# Signed Networks in Social Networks

Last Updated : 01 Oct, 2020

Prerequisite: Introduction to Social Networks

In Social Networks, Network is of 2 types- Unsigned Network and Signed Network. In the unsigned network, there are no signs between any nodes, and in the signed network, there is always a sign between 2 nodes either + or -. The ‘+’ sign indicates friendship between 2 nodes and the ‘-‘ sign indicates enmity between 2 nodes.

Our task is to create a signed network on N nodes using python language.

Approach:

1. Create a graph and add nodes to it.
2. Add every possible edge and assign a sign to it.
3. Get a list of all possible triangles in a network.
4. Store the sign details of all the triangles in the network.
5. Count the total number of the unstable triangle in the network
6. Now take an unstable triangle from the list and make it stable.
7. Again count a number of the unstable triangles.
8. Repeat steps 6 and 7 until there is no unstable triangle.
9. Now form a coalition(friend nodes in coalition 1 with red color and enemy nodes in other coalition with blue color) and display the graph.

Below is the implementation.

## Python3

 `import` `networkx as nx ` `import` `matplotlib.pyplot as plt ` `import` `random ` `import` `itertools ` ` `  ` `  `def` `get_signs_of_graph(g, tris_list): ` `     `  `    ``# eg-['A-B','B-C','C-A'] ` `    ``all_signs ``=` `[] ` `     `  `    ``for` `i ``in` `range``(``len``(tris_list)): ` `        ``t ``=` `[] ` `        ``t.append(g[tris_list[i][``0``]][tris_list[i][``1``]][``'sign'``]) ` `        ``t.append(g[tris_list[i][``1``]][tris_list[i][``2``]][``'sign'``]) ` `        ``t.append(g[tris_list[i][``2``]][tris_list[i][``0``]][``'sign'``]) ` `        ``all_signs.append(t) ` `    ``return` `all_signs ` ` `  `def` `unstablecount(all_signs): ` `    ``stable ``=` `0` `    ``unstable ``=` `0` `     `  `    ``for` `i ``in` `range``(``len``(all_signs)): ` `        ``if` `(((all_signs[i]).count(``'+'``)) ``=``=` `1` `or` `((all_signs[i]).count(``'+'``)) ``=``=` `3``): ` `            ``stable ``+``=` `1` `    ``unstable ``=` `len``(all_signs) ``-` `stable ` `    ``return` `unstable ` ` `  ` `  `def` `move_graph_to_stable(g, tris_list, all_signs): ` `    ``found_unstable ``=` `False` `    ``ran ``=` `0` `     `  `    ``while` `(found_unstable ``=``=` `False``): ` `        ``ran ``=` `random.randint(``0``, ``len``(tris_list) ``-` `1``) ` `        ``if` `(all_signs[ran].count(``'+'``) ``%` `2` `=``=` `0``): ` `            ``found_unstable ``=` `True` `        ``else``: ` `            ``continue` ` `  `    ``r ``=` `random.randint(``1``, ``3``) ` `     `  `    ``if` `(all_signs[ran].count(``'+'``) ``=``=` `2``): ` `         `  `        ``if` `(r ``=``=` `1``): ` `            ``if` `(g[tris_list[ran][``0``]][tris_list[ran][``1``]][``'sign'``] ``=``=` `'+'``): ` `                ``g[tris_list[ran][``0``]][tris_list[ran][``1``]][``'sign'``] ``=` `'-'` `            ``else``: ` `                ``g[tris_list[ran][``0``]][tris_list[ran][``1``]][``'sign'``] ``=` `'+'` `         `  `        ``elif` `(r ``=``=` `2``): ` `            ``if` `(g[tris_list[ran][``1``]][tris_list[ran][``2``]][``'sign'``] ``=``=` `'+'``): ` `                ``g[tris_list[ran][``1``]][tris_list[ran][``2``]][``'sign'``] ``=` `'-'` `            ``else``: ` `                ``g[tris_list[ran][``1``]][tris_list[ran][``2``]][``'sign'``] ``=` `'+'` `         `  `        ``else``: ` `            ``if` `(g[tris_list[ran][``0``]][tris_list[ran][``2``]][``'sign'``] ``=``=` `'+'``): ` `                ``g[tris_list[ran][``0``]][tris_list[ran][``2``]][``'sign'``] ``=` `'-'` `            ``else``: ` `                ``g[tris_list[ran][``0``]][tris_list[ran][``2``]][``'sign'``] ``=` `'+'` `     `  `    ``else``: ` `         `  `        ``if` `(r ``=``=` `1``): ` `            ``g[tris_list[ran][``0``]][tris_list[ran][``1``]][``'sign'``] ``=` `'+'` `         `  `        ``elif` `(r ``=``=` `2``): ` `            ``g[tris_list[ran][``1``]][tris_list[ran][``2``]][``'sign'``] ``=` `'+'` `         `  `        ``else``: ` `            ``g[tris_list[ran][``0``]][tris_list[ran][``2``]][``'sign'``] ``=` `'+'` ` `  `    ``return` `g ` ` `  ` `  `def` `Coalition(g): ` `   `  `    ``f ``=` `[] ` `    ``s ``=` `[] ` `    ``nodes ``=` `g.nodes() ` `    ``r ``=` `random.choice(``list``(nodes)) ` ` `  `    ``f.append(r) ` `    ``processed_nodes ``=` `[] ` `    ``to_be_processed ``=` `[r] ` ` `  `    ``for` `each ``in` `to_be_processed: ` `        ``if` `each ``not` `in` `processed_nodes: ` `            ``neigh ``=` `list``(g.neighbors(each)) ` `            ``for` `i ``in` `range``(``len``(neigh)): ` `                ``if` `(g[each][neigh[i]][``'sign'``] ``=``=` `'+'``): ` `                    ``if` `(neigh[i] ``not` `in` `f): ` `                        ``f.append(neigh[i]) ` `                    ``if` `(neigh[i] ``not` `in` `to_be_processed): ` `                        ``to_be_processed.append(neigh[i]) ` `                ``elif` `(g[each][neigh[i]][``'sign'``] ``=``=` `'-'``): ` `                    ``if` `(neigh[i] ``not` `in` `s): ` `                        ``s.append(neigh[i]) ` `                        ``processed_nodes.append(neigh[i]) ` ` `  `            ``processed_nodes.append(each) ` ` `  `    ``return` `f, s ` ` `  ` `  `# 1.Create graph ` `g ``=` `nx.Graph() ` `n ``=` `8` `g.add_nodes_from(``range``(``1``, n ``+` `1``)) ` `map` `=` `{``1``: ``"A"``, ``2``: ``"B"``, ``3``: ``"C"``, ``4``: ``"D"``, ``5``: ``"E"``, ` `       ``6``: ``"F"``, ``7``: ``"G"``, ``8``: ``"H"``, ``9``: ``"I"``, ``10``: ``"J"``} ` `signs ``=` `[``'+'``, ``'-'``] ` `g ``=` `nx.relabel_nodes(g, ``map``) ` ` `  `# 2.Add every possible edge and assign sign ` `for` `i ``in` `g.nodes(): ` `    ``for` `j ``in` `g.nodes(): ` `        ``if` `(i !``=` `j): ` `            ``g.add_edge(i, j, sign``=``random.choice(signs)) ` ` `  `# 3.Display graph ` `edge_attributes ``=` `nx.get_edge_attributes(g, ``'sign'``) ` `pos ``=` `nx.circular_layout(g) ` `nx.draw(g, pos, node_size``=``3000``, with_labels``=``1``) ` `nx.draw_networkx_edge_labels( ` `    ``g, pos, edge_labels``=``edge_attributes, font_size``=``20``, font_color``=``'blue'``) ` `plt.show() ` ` `  `# 4.1.Get list of all the triangles in network ` `nodes ``=` `g.nodes() ` `tris_list ``=` `[``list``(x) ``for` `x ``in` `itertools.combinations(nodes, ``3``)] ` ` `  `# 4.2.Store the sign details of all the triangles ` `all_signs ``=` `get_signs_of_graph(g, tris_list) ` ` `  `# 4.3.Count total number of unstable triangle ` `# in the network ` `unstable ``=` `unstablecount(all_signs) ` ` `  `# 5 chose the triangle in the graph that is unstable ` `# and make the triangle stable ` `unstable_track ``=` `[unstable] ` ` `  `while` `(unstable !``=` `0``): ` `    ``g ``=` `move_graph_to_stable(g, tris_list, all_signs) ` `    ``all_signs ``=` `get_signs_of_graph(g, tris_list) ` `    ``unstable ``=` `unstablecount(all_signs) ` `    ``unstable_track.append(unstable) ` ` `  `# 6 Form the coalition ` `first, second ``=` `Coalition(g) ` `print``(first) ` `print``(second) ` ` `  `edge_labels ``=` `nx.get_edge_attributes(g, ``'sign'``) ` `pos ``=` `nx.circular_layout(g) ` ` `  `nx.draw_networkx_nodes(g, pos, nodelist``=``first, ` `                       ``node_color``=``'red'``, node_size``=``4000``) ` `nx.draw_networkx_nodes(g, pos, nodelist``=``second, ` `                       ``node_color``=``'blue'``, node_size``=``4000``) ` `nx.draw_networkx_labels(g, pos) ` `nx.draw_networkx_edges(g, pos) ` `nx.draw_networkx_edge_labels(g, pos, edge_labels``=``edge_labels, font_color``=``"red"``) ` `plt.show() `

Output:

```['G', 'B', 'C', 'H']
['A', 'D', 'E', 'F']
```

Initial Signed Network without coalition

Final Signed Network with coalition