{ "cells": [ { "cell_type": "markdown", "id": "f22f51eb", "metadata": {}, "source": [ "# Dipole Moment" ] }, { "cell_type": "markdown", "id": "bc8c4a08", "metadata": {}, "source": [ "Dipole Polarization (Morales et al., 2015) measures the polarization of an opinion distribution, drawing inspiration from the electric dipole moment. It evaluates polarization based on two main factors: how evenly the population is split between two opposing views, and how extreme the distance is between those contrasting views.\n", "\n", "Assuming node opinions are distributed continuously on a scale from $-1$ (negative pole) to $1$ (positive pole), we calculate the relative population sizes of the positive and negative groups ($A^+$ and $A^-$), as well as their respective average opinions, referred to as \"gravity centers\" ($gc^+$ and $gc^-$). \n", "\n", "First, the normalized difference in population size is defined as:\n", "\n", "$$\n", "\\Delta A = |A^+ - A^-|\n", "$$\n", "\n", "Then, the normalized distance between the two average opinions (the pole distance) is calculated as:\n", "\n", "$$\n", "d = \\frac{|gc^+ - gc^-|}{2}\n", "$$\n", "\n", "Finally, the Dipole Polarization index $\\mu$ is calculated with:\n", "\n", "$$\n", "\\mu = (1 - \\Delta A)d\n", "$$\n", "\n", "This index naturally bounds between $0$ and $1$. The $(1 - \\Delta A)$ term ensures that polarization is highest only when the network is divided into two groups of the exact same size ($\\Delta A = 0$). The $d$ multiplier dictates that these evenly matched groups must also hold completely conflicting, extreme opinions to achieve maximum polarization ($d = 1$). If the network shares a consensus or the groups are not ideologically separated, the pole distance is $0$, resulting in zero polarization.\n", "\n", "When estimating how opinions spread through a network, we look at how individuals (nodes) update their views based on their social connections. \n", "\n", "**In the original model proposed by Morales et al. (2015), a person's new opinion is calculated strictly as the average of their incoming neighbors' opinions**. It explicitly ignores their own previous opinion:\n", "\n", "$$\n", "X_i(t) = \\frac{\\sum_j A_{ij}X_j(t-1)}{k_i^{in}}\n", "$$\n", "\n", "where $A_{ij}$ represents the network connection from node $j$ to node $i$, and $k_i^{in}$ is the total number of incoming connections (indegree). To provide more flexibility in modeling social dynamics, the `netseg` allows including the self opinion also.\n", "\n", "\n", "Dipole moment varies heavily with the parameter, `k_top`. *. If the influential nodes are not given manually, influential nodes will be calculated by their degree and ```k_top``` parameter. The parameter expects an integer value, indicating how many of the nodes will be considered as an influential node. If used with ```balanced``` is set to ```True```, from each group $\\frac{k_{\\text{top}}}{|M|}$ ($|M|$ is the number of groups) nodes will be selected as influential nodes. If ```balanced``` is set to ```False```, $k_{\\text{top}}$ highest degree nodes will be selected from the graph.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "f1d4e98f", "metadata": {}, "outputs": [], "source": [ "from netseg import dipole_moment\n", "import igraph as ig \n", "import warnings\n", "import matplotlib.pyplot as plt \n", "from matplotlib.colors import LinearSegmentedColormap, to_hex, Normalize, BoundaryNorm\n", "import random \n", "import numpy as np \n", "from time import perf_counter\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "from matplotlib.cm import ScalarMappable\n", "import matplotlib.patches as mpatches\n", "\n", "%config InlineBackend.figure_format = 'retina'\n", "\n", "COLORS = [\n", " '#2C486F',\n", " '#436796',\n", " '#5E8FAE',\n", " '#80BDD6',\n", " '#B1DDE0',\n", " \"#fdf8e7\",\n", " '#F8E5B2',\n", " '#F3CF63',\n", " '#E9A64C',\n", " '#E3843B',\n", " '#DA584E'\n", " ]\n", "\n", "def make_symmetric_sbm(p_in, p_out, n_groups, nodes_per_group, membership, **kwargs):\n", " pref_matrix = [\n", " [p_in if i == j else p_out for j in range(n_groups)] \n", " for i in range(n_groups)\n", " ]\n", " block_sizes = [nodes_per_group] * n_groups\n", " g = ig.Graph.SBM(pref_matrix, block_sizes, **kwargs)\n", " \n", " g.vs['membership'] = membership\n", " \n", " return g " ] }, { "cell_type": "markdown", "id": "81fdc5d0", "metadata": {}, "source": [ "## Basic Usage" ] }, { "cell_type": "markdown", "id": "912d3f16", "metadata": {}, "source": [ "Most simple way to use `netseg` to calculate the dipole moment can be shown as following, " ] }, { "cell_type": "code", "execution_count": null, "id": "22128c9e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.2893930981512981)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "membership= [0 if i < 100 else 1 for i in range(200)]\n", "random.seed(2)\n", "g = make_symmetric_sbm(0.08, 0.004, 2, 100,membership, directed = True)\n", "dipole_moment(\"membership\", g, ego_included= True, k_top= 10, balanced= True)" ] }, { "cell_type": "markdown", "id": "dcdb2b27", "metadata": {}, "source": [ "Notice that, we are using `ego_included = True`. As explained before, if this parameter is set to `True`, opinion of the ego node also included in the opinion propagation step. If set to False, only the neighbors are included. Although this does not change the results drastically, it can be altered according to your choice.\n", "\n", "We are also setting the `k_top` parameter to $10$ and `balanced` to `True`. As mentioned, if you do not provide influential nodes to `dipole_moment`, it will detect the influential nodes as highest degree nodes. If balanced is set to `True`, from each unqiue group `k_top`/ 2 nodes will be selected as influential nodes, if balanced is set to `False`, the highest `k_top` nodes will be selected as influential nodes, disregarding the group membership. " ] }, { "cell_type": "markdown", "id": "a998e61f", "metadata": {}, "source": [ "## Picking Influential Nodes\n", "\n", "There is no one size fits all selection for the influential nodes. Of course, depending on the context, influential nodes can be news sources, elites, etc. `netseg` provides using degree as influential node selection but also accepts and encourages using a list of integers to represent influential nodes. \n", "\n", "If a list of influential nodes is not supplied directly, users should be aware that `k_top` parameter might vastly impact the results as can be seen in the following block. " ] }, { "cell_type": "code", "execution_count": 5, "id": "e51cc581", "metadata": {}, "outputs": [ { "data": { "image/png": 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3kdBbt13azg+9nTX+Occ9f/yu4T3/obezjnuB0FvXTNgFQ28XOe6ZwNqZsS4UeuvuuP4Cm10ftwsFRTs+I/QGAAAQYoRsgUtw04KJWrczV9v3F3a73Toh8MvnNugrH1zBevZj4TabPv22ufrOs2tVUlnnd78/vrFLQxJiNH5kckjnBwCDwdjkWL1VWqO+5kR9k6kthZXmZObIuOjOTrejE5yK4B2CAAAAAHBFWKGV8elDTH38PfO0+3CJ6W67fmeuPI3NvRrTCn5Z54Ktioqwa/60DC2fO06zJ6UpgjddAhiEWry+jqBse5WfG5ztuG1dprZtkGVno6PsSk6IUXKC07xRo7nFF7RjWW/6sEK2AAAAAEKLkC1wiSdq73//Un30oWf9npj9z5bDWjxzjOZlZ7Cm/ZgzKkL33zpP335mjeoaun+srUsTPfqvLXrgrqUamhAT8jkCwEA2ISVOsZHhqm8O3snoy2W9UFBc22hqQ0GFbGFSWoLTBG4zXTEalRAtu43LcgAAAADAlXgTvdWB1qrP3bVIb+4pMIHbrfsK1OLt3eXGm1q8Wr39qKn4mGgtnpWlFXPHa3LWcNmsPwgBoB9rbvGaRjKm62y1uzMsa4K0NWdu19Q3arCJcUSa4GxSgtOEaM/9eHpb127nd331CRNABgAAADCwELIFLtHQpFh96vb5+vGTa/zu88hTazVlzAjFxUSxrv2Y1aX2c++4Rj/42wYTqO2OFcB9+MXN+uadS0wwFwAQGOG2MF2Tlqw3jp0K+JJaIVhfa5uKaxsUyKvRWWMVVHtMrVW57LYw093WhG4TY0zXW154BQAAAIDQioq0a/GsMabq3E1at/OYCdzmHCnp9Zi17ka9tG6/qWFJcVo+d6wJ3GaMTAro3AHgcjU0tXR0nXWfFZa1ArUVHbetqvM0DbrFtl7DS+4SmE2yArPxTiW7Tgdo28Oz0ZG89gMAAACgHSFboAdunD9Ba3ccM5cJ6451cuKXz23QVz64gnXt58aPTNZHrpup37y63e8+JZV1+sW/t+r+d84zXTIAAIFxTVqS9p2qVWld4DpkjIiL1j3TRpuwa7O3VcdrPMqrciuvyhPQ41i8rW3KrXKbksoUGW5ThutM6HZYbJTpkg8AAAAACF2g6uZFk0ydqqzX6u1HtGrrER0rquj1mCcr6/SXV3eZGpOarOVzx2n5nHEakhgb0LkDwGltbW3yNFrhWfdZYdlzg7PWbWu/wcYVF62k+Bglu/wEZ+Pbw7OREbw8DgAAAKBn+CsC6AErEHP/+5fqow89K09jc7f7/GfLYS2eOUbzsjNY235u/oQ0naiq04tvHvK7z97jp/TU2j26d9m0kM4NAAZ6N9t3ThypP+7IV5OfjuI9EWW36V2TRnZ2k4202zQ2OdaUpaHFZ7rQWqHb/CqPTrkD28Gj2deqwxX1piwOe7gJ3J4O3aY4IwndAgAAAEAIr1h25/UzTOWXVGrl1sNatfWoCc32lhXWter3L2xR9riRWjF3nBbNGMMVzwBccni23tNswrEVZ3WdPf35mRBtY7N3UK2qLSxMrjhHZ3DWCsqaLrSus28nxjtkDw+/0tMFAAAAMEARsgV6cRL2U7fP14+fXON3n0eeWqspY0ZwEnUAeOc1E1VaWa+tR4r97rNyd65GJMbquuljQjo3ABjIhsZG6X3T0/TUW4WXFbS1Arbvm5amITFRfvdxRIRrwpA4UxZ3s9eEbU93uq1s6P6NNb3V4PXpQFmdKUtspBW6jVFmR+jWFR1B6BYAAAAAQiBjZJI+8s5r9KFbrta+3BMmcGtdyayul2++bGuTdh8uMfWzZ9Zr7uR0E7i9JjudzonAINTa2qZad+NZIdmuwdmun7d4fRpMrDfDt4dkz3Sa7RqcNZ1oXU65Yh0KD+dKggAAAACuLEK2QC/cOH+C1u08pm37Crvdbp0Q+cVfN+irH1rB+g6Ad0l/7IZZKq/1KPdkld/9nlqbo6EJMZqWOTyk8wOAgSwtwamPzM7QC/tLVFrX2OP7j4iLNh1sLxSw7U5MpF2Th8WbstQ2tpiwbb4J3bpV0xTYjiH1zT7tPVlrypIQZTdh29PB2/joiIAeDwAAAABwfthr6tgRpj5zx0Jt31+olVuPaPPufDW19O5vwBZvqzbuzjPljI7UoplZJnA7bfxIhdsIjAH9ma+1VTV1jWcFZ9s/nh2crar1yBuAqzT1JxF2m5LizwRn2z+eH6RNiHV0XnUKAAAAQO9Zz6/78/j9RVibdQ0SDDpFRUVKS0sztwsLC5Wamnqlp9TvlFXV6yPfflaeRv/d7b7z6Zs0LzsjpPNCcFS7G/XtZ9aosq7B7z7RkXZ9844lSk1pD2UBAALD19qmLYWV2lJYYQKpF2N1hr0mLVnXpCUpPMAn662nztUmdOvuDN5eypwuR5IjsrPLbUai04SAAQAAgMF87rCvzw8Dh3Xud+NbeSZwu/NAkVoD8HKKFTZbNmesCdyOTUvhSiZAH+LztZpgbEVtR1i2uqPrrPW16jNB2qo6j+lSO5hERdhNULYzLNs1ONtx2+o+Gx8TNaj/v3bXV59QebU7aOOnuGL0zP/eG7TxAQAAgP6uKEjnDQnZDlKciA6MVzYe0I+fXHPBNP/vH7xT8THRAToirqTjZTX6n7+uU+MFulekxDn14N1LFe/sWddEAMClhW0PltfpWEW96Wxb7mmWt7VNdluYUpyRpnPtmORYTUiJC3i49kKhW2seVug234RuPWoI8uX9hsZEmbCtCd26nIqOCA/q8QAAADD49PVzh319fhiYrODdmu1HTeD2YP6pgIw5erhLy+eM0/K54zVyCG/cB4KlxeszQVm/wVmzza3qugYNttZEjqiIbsKy7bfbO9G2f4xxRA7q8Oyl+vT3njc/W8Five74y6/fFrTxAQAAgP6uiJAt+sMP1GBjBWu+8fOXtXXfcb/7XHv1eH31QytCOi8Ez1u5pXrkn1t0ofNsY0ck6SvvWahIO6EnABiMzw1O1jedCd1We9QcxMsCWi9tDI+L7ux0OzrBqUg7lx0FAADAwD532Nfnh4Gv6GS1Vm07YgK3xadqAjLmxMxhprvt0tlj5YpzBGRMYKBrbvGawOy5YdmK6rNv17obNdhYodiLBWetrzmjI6/0VAEAAAAgYAjZIqA4ER04ZVX1+uhDz8rd0Ox3n4c+daPmT8sM4FFxJb2686j+sm7PBfe55qpUffLG2byzGwAGOevSgSV1jZ2h2+M1HtN9N1isBr6j4h2dnW7T4h2yhxO6BQAAwMA6d9jX54fB9UbLQwVlWrX1sFZvP6qq2obLHtNmC9PsiWkmcGudU3ZERwRkrkB/0tDU0h6ctbrN1pwJy7Z/3hGorXGr3uP/dZmBKi4m6pzwbIxSOj6e7khrfYyO5P8dAAAAAAafoiCdN7QHZBRgEBuSGKtP3b5AP3pitd99HnlqnaaMHaH4mOiQzg3BccOMMSqtrNOavfl+99lyqEgjEuP0zmsm8DAAwCBmvTiamuAwtShD8ra2qrimI3Rb7VFhjUeBzNxaYxXWNJhan1+hcFuYCdpagdvMJKdGxjnM1wAAAAAAl8+6dPqEjKGmPvGe+dp1qFirth7Rhrdy5Wls6fWbNa0rp1kVHWk3QVsrcDtrUqrs4Vw5C/07lG79XnQNyXYXnLU+9vb3pz9zxUWfFZxNjncq2XUmOGttS4x3KjKC/w8AAAAAQKgRsgUC4IZ5V2ndzmPauvd4t9utk0S/eHaDvvbha1nvAXLy/J5l03Sqxq39hWV+93thywENT4w1XW0BALDYbTalJzpNWVp8raa7rdXl1greltQ2KpB9bn2tbSbMa9XqPCkiPEzpCU5lWKHbRKeGx0XLFkboFgAAAAAuV3i4TbMnpZn6fPNibc7J18qtR7Rt33F5fa29GrOx2atV246YSoiN1pJZY7Ri7nhNyhrGFbTQp8KzdZ6mjpBsR9fZLh9PB2etsn6mBxPrnIsrzqFkV0en2XinUrrcNuFZlxWeta5ERHgWAAAAAPqqsDbrr18MOlxSLfDKq+r1kYeelbvB/+WJvv3JG7VgemYQjo4rwd3YrO88u1alVfV+94kIt+mrty3S2BFJIZ0bAKB/avT6dLzaCtxawVu3TtQ3BfV40Xab0l1O0+k2I9GpoTFRvFALAACAPn/usK/PD+iqpr5R63ceM4HbPUdLA7I4w1PitHzOOBO4TR+RyIIjKKyuyrXuxjNdZ/0EZ63PW7y+QfUohNtsSkpwKCm+S6dZ19nBWevrVsDW2hcAAAAA0L/PGxKyHaQ4ER0cr206qB8+sdrvduvdyL9/4C7TdQADw8nqen37mTVyX+DyVfHOKD1411KlxLd3LQQA4FJ5mr3tnWg7Ot2We/y/mScQnBHhpsPt6U63SY5IQrcAAACDUF8/d9jX5wf4c7KiznSltQK3+SWVAVmosWkpWjF3nJbNHquUxFgWHxfla21VTV3jWcHZ02HZii63q2o9ve7C3F9F2G1nB2etjrMJzvOCtAmxDtlsXBkIAAAAAPoaQrboFz9Qg53VGPobv3hZW/ce97uPdcLzax++NqTzQnAdLCrX//19g7kktz+pyfH6f3csliMqgocDANBrdU0tHYHb9k63VRd4k0cgxEXZ27vcdnS7dTn4dwwAAGAw6OvnDvv6/IBLkVtcYcK2q7YeUdkFrpR1qcLCpOnjR2n53HFaNDNLsY4oHohBxudrNcHYCquqzw/OdoZn6zymS+1gEhVh7xKWjTGB2fODtDGK5wo/AAAAANCvFdHJFv3hBwpSeVW9PvLQs3I3+O809+1P3qgF0zNZrgFk/b4C/f4/Oy+4z7SMYfrCLfN4hzsAIGCqG1qUX+02oVur021dkzeoq5sYHdHZ5TYj0ak43jwCAAAwIPX1c4d9fX5AT1hhx73HSk3gdt2OY6rzNF32AkbYw3XN1HQTuL16SroiI8J5UPqxFq9PlRcKznZsq6lvUNvgys6aphbddZ1N6RK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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 633, "width": 1388 } }, "output_type": "display_data" } ], "source": [ "network_sizes = [200, 400, 800, 1600]\n", "absolute_k_tops = [10, 20, 40, 80]\n", "relative_k_tops = [0.05, 0.10, 0.15, 0.20]\n", "\n", "res_abs = {k: [] for k in absolute_k_tops}\n", "res_rel = {k: [] for k in relative_k_tops}\n", "\n", "random.seed(4)\n", "np.random.seed(4)\n", "\n", "\n", "with warnings.catch_warnings():\n", " warnings.simplefilter(\"ignore\")\n", " for N in network_sizes:\n", " nodes_per_group = N // 2\n", " membership = [0 if i < nodes_per_group else 1 for i in range(N)]\n", " p_in = 16.0 / N\n", " p_out = 0.8 / N\n", " g = make_symmetric_sbm(p_in, p_out, 2, nodes_per_group, membership)\n", " for k in absolute_k_tops:\n", " if k >= N: \n", " res_abs[k].append(np.nan)\n", " else:\n", " score = dipole_moment(membership=membership, graph=g, ego_included=False, mode=\"out\", k_top=k)\n", " res_abs[k].append(score)\n", " for pct in relative_k_tops:\n", " k = max(3, int(N * pct)) \n", " if k >= N:\n", " res_rel[pct].append(np.nan)\n", " else:\n", " score = dipole_moment(membership=membership, graph=g, ego_included=False, mode=\"out\", k_top=k)\n", " res_rel[pct].append(score)\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14, 6), sharey=True)\n", "\n", "for idx, k in enumerate(absolute_k_tops):\n", " axes[0].plot(network_sizes, res_abs[k], marker='o', color=COLORS[idx], linewidth=2.5, markersize=8, label=f'k_top = {k}')\n", "axes[0].set_title('Fixed Absolute $k_{top}$', fontsize=14, fontweight='bold', pad=15)\n", "axes[0].set_xlabel('Network Size (N)', fontsize=12)\n", "axes[0].set_ylabel('Dipole Moment', fontsize=12)\n", "axes[0].set_xticks(network_sizes)\n", "axes[0].legend(title='Absolute count', frameon=True)\n", "for idx, pct in enumerate(relative_k_tops):\n", " axes[1].plot(network_sizes, res_rel[pct], marker='s', color=COLORS[idx], linewidth=2.5, markersize=8, label=f'k_top = {int(pct*100)}%')\n", "axes[1].set_title('Fixed Relative $k_{top}$ (%)', fontsize=14, fontweight='bold', pad=15)\n", "axes[1].set_xlabel('Network Size (N)', fontsize=12)\n", "axes[1].set_xticks(network_sizes)\n", "axes[1].legend(title='Percentage of nodes', frameon=True)\n", "fig.tight_layout()\n", "plt.suptitle('Impact of Influential Node Selection on Dipole Moment', fontsize=16, fontweight='bold', y=1.05)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b431f434", "metadata": {}, "source": [ "## References\n", "\n", "* Morales, Alfredo Jose, et al. \"Measuring political polarization: Twitter shows the two sides of Venezuela.\" Chaos: An Interdisciplinary Journal of Nonlinear Science 25.3 (2015)." ] } ], "metadata": { "kernelspec": { "display_name": "netseg", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.4" } }, "nbformat": 4, "nbformat_minor": 5 }