "    (5, 13),\n",
    "    (6, 9),\n",
    "    (6, 10),\n",
    "    (7, 8),\n",
    "    (8, 1),\n",
    "    (8, 2),\n",
    "    (10, 11),\n",
    "    (13, 12),\n",
    "    (15, 14),\n",
    "    (16, 14),\n",
    "    (16, 15),\n",
    "]\n",
    "```\n",
    "\n",
    "Try searching for FFLs."
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    "<br />"
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