first commit

.idea/.gitignore

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+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

.idea/Graphs.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="FacetManager">
+    <facet type="django" name="Django">
+      <configuration>
+        <option name="rootFolder" value="$MODULE_DIR$" />
+        <option name="settingsModule" value="Graphs/settings.py" />
+        <option name="manageScript" value="$MODULE_DIR$/manage.py" />
+        <option name="environment" value="&lt;map/&gt;" />
+        <option name="doNotUseTestRunner" value="false" />
+        <option name="trackFilePattern" value="migrations" />
+      </configuration>
+    </facet>
+  </component>
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="TemplatesService">
+    <option name="TEMPLATE_CONFIGURATION" value="Django" />
+    <option name="TEMPLATE_FOLDERS">
+      <list>
+        <option value="$MODULE_DIR$/templates" />
+      </list>
+    </option>
+  </component>
+</module>

.idea/dataSources.xml

@@ -0,0 +1,12 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="DataSourceManagerImpl" format="xml" multifile-model="true">
+    <data-source source="LOCAL" name="db" uuid="0fa9eba3-0541-4f73-9641-aa1e25dcaa32">
+      <driver-ref>sqlite.xerial</driver-ref>
+      <synchronize>true</synchronize>
+      <jdbc-driver>org.sqlite.JDBC</jdbc-driver>
+      <jdbc-url>jdbc:sqlite:$PROJECT_DIR$/db.sqlite3</jdbc-url>
+      <working-dir>$ProjectFileDir$</working-dir>
+    </data-source>
+  </component>
+</project>

.idea/inspectionProfiles/Project_Default.xml

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+<component name="InspectionProjectProfileManager">
+  <profile version="1.0">
+    <option name="myName" value="Project Default" />
+    <inspection_tool class="Eslint" enabled="true" level="WARNING" enabled_by_default="true" />
+  </profile>
+</component>

.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

@@ -0,0 +1,7 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Poetry (Graphs) (2)" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Poetry (Graphs) (2)" project-jdk-type="Python SDK" />
+</project>

.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/Graphs.iml" filepath="$PROJECT_DIR$/.idea/Graphs.iml" />
+    </modules>
+  </component>
+</project>

.idea/ruff.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="RuffConfigService">
+    <option name="globalRuffExecutablePath" value="$USER_HOME$/.local/bin/ruff" />
+  </component>
+</project>

Graphs/asgi.py

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+"""
+ASGI config for Graphs project.
+
+It exposes the ASGI callable as a module-level variable named ``application``.
+
+For more information on this file, see
+https://docs.djangoproject.com/en/4.2/howto/deployment/asgi/
+"""
+
+import os
+
+from django.core.asgi import get_asgi_application
+
+os.environ.setdefault('DJANGO_SETTINGS_MODULE', 'Graphs.settings')
+
+application = get_asgi_application()

Graphs/settings.py

@@ -0,0 +1,125 @@
+"""
+Django settings for Graphs project.
+
+Generated by 'django-admin startproject' using Django 4.2.5.
+
+For more information on this file, see
+https://docs.djangoproject.com/en/4.2/topics/settings/
+
+For the full list of settings and their values, see
+https://docs.djangoproject.com/en/4.2/ref/settings/
+"""
+
+from pathlib import Path
+
+# Build paths inside the project like this: BASE_DIR / 'subdir'.
+BASE_DIR = Path(__file__).resolve().parent.parent
+
+
+# Quick-start development settings - unsuitable for production
+# See https://docs.djangoproject.com/en/4.2/howto/deployment/checklist/
+
+# SECURITY WARNING: keep the secret key used in production secret!
+SECRET_KEY = 'django-insecure-_d+6%0z5*@jzz-wkemhw-qe5$pa_jv)vq4&oc=(5$-n0#oosso'
+
+# SECURITY WARNING: don't run with debug turned on in production!
+DEBUG = True
+
+ALLOWED_HOSTS = []
+
+
+# Application definition
+
+INSTALLED_APPS = [
+    'django.contrib.admin',
+    'django.contrib.auth',
+    'django.contrib.contenttypes',
+    'django.contrib.sessions',
+    'django.contrib.messages',
+    'django.contrib.staticfiles',
+    'src.apps.SrcConfig',
+]
+
+MIDDLEWARE = [
+    'django.middleware.security.SecurityMiddleware',
+    'django.contrib.sessions.middleware.SessionMiddleware',
+    'django.middleware.common.CommonMiddleware',
+    'django.middleware.csrf.CsrfViewMiddleware',
+    'django.contrib.auth.middleware.AuthenticationMiddleware',
+    'django.contrib.messages.middleware.MessageMiddleware',
+    'django.middleware.clickjacking.XFrameOptionsMiddleware',
+]
+
+ROOT_URLCONF = 'Graphs.urls'
+
+TEMPLATES = [
+    {
+        'BACKEND': 'django.template.backends.django.DjangoTemplates',
+        'DIRS': [BASE_DIR / 'templates']
+        ,
+        'APP_DIRS': True,
+        'OPTIONS': {
+            'context_processors': [
+                'django.template.context_processors.debug',
+                'django.template.context_processors.request',
+                'django.contrib.auth.context_processors.auth',
+                'django.contrib.messages.context_processors.messages',
+            ],
+        },
+    },
+]
+
+WSGI_APPLICATION = 'Graphs.wsgi.application'
+
+
+# Database
+# https://docs.djangoproject.com/en/4.2/ref/settings/#databases
+
+DATABASES = {
+    'default': {
+        'ENGINE': 'django.db.backends.sqlite3',
+        'NAME': BASE_DIR / 'db.sqlite3',
+    }
+}
+
+
+# Password validation
+# https://docs.djangoproject.com/en/4.2/ref/settings/#auth-password-validators
+
+AUTH_PASSWORD_VALIDATORS = [
+    {
+        'NAME': 'django.contrib.auth.password_validation.UserAttributeSimilarityValidator',
+    },
+    {
+        'NAME': 'django.contrib.auth.password_validation.MinimumLengthValidator',
+    },
+    {
+        'NAME': 'django.contrib.auth.password_validation.CommonPasswordValidator',
+    },
+    {
+        'NAME': 'django.contrib.auth.password_validation.NumericPasswordValidator',
+    },
+]
+
+
+# Internationalization
+# https://docs.djangoproject.com/en/4.2/topics/i18n/
+
+LANGUAGE_CODE = 'en-us'
+
+TIME_ZONE = 'UTC'
+
+USE_I18N = True
+
+USE_TZ = True
+
+
+# Static files (CSS, JavaScript, Images)
+# https://docs.djangoproject.com/en/4.2/howto/static-files/
+
+STATIC_URL = 'static/'
+
+# Default primary key field type
+# https://docs.djangoproject.com/en/4.2/ref/settings/#default-auto-field
+
+DEFAULT_AUTO_FIELD = 'django.db.models.BigAutoField'

Graphs/urls.py

@@ -0,0 +1,11 @@
+from django.contrib import admin
+from django.urls import path
+
+from src.views import IndexView, TypeView, InfoView
+
+urlpatterns = [
+    path('admin/', admin.site.urls),
+    path('', IndexView.as_view(), name='index'),
+    path('<str:type>/', TypeView.as_view(), name='type'),
+    path('<str:type>/<int:info>/', InfoView.as_view(), name='info'),
+]

Graphs/wsgi.py

@@ -0,0 +1,16 @@
+"""
+WSGI config for Graphs project.
+
+It exposes the WSGI callable as a module-level variable named ``application``.
+
+For more information on this file, see
+https://docs.djangoproject.com/en/4.2/howto/deployment/wsgi/
+"""
+
+import os
+
+from django.core.wsgi import get_wsgi_application
+
+os.environ.setdefault('DJANGO_SETTINGS_MODULE', 'Graphs.settings')
+
+application = get_wsgi_application()

manage.py

@@ -0,0 +1,22 @@
+#!/usr/bin/env python
+"""Django's command-line utility for administrative tasks."""
+import os
+import sys
+
+
+def main():
+    """Run administrative tasks."""
+    os.environ.setdefault('DJANGO_SETTINGS_MODULE', 'Graphs.settings')
+    try:
+        from django.core.management import execute_from_command_line
+    except ImportError as exc:
+        raise ImportError(
+            "Couldn't import Django. Are you sure it's installed and "
+            "available on your PYTHONPATH environment variable? Did you "
+            "forget to activate a virtual environment?"
+        ) from exc
+    execute_from_command_line(sys.argv)
+
+
+if __name__ == '__main__':
+    main()

poetry.lock

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+# This file is automatically @generated by Poetry 1.8.3 and should not be changed by hand.
+
+[[package]]
+name = "asgiref"
+version = "3.8.1"
+description = "ASGI specs, helper code, and adapters"
+optional = false
+python-versions = ">=3.8"
+files = [
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+    {file = "asgiref-3.8.1.tar.gz", hash = "sha256:c343bd80a0bec947a9860adb4c432ffa7db769836c64238fc34bdc3fec84d590"},
+]
+
+[package.dependencies]
+typing-extensions = {version = ">=4", markers = "python_version < \"3.11\""}
+
+[package.extras]
+tests = ["mypy (>=0.800)", "pytest", "pytest-asyncio"]
+
+[[package]]
+name = "django"
+version = "4.2.20"
+description = "A high-level Python web framework that encourages rapid development and clean, pragmatic design."
+optional = false
+python-versions = ">=3.8"
+files = [
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+    {file = "Django-4.2.20.tar.gz", hash = "sha256:92bac5b4432a64532abb73b2ac27203f485e40225d2640a7fbef2b62b876e789"},
+]
+
+[package.dependencies]
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+sqlparse = ">=0.3.1"
+tzdata = {version = "*", markers = "sys_platform == \"win32\""}
+
+[package.extras]
+argon2 = ["argon2-cffi (>=19.1.0)"]
+bcrypt = ["bcrypt"]
+
+[[package]]
+name = "networkx"
+version = "3.4.2"
+description = "Python package for creating and manipulating graphs and networks"
+optional = false
+python-versions = ">=3.10"
+files = [
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+default = ["matplotlib (>=3.7)", "numpy (>=1.24)", "pandas (>=2.0)", "scipy (>=1.10,!=1.11.0,!=1.11.1)"]
+developer = ["changelist (==0.5)", "mypy (>=1.1)", "pre-commit (>=3.2)", "rtoml"]
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+extra = ["lxml (>=4.6)", "pydot (>=3.0.1)", "pygraphviz (>=1.14)", "sympy (>=1.10)"]
+test = ["pytest (>=7.2)", "pytest-cov (>=4.0)"]
+
+[[package]]
+name = "numpy"
+version = "1.26.4"
+description = "Fundamental package for array computing in Python"
+optional = false
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+files = [
+    {file = "typing_extensions-4.12.2-py3-none-any.whl", hash = "sha256:04e5ca0351e0f3f85c6853954072df659d0d13fac324d0072316b67d7794700d"},
+    {file = "typing_extensions-4.12.2.tar.gz", hash = "sha256:1a7ead55c7e559dd4dee8856e3a88b41225abfe1ce8df57b7c13915fe121ffb8"},
+]
+
+[[package]]
+name = "tzdata"
+version = "2025.1"
+description = "Provider of IANA time zone data"
+optional = false
+python-versions = ">=2"
+files = [
+    {file = "tzdata-2025.1-py2.py3-none-any.whl", hash = "sha256:7e127113816800496f027041c570f50bcd464a020098a3b6b199517772303639"},
+    {file = "tzdata-2025.1.tar.gz", hash = "sha256:24894909e88cdb28bd1636c6887801df64cb485bd593f2fd83ef29075a81d694"},
+]
+
+[metadata]
+lock-version = "2.0"
+python-versions = "^3.10"
+content-hash = "cf0c35bc75496d42ca7e5bae99bc0636ca80a3235326d52974de95a1169f310c"

pyproject.toml

@@ -0,0 +1,17 @@
+[tool.poetry]
+name = "graphs"
+version = "0.1.0"
+description = ""
+authors = ["KUB0570 <nikola.kubeczkova.st@vsb.cz>"]
+readme = "README.md"
+
+[tool.poetry.dependencies]
+python = "^3.10"
+django = "^4.2.5"
+numpy = "^1.26.3"
+networkx = "^3.2.1"
+
+
+[build-system]
+requires = ["poetry-core"]
+build-backend = "poetry.core.masonry.api"

src/admin.py

@@ -0,0 +1,24 @@
+# from django.contrib import admin
+# from src.models import Graph, Vertex, Arc
+#
+#
+# @admin.register(Graph)
+# class GraphAdmin(admin.ModelAdmin):
+#     list_display = [
+#         "graph_type",
+#         "antimagic",
+#         "strong",
+#         "vertex",
+#         "arc"
+#     ]
+#
+#
+# @admin.register(Vertex)
+# class VertexAdmin(admin.ModelAdmin):
+#     list_display = ["graph", "in_weight", "out_weight", "label"]
+#
+#
+# @admin.register(Arc)
+# class ArcAdmin(admin.ModelAdmin):
+#     list_display = ["vertex_in", "vertex_out", "label"]
+#

src/apps.py

@@ -0,0 +1,6 @@
+from django.apps import AppConfig
+
+
+class SrcConfig(AppConfig):
+    default_auto_field = 'django.db.models.BigAutoField'
+    name = 'src'

src/management/commands/core.py

@@ -0,0 +1,21 @@
+from src.models import Arc
+
+
+def create_arc(vertex_in, vertex_out, arc_num, label=None):
+    Arc.objects.create(
+        vertex_in=vertex_in,
+        vertex_out=vertex_out,
+        label=label
+    )
+    return arc_num+1
+
+
+def get_arc(first, second, n, idx):
+    if Arc.objects.filter(vertex_out=first, vertex_in=second).exists():
+        arc = Arc.objects.get(vertex_out=first, vertex_in=second)
+    else:
+        arc = Arc.objects.get(vertex_out=second, vertex_in=first)
+    first = second
+    arc.label = n + idx
+    arc.save()
+    return first

src/management/commands/create_cycle.py

@@ -0,0 +1,116 @@
+from django.core.management.base import BaseCommand
+from django.db import transaction
+
+from src.management.commands.default import delete_graphs
+from src.management.commands.core import create_arc, get_arc
+from src.models import Graph, Vertex, Arc
+import time
+
+
+class Command(BaseCommand):
+    def add_arguments(self, parser):
+        parser.add_argument('min', type=int)
+        parser.add_argument('max', type=int)
+
+    def handle(self, *args, **options):
+        delete_graphs(Graph.CYCLE)
+
+        min = options['min']
+        max = options['max']
+
+        s_time = time.time()
+        for n in range(min, max + 1):
+            start_time = time.time()
+            self.create_cycle(n)
+            end_time = time.time()
+            elapsed_time = end_time - start_time
+
+            print("Čas trvání", n, "vrcholů:", elapsed_time, "sekund")
+
+        e_time = time.time()
+        eed_time = e_time - s_time
+
+        print("Celkový čas trvání:", eed_time, "sekund")
+
+    def create_cycle(self, n):
+        with transaction.atomic():
+            for i in range(2 ** n):
+                binary_number = bin(i)[2:].zfill(n)
+                if binary_number[:2] not in ['01', '10']:
+                    continue
+                graph = self.create_graph(binary_number)
+                vertex = None
+                vertices = Vertex.objects.filter(graph=graph)
+                vertices_list = []
+
+                for num, v in enumerate(vertices):
+                    vertices_list.append(v)
+                    if v.max_degree == 2 and not vertex:
+                        vertex = v
+
+                right = vertices_list.index(vertex)
+                left = vertices_list.index(vertex)-1
+                section = True
+
+                right_ark = vertices_list[right % n]
+                left_ark = vertices_list[right % n]
+                for idx in range(n):
+                    location = (right % n) if section else left
+                    now = vertices_list[location]
+                    now.index = idx + 1
+                    now.save()
+                    if section:
+                        if right_ark != now:
+                            right_ark = get_arc(first=right_ark, second=now, n=n, idx=idx)
+                        right += 1
+                    else:
+                        left_ark = get_arc(first=left_ark, second=now, n=n, idx=idx)
+                        left -= 1
+
+                    if now.max_degree == 2:
+                        section = not section
+
+                if Arc.objects.filter(vertex_out=right_ark, vertex_in=left_ark).exists():
+                    arc = Arc.objects.get(vertex_out=right_ark, vertex_in=left_ark)
+                else:
+                    arc = Arc.objects.get(vertex_out=left_ark, vertex_in=right_ark)
+                arc.label = n + n
+                arc.save()
+
+                sorted_vertices = sorted(vertices_list, key=lambda vertex: (vertex.max_degree, vertex.index))
+                for num, v in enumerate(sorted_vertices):
+                    v.label = num + 1
+                    v.save()
+
+                graph.update()
+
+    @staticmethod
+    def create_graph(binary_number):
+        prev_vertex = None
+        first_vertex = None
+        first_bit = None
+        arc_num = 1
+        graph = Graph.objects.create(
+            graph_type=Graph.CYCLE,
+            binary=binary_number,
+        )
+
+        for j, bit in enumerate(binary_number):
+            vertex = Vertex.objects.create(graph=graph, label=j + 1)
+            if prev_vertex:
+                arc_num = create_arc(
+                    vertex_in=prev_vertex if bit == '0' else vertex,
+                    vertex_out=vertex if bit == '0' else prev_vertex,
+                    arc_num=arc_num
+                )
+            else:
+                first_vertex = vertex
+                first_bit = bit
+            prev_vertex = vertex
+        create_arc(
+            vertex_in=prev_vertex if first_bit == '0' else first_vertex,
+            vertex_out=first_vertex if first_bit == '0' else prev_vertex,
+            arc_num=arc_num
+        )
+        return graph
+

src/management/commands/create_graph.py

@@ -0,0 +1,31 @@
+from django.core.management.base import BaseCommand
+
+from src.management.commands.default import (
+    delete_graphs,
+    GRAPHS
+)
+
+
+class Command(BaseCommand):
+    def add_arguments(self, parser):
+        parser.add_argument('graph', nargs='+', type=str)
+        parser.add_argument('--min', type=int, default=3)
+        parser.add_argument('--max', type=int, default=5)
+
+    def handle(self, *args, **options):
+        delete_graphs("all")
+        graphs = options['graph']
+        min = options['min']
+        max = options['max']
+
+        component = None
+        for graph in graphs:
+            component = GRAPHS[graph](component)
+
+        for n in range(min, max + 1):
+            for i in range(2 ** (n - 1)):
+                binary_number = bin(i)[2:].zfill(n)
+
+                if i >= 2 ** (n - 1) / 2 - 1:
+                    break
+

src/management/commands/create_path.py

@@ -0,0 +1,108 @@
+from django.core.management.base import BaseCommand
+from django.db import transaction
+from django.db.models import Count, Max, F, OuterRef, Subquery, ExpressionWrapper, IntegerField
+from django.db.models.functions import Coalesce
+
+from src.management.commands.default import delete_graphs
+from src.management.commands.core import create_arc
+from src.models import Graph, Vertex, Arc
+import time
+
+
+class Command(BaseCommand):
+    def add_arguments(self, parser):
+        parser.add_argument('min', type=int)
+        parser.add_argument('max', type=int)
+
+    def handle(self, *args, **options):
+        delete_graphs("all")
+
+        min = options['min']
+        max = options['max']
+
+        s_time = time.time()
+        for n in range(min, max + 1):
+            start_time = time.time()
+            self.create_path(n)
+            end_time = time.time()
+            elapsed_time = end_time - start_time
+
+            print("Čas trvání", n, "vrcholů:", elapsed_time, "sekund")
+        e_time = time.time()
+        eed_time = e_time - s_time
+
+        print("Celkový čas trvání:", eed_time, "sekund")
+
+    def create_path(self, n):
+        with transaction.atomic():
+            for i in range(2 ** (n-1)):
+                binary_number = bin(i)[2:].zfill(n)
+                graph = self.create_graph(n, binary_number)
+
+                arc_count_in_subquery = (
+                    Arc.objects
+                    .filter(vertex_in=OuterRef('pk'))
+                    .values('vertex_in')
+                    .annotate(arc_count_in=Count('label'))
+                    .values('arc_count_in')
+                    .order_by('-arc_count_in')
+                    [:1]
+                )
+
+                arc_count_out_subquery = (
+                    Arc.objects
+                    .filter(vertex_out=OuterRef('pk'))
+                    .values('vertex_out')
+                    .annotate(arc_count_out=Count('label'))
+                    .values('arc_count_out')
+                    .order_by('-arc_count_out')
+                    [:1]
+                )
+
+                # Získání maximálního počtu arků pro každý vrchol
+                vertices = (
+                    Vertex.objects
+                    .filter(graph=graph)
+                    .annotate(arc_count_in=Coalesce(Subquery(arc_count_in_subquery, output_field=IntegerField()), 0))
+                    .annotate(arc_count_out=Coalesce(Subquery(arc_count_out_subquery, output_field=IntegerField()), 0))
+                    .annotate(max_arc_count=ExpressionWrapper(
+                        Max(F('arc_count_in'), F('arc_count_out')),
+                        output_field=IntegerField()
+                    ))
+                    .order_by('max_arc_count', 'label')
+                )
+                for num, v in enumerate(vertices):
+                    v.label = num + 1
+                    v.save()
+                graph.update()
+
+                if i >= 2 ** (n - 1) / 2 - 1:
+                    break
+
+    @staticmethod
+    def create_graph(n, binary_number):
+        prev_vertex = None
+        arc_num = 0
+        graph = Graph.objects.create(
+            graph_type=Graph.PATH,
+            binary=binary_number[1:],
+        )
+
+        for j, bit in enumerate(binary_number):
+            vertex = Vertex.objects.create(graph=graph, index=j + 1)
+            if prev_vertex:
+                arc_num = create_arc(
+                    vertex_in=prev_vertex if bit == '0' else vertex,
+                    vertex_out=vertex if bit == '0' else prev_vertex,
+                    arc_num=arc_num,
+                    label=n + arc_num
+                )
+            prev_vertex = vertex
+        return graph
+
+
+        # for i in range(2 ** (n - 1)):
+        #     binary_number = bin(i)[2:].zfill(n)
+        #
+        #     if i >= 2 ** (n - 1) / 2 - 1:
+        #         break

src/management/commands/create_tadpole.py

@@ -0,0 +1,97 @@
+from django.core.management.base import BaseCommand
+from django.db import transaction
+
+from src.management.commands.default import delete_graphs, count_change
+from src.management.commands.core import create_arc, get_arc
+from src.models import Graph, Vertex, Arc
+
+
+class Command(BaseCommand):
+    def add_arguments(self, parser):
+        parser.add_argument('min_n', type=int)
+        parser.add_argument('max_n', type=int)
+        parser.add_argument('min_m', type=int)
+        parser.add_argument('max_m', type=int)
+
+    def handle(self, *args, **options):
+        delete_graphs("all")
+
+        min_n = options['min_n']
+        max_n = options['max_n']
+        min_m = options['min_m']
+        max_m = options['max_m']
+        for n in range(min_n, max_n + 1):
+            for m in range(min_m, max_m + 1):
+                self.create_tadpole(n, m)
+
+    def create_tadpole(self, n, m):
+        with transaction.atomic():
+            for i in range(1, (2 ** n)):
+                for j in range(1, (2 ** m)):
+                    binary_number_n = bin(i)[2:].zfill(n)
+                    binary_number_m = bin(j)[2:].zfill(m)
+
+                    print(binary_number_n, binary_number_m)
+                    graph = self.create_graph(binary_number_n, binary_number_m)
+                    if graph:
+                        graph.update()
+
+    def create_graph(self, binary_number_n, binary_number_m):
+        length = len(binary_number_n+binary_number_m)
+        graph = Graph.objects.create(
+            graph_type=Graph.TADPOLE,
+            binary=binary_number_n + binary_number_m,
+        )
+
+        a = count_change(binary_number_n+binary_number_n[0]) + count_change(binary_number_m)
+        if binary_number_n[0] == binary_number_m[0] and binary_number_n[-1] != binary_number_m[0]:
+            return self.max_degree_3(binary_number_n, binary_number_m, graph, length, a)
+        else:
+            return self.max_degree_2()
+
+    @staticmethod
+    def max_degree_3(binary_number_n, binary_number_m, graph, length, a):
+        arc_num = 1
+        labeling = [i for i in range(1, length + 1)]
+        label = length - a + 1
+        labeling.remove(label)
+        prev_vertex = vertex3 = Vertex.objects.create(graph=graph, label=label)
+        for j, bit in enumerate(binary_number_n):
+            vertex = vertex3 if j == len(binary_number_n) - 1 else Vertex.objects.create(graph=graph)
+            arc_num = create_arc(
+                vertex_in=prev_vertex if bit == '0' else vertex,
+                vertex_out=vertex if bit == '0' else prev_vertex,
+                arc_num=arc_num,
+                label=arc_num + length
+            )
+            prev_vertex = vertex
+
+        prev_vertex = vertex3
+        for j, bit in enumerate(binary_number_m):
+            vertex = Vertex.objects.create(graph=graph)
+            arc_num = create_arc(
+                vertex_in=prev_vertex if bit == '0' else vertex,
+                vertex_out=vertex if bit == '0' else prev_vertex,
+                arc_num=arc_num,
+                label=arc_num + length
+            )
+            prev_vertex = vertex
+
+        vertices = Vertex.objects.filter(graph=graph)
+        for vertex in vertices:
+            if vertex.max_degree == 2:
+                label = min([x for x in labeling if x > (length - a + 1)])
+                labeling.remove(label)
+                vertex.label = label
+                vertex.save()
+            if vertex.max_degree == 1:
+                label = min([x for x in labeling if x < (length - a + 1)])
+                labeling.remove(label)
+                vertex.label = label
+                vertex.save()
+        return graph
+
+    @staticmethod
+    def max_degree_2():
+        return None
+

src/management/commands/default.py

@@ -0,0 +1,55 @@
+from src.management.commands.path import path
+from src.models import Graph, Vertex, Arc
+
+
+def delete_graphs(type_of_graph):
+    if type_of_graph == "all":
+        Graph.objects.all().delete()
+        Vertex.objects.all().delete()
+        Arc.objects.all().delete()
+    else:
+        Graph.objects.filter(graph_type=type_of_graph).delete()
+        Vertex.objects.filter(graph__graph_type=type_of_graph).delete()
+        Arc.objects.filter(vertex_in__graph__graph_type=type_of_graph).delete()
+
+
+def count_change(binary_number):
+    change = 0
+    actual_bit = binary_number[0]
+
+    for bit in binary_number:
+        if bit != actual_bit:
+            change += 1
+            actual_bit = bit
+    return change
+
+
+def create_path(n, binary_number, graph=None):
+    if graph:
+        return path()
+    return print("new path")
+
+
+def create_cycle(graph=None):
+    if graph:
+        return print("cycle")
+    return print("new cycle")
+
+
+# def create_tadpole(graph=None):
+#     if graph:
+#         return print("tadpole")
+#     return print("new tadpole")
+
+
+GRAPHS = {
+    Graph.CYCLE: create_cycle,
+    Graph.PATH: create_path,
+    # Graph.TADPOLE: create_tadpole,
+}
+
+
+# def unite_graph(function, graph=None):
+#     if graph:
+#         return function(graph)
+#     return function()

src/management/commands/path.py

@@ -0,0 +1,74 @@
+from django.db import transaction
+from django.db.models import OuterRef, Count, Subquery, ExpressionWrapper, IntegerField, F, Max
+from django.db.models.functions import Coalesce
+
+from src.management.commands.core import create_arc
+from src.models import Arc, Vertex, Graph
+
+
+def path(n, binary_number):
+    with transaction.atomic():
+        graph = create_path(n, binary_number)
+
+        arc_count_in_subquery = (
+            Arc.objects
+            .filter(vertex_in=OuterRef('pk'))
+            .values('vertex_in')
+            .annotate(arc_count_in=Count('label'))
+            .values('arc_count_in')
+            .order_by('-arc_count_in')
+            [:1]
+        )
+
+        arc_count_out_subquery = (
+            Arc.objects
+            .filter(vertex_out=OuterRef('pk'))
+            .values('vertex_out')
+            .annotate(arc_count_out=Count('label'))
+            .values('arc_count_out')
+            .order_by('-arc_count_out')
+            [:1]
+        )
+
+        # Získání maximálního počtu arků pro každý vrchol
+        vertices = (
+            Vertex.objects
+            .filter(graph=graph)
+            .annotate(arc_count_in=Coalesce(Subquery(arc_count_in_subquery, output_field=IntegerField()), 0))
+            .annotate(arc_count_out=Coalesce(Subquery(arc_count_out_subquery, output_field=IntegerField()), 0))
+            .annotate(max_arc_count=ExpressionWrapper(
+                Max(F('arc_count_in'), F('arc_count_out')),
+                output_field=IntegerField()
+            ))
+            .order_by('max_arc_count', 'label')
+        )
+        for num, v in enumerate(vertices):
+            v.label = num + 1
+            v.save()
+        graph.update()
+
+
+def create_path(n, binary_number, graph=None):
+    prev_vertex = None
+    arc_num = 0
+    if graph:
+        graph.components += 1
+        graph.graph_type = Graph.UNITED
+        graph.save()
+    else:
+        graph = Graph.objects.create(
+            graph_type=Graph.PATH,
+            binary=binary_number[1:],
+        )
+
+    for j, bit in enumerate(binary_number):
+        vertex = Vertex.objects.create(graph=graph, index=j + 1)
+        if prev_vertex:
+            arc_num = create_arc(
+                vertex_in=prev_vertex if bit == '0' else vertex,
+                vertex_out=vertex if bit == '0' else prev_vertex,
+                arc_num=arc_num,
+                label=n + arc_num
+            )
+        prev_vertex = vertex
+    return graph

src/management/commands/visualizate.py

@@ -0,0 +1,67 @@
+from django.core.management.base import BaseCommand
+
+import numpy as np
+import networkx as nx
+import matplotlib.pyplot as plt
+from src.models import Graph, Vertex, Arc
+
+
+class Command(BaseCommand):
+    def add_arguments(self, parser):
+        parser.add_argument('id', type=int)
+        # parser.add_argument('graph_type', type=str)
+        # parser.add_argument('binary', type=str)
+
+    def handle(self, *args, **options):
+        id = options['id']
+        # graph_type = options['graph_type']
+        # binary = options['binary']
+
+        graph = Graph.objects.filter(
+            # graph_type=graph_type, binary=binary
+            id=id
+        ).first()
+
+        if not graph:
+            return
+
+        vertices = Vertex.objects.filter(graph=graph)
+        arcs = Arc.objects.filter(vertex_in__graph=graph)
+
+        adjacency_matrix = np.zeros((len(vertices), len(vertices)))
+
+        for arc in arcs:
+            adjacency_matrix[arc.vertex_in.index - 1][arc.vertex_out.index - 1] = 1
+            adjacency_matrix[arc.vertex_out.index - 1][arc.vertex_in.index - 1] = 1
+
+        # Create a degree matrix
+        degree_matrix = np.diag(np.sum(adjacency_matrix, axis=1))
+
+        # Create Laplacian matrix
+        laplacian_matrix = degree_matrix - adjacency_matrix
+
+        # Calculate eigenvalues and eigenvectors of the Laplacian matrix
+        eigenvalues, eigenvectors = np.linalg.eigh(laplacian_matrix)
+
+        # Get the second smallest eigenvector (the smallest is constant)
+        second_smallest_eigenvector = eigenvectors[:, 1]
+
+        # Use the eigenvector values as x, y coordinates for visualization
+        x_coordinates = second_smallest_eigenvector.real
+        y_coordinates = eigenvectors[:, 2].real  # You can choose a different eigenvector if needed
+
+        # Visualize the graph using matplotlib
+        plt.scatter(x_coordinates, y_coordinates, c='blue', s=100)
+        for i, vertex in enumerate(vertices):
+            plt.text(x_coordinates[i], y_coordinates[i], str(vertex.index))
+
+        # Draw lines between connected vertices
+        for arc in arcs:
+            index_in = arc.vertex_in.index - 1
+            index_out = arc.vertex_out.index - 1
+            plt.plot([x_coordinates[index_in], x_coordinates[index_out]],
+                     [y_coordinates[index_in], y_coordinates[index_out]],
+                     color='gray', linestyle='-', linewidth=1)
+
+        plt.title('Graph Visualization with Edges using Laplacian Eigenmaps')
+        plt.show()

src/migrations/0001_initial.py

@@ -0,0 +1,45 @@
+# Generated by Django 4.2.5 on 2024-01-29 16:19
+
+from django.db import migrations, models
+import django.db.models.deletion
+
+
+class Migration(migrations.Migration):
+
+    initial = True
+
+    dependencies = [
+    ]
+
+    operations = [
+        migrations.CreateModel(
+            name='Graph',
+            fields=[
+                ('id', models.BigAutoField(auto_created=True, primary_key=True, serialize=False, verbose_name='ID')),
+                ('graph_type', models.CharField(choices=[('cycle', 'cycle'), ('path', 'path')], max_length=8)),
+                ('arcs', models.CharField(blank=True, max_length=128, null=True)),
+                ('arc_binary', models.IntegerField(blank=True, null=True)),
+                ('antimagic', models.BooleanField(default=False)),
+                ('super', models.BooleanField(default=False)),
+                ('strict', models.BooleanField(default=False)),
+            ],
+        ),
+        migrations.CreateModel(
+            name='Vertex',
+            fields=[
+                ('id', models.BigAutoField(auto_created=True, primary_key=True, serialize=False, verbose_name='ID')),
+                ('index', models.IntegerField(blank=True, default=0, null=True)),
+                ('label', models.IntegerField(blank=True, default=0, null=True)),
+                ('graph', models.ForeignKey(blank=True, null=True, on_delete=django.db.models.deletion.CASCADE, related_name='vertices', to='src.graph')),
+            ],
+        ),
+        migrations.CreateModel(
+            name='Arc',
+            fields=[
+                ('id', models.BigAutoField(auto_created=True, primary_key=True, serialize=False, verbose_name='ID')),
+                ('label', models.IntegerField(blank=True, default=0, null=True)),
+                ('vertex_in', models.ForeignKey(on_delete=django.db.models.deletion.CASCADE, related_name='in_arcs', to='src.vertex')),
+                ('vertex_out', models.ForeignKey(on_delete=django.db.models.deletion.CASCADE, related_name='out_arcs', to='src.vertex')),
+            ],
+        ),
+    ]

src/migrations/0002_alter_graph_arc_binary.py

@@ -0,0 +1,18 @@
+# Generated by Django 4.2.5 on 2024-01-29 18:43
+
+from django.db import migrations, models
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('src', '0001_initial'),
+    ]
+
+    operations = [
+        migrations.AlterField(
+            model_name='graph',
+            name='arc_binary',
+            field=models.CharField(blank=True, max_length=2048, null=True),
+        ),
+    ]

src/migrations/0003_rename_arc_binary_graph_binary_remove_graph_arcs.py

@@ -0,0 +1,22 @@
+# Generated by Django 4.2.5 on 2024-01-29 18:46
+
+from django.db import migrations
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('src', '0002_alter_graph_arc_binary'),
+    ]
+
+    operations = [
+        migrations.RenameField(
+            model_name='graph',
+            old_name='arc_binary',
+            new_name='binary',
+        ),
+        migrations.RemoveField(
+            model_name='graph',
+            name='arcs',
+        ),
+    ]

src/migrations/0004_graph_components.py

@@ -0,0 +1,18 @@
+# Generated by Django 4.2.5 on 2024-03-05 10:52
+
+from django.db import migrations, models
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('src', '0003_rename_arc_binary_graph_binary_remove_graph_arcs'),
+    ]
+
+    operations = [
+        migrations.AddField(
+            model_name='graph',
+            name='components',
+            field=models.IntegerField(default=1),
+        ),
+    ]

src/migrations/0005_rename_strict_graph_strong_remove_graph_super_and_more.py

@@ -0,0 +1,27 @@
+# Generated by Django 4.2.5 on 2024-04-25 07:11
+
+from django.db import migrations, models
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('src', '0004_graph_components'),
+    ]
+
+    operations = [
+        migrations.RenameField(
+            model_name='graph',
+            old_name='strict',
+            new_name='strong',
+        ),
+        migrations.RemoveField(
+            model_name='graph',
+            name='super',
+        ),
+        migrations.AlterField(
+            model_name='graph',
+            name='graph_type',
+            field=models.CharField(choices=[('cycle', 'cycle'), ('path', 'path'), ('tadpole', 'tadpole'), ('united', 'united')], max_length=8),
+        ),
+    ]

src/models.py

@@ -0,0 +1,100 @@
+from django.db import models
+
+
+class Graph(models.Model):
+    CYCLE = "cycle"
+    PATH = "path"
+    TADPOLE = "tadpole"
+    UNITED = "united"
+
+    GRAPHS = (
+        (CYCLE, "cycle"),
+        (PATH, "path"),
+        (TADPOLE, "tadpole"),
+        (UNITED, "united")
+    )
+
+    graph_type = models.CharField(max_length=8, choices=GRAPHS)
+    binary = models.CharField(max_length=2048, blank=True, null=True)
+    components = models.IntegerField(default=1)
+
+    antimagic = models.BooleanField(default=False)
+    strong = models.BooleanField(default=False)
+
+    @property
+    def vertex_count(self):
+        return self.vertices.filter(graph=self).count()
+
+    @property
+    def arc_count(self):
+        return self.vertices.filter(in_arcs__isnull=False).count()
+        # return Arc.objects.filter(vertex_in__graph=self).count()
+
+    def get_properties(self):
+        return {
+            'vertex': self.vertex_count,
+            'arc': self.arc_count,
+        }
+
+    def update(self):
+        vertices = self.vertices.all()
+        in_weight = []
+        out_weight = []
+        labels = []
+
+        for vertex in vertices:
+            labels.append(vertex.label)
+            in_weight.append(vertex.in_weight)
+            out_weight.append(vertex.out_weight)
+
+        self.antimagic = len(in_weight) == len(set(in_weight)) and len(out_weight) == len(set(out_weight))
+        self.strong = len(in_weight + out_weight) == len(set(in_weight + out_weight))
+        self.save()
+
+    def __str__(self):
+        return f"{self.graph_type}, {self.vertex_count};{self.arc_count}"
+
+
+class Vertex(models.Model):
+    graph = models.ForeignKey(Graph, on_delete=models.CASCADE, blank=True, null=True, related_name="vertices")
+    index = models.IntegerField(default=0, null=True, blank=True)
+    label = models.IntegerField(default=0, null=True, blank=True)
+
+    @property
+    def max_degree(self):
+        sum_in = self.in_arcs.all().count()
+        sum_out = self.out_arcs.all().count()
+        # in_arcs = Arc.objects.filter(vertex_in=self)
+        # sum_in = sum(1 for _ in in_arcs)
+        # out_arcs = Arc.objects.filter(vertex_out=self)
+        # sum_out = sum(1 for _ in out_arcs)
+        return sum_in if sum_in > sum_out else sum_out
+
+    @property
+    def in_weight(self):
+        in_arcs = Arc.objects.filter(vertex_in=self)
+        return self.label + sum(arc.label for arc in in_arcs)
+
+    @property
+    def out_weight(self):
+        out_arcs = Arc.objects.filter(vertex_out=self)
+        return self.label + sum(arc.label for arc in out_arcs)
+
+    def get_properties(self):
+        return {
+            'in_weight': self.in_weight,
+            'out_weight': self.out_weight,
+            'max_degree': self.max_degree,
+        }
+
+    def __str__(self):
+        return f"{self.id}, {self.label}, {self.index}"
+
+
+class Arc(models.Model):
+    vertex_in = models.ForeignKey(Vertex, on_delete=models.CASCADE, related_name='in_arcs')
+    vertex_out = models.ForeignKey(Vertex, on_delete=models.CASCADE, related_name='out_arcs')
+    label = models.IntegerField(default=0, null=True, blank=True)
+
+    def __str__(self):
+        return f"{self.id}, ({self.vertex_in.label}, {self.vertex_out.label}) {self.label}"

src/tests.py

@@ -0,0 +1,3 @@
+from django.test import TestCase
+
+# Create your tests here.

src/views.py

@@ -0,0 +1,37 @@
+from django.views.generic import TemplateView
+
+from src.models import Graph, Vertex, Arc
+
+
+class IndexView(TemplateView):
+    template_name = "index.html"
+
+    def get_context_data(self):
+        return {
+            "graphs": [Graph.CYCLE, Graph.PATH],
+        }
+
+
+class TypeView(TemplateView):
+    template_name = "type.html"
+
+    def get_context_data(self, **kwargs):
+        return {
+            "kwargs": kwargs,
+            "graphs": Graph.objects.filter(
+                graph_type=kwargs.get("type")
+            ).order_by("binary"),
+        }
+
+
+class InfoView(TemplateView):
+    template_name = "info.html"
+
+    def get_context_data(self, **kwargs):
+        graph = Graph.objects.get(id=kwargs.get("info"))
+        return {
+            "arcs": Arc.objects.filter(vertex_in__graph=graph).order_by("id"),
+            "vertices": Vertex.objects.filter(graph=graph).order_by("id"),
+            "graph": graph,
+            "type_name": graph.graph_type,
+        }

templates/index.html

@@ -0,0 +1,14 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title>Beeebooo</title>
+</head>
+<body>
+{% for graph in graphs %}
+<div>
+    <a href="{% url "type" type=graph %}">{{ graph }}</a>
+</div>
+{% endfor %}
+</body>
+</html>

templates/info.html

@@ -0,0 +1,98 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title>Title</title>
+</head>
+<body>
+<h3>INFO</h3>
+<table>
+  <tr>
+    <th>Vrcholy</th>
+    <th>Arky</th>
+    <th>Binary</th>
+      
+    <th>Antimagic</th>
+    <th>Super</th>
+    <th>Strict</th>
+  </tr>
+  <tr>
+    <td>{{ graph.get_properties.vertex }}</td>
+    <td>{{ graph.get_properties.arc }}</td>
+    <td>{{ graph.binary }}</td>
+  
+    <td>{% if graph.antimagic %}{{ graph.antimagic }}{% else %}---{% endif %}</td>
+    <td>{% if graph.strong %}{{ graph.strong }}{% else %}---{% endif %}</td>
+  </tr>
+</table>
+
+<br>
+
+{% for arc in arcs %}
+    {% if forloop.last and type_name == "cyklus" %}
+        {% if arc.vertex_out.id > arc.vertex_in.id %}
+            ({{ arc.vertex_out.label }})--{{ arc.label }}-->({{ arc.vertex_in.label }})
+        {% else %}
+            ({{ arc.vertex_in.label }})<--{{ arc.label }}--({{ arc.vertex_out.label }})
+        {% endif %}
+    {% elif forloop.last and type_name == "cesta" %}
+        {% if arc.vertex_out.id > arc.vertex_in.id %}
+            ({{ arc.vertex_out.label }})--{{ arc.label }}-->({{ arc.vertex_in.label }})
+        {% else %}
+            ({{ arc.vertex_in.label }})<--{{ arc.label }}--({{ arc.vertex_out.label }})
+        {% endif %}
+    {% else %}
+        {% if arc.vertex_out.id > arc.vertex_in.id %}
+            ({{ arc.vertex_in.label }})<--{{ arc.label }}--
+        {% else %}
+            ({{ arc.vertex_out.label }})--{{ arc.label }}-->
+        {% endif %}
+    {% endif %}
+{% endfor %}
+<br>
+{% for vertex in vertices %}
+    {{ vertex.get_properties.in_weight }} --------
+{% endfor %}
+<br>
+{% for vertex in vertices %}
+    {{ vertex.get_properties.out_weight }} --------
+{% endfor %}
+
+
+<h3>Arky</h3>
+<table>
+  <tr>
+    <th>OUT</th>
+    <th>IN</th>
+    <th>Váha</th>
+  </tr>
+    {% for arc in arcs %}
+  <tr>
+    <td>{{ arc.vertex_out.label }}</td>
+    <td>{{ arc.vertex_in.label }}</td>
+    <td>{{ arc.label }}</td>
+  </tr>
+{% endfor %}
+</table>
+<h3>Váhy</h3>
+<table>
+  <tr>
+    <th>Váha</th>
+    <th>index</th>
+    <th>m_d</th>
+    <th>OUT</th>
+    <th>IN</th>
+  </tr>
+    {% for vertex in vertices %}
+  <tr>
+    <td>{{ vertex.label }}</td>
+      <td>{{ vertex.index }}</td>
+    <td>{{ vertex.get_properties.max_degree }}</td>
+    <td>{{ vertex.get_properties.out_weight }}</td>
+    <td>{{ vertex.get_properties.in_weight }}</td>
+  </tr>
+{% endfor %}
+</table>
+
+</body>
+</html>

templates/type.html

@@ -0,0 +1,32 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <title>Ahoj</title>
+</head>
+<body>
+<table>
+  <tr>
+    <th>-></th>
+    <th>Vrcholy</th>
+    <th>Arky</th>
+    <th>Binary</th>
+      
+    <th>Antimagic</th>
+    <th>Super</th>
+    <th>Strict</th>
+  </tr>
+    {% for graph in graphs %}
+      <tr>
+        <td><a href="{% url "info" type=kwargs.type info=graph.id %}">o</a></td>
+        <td>{{ graph.get_properties.vertex }}</td>
+        <td>{{ graph.get_properties.arc }}</td>
+        <td>{{ graph.binary }}</td>
+      
+        <td>{% if graph.antimagic %}{{ graph.antimagic }}{% else %}---{% endif %}</td>
+        <td>{% if graph.strong %}{{ graph.strong }}{% else %}---{% endif %}</td>
+      </tr>
+    {% endfor %}
+</table>
+</body>
+</html>