""" FP-GraphMiner - A Fast Frequent Pattern Mining Algorithm for Network Graphs A novel Frequent Pattern Graph Mining algorithm, FP-GraphMiner, that compactly represents a set of network graphs as a Frequent Pattern Graph (or FP-Graph). This graph can be used to efficiently mine frequent subgraphs including maximal frequent subgraphs and maximum common subgraphs. URL: https://www.researchgate.net/publication/235255851 """ # fmt: off edge_array = [ ['ab-e1', 'ac-e3', 'ad-e5', 'bc-e4', 'bd-e2', 'be-e6', 'bh-e12', 'cd-e2', 'ce-e4', 'de-e1', 'df-e8', 'dg-e5', 'dh-e10', 'ef-e3', 'eg-e2', 'fg-e6', 'gh-e6', 'hi-e3'], ['ab-e1', 'ac-e3', 'ad-e5', 'bc-e4', 'bd-e2', 'be-e6', 'cd-e2', 'de-e1', 'df-e8', 'ef-e3', 'eg-e2', 'fg-e6'], ['ab-e1', 'ac-e3', 'bc-e4', 'bd-e2', 'de-e1', 'df-e8', 'dg-e5', 'ef-e3', 'eg-e2', 'eh-e12', 'fg-e6', 'fh-e10', 'gh-e6'], ['ab-e1', 'ac-e3', 'bc-e4', 'bd-e2', 'bh-e12', 'cd-e2', 'df-e8', 'dh-e10'], ['ab-e1', 'ac-e3', 'ad-e5', 'bc-e4', 'bd-e2', 'cd-e2', 'ce-e4', 'de-e1', 'df-e8', 'dg-e5', 'ef-e3', 'eg-e2', 'fg-e6'] ] # fmt: on def get_distinct_edge(edge_array): """ Return Distinct edges from edge array of multiple graphs >>> sorted(get_distinct_edge(edge_array)) ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h'] """ distinct_edge = set() for row in edge_array: for item in row: distinct_edge.add(item[0]) return list(distinct_edge) def get_bitcode(edge_array, distinct_edge): """ Return bitcode of distinct_edge """ bitcode = ["0"] * len(edge_array) for i, row in enumerate(edge_array): for item in row: if distinct_edge in item[0]: bitcode[i] = "1" break return "".join(bitcode) def get_frequency_table(edge_array): """ Returns Frequency Table """ distinct_edge = get_distinct_edge(edge_array) frequency_table = dict() for item in distinct_edge: bit = get_bitcode(edge_array, item) # print('bit',bit) # bt=''.join(bit) s = bit.count("1") frequency_table[item] = [s, bit] # Store [Distinct edge, WT(Bitcode), Bitcode] in descending order sorted_frequency_table = [ [k, v[0], v[1]] for k, v in sorted(frequency_table.items(), key=lambda v: v[1][0], reverse=True) ] return sorted_frequency_table def get_nodes(frequency_table): """ Returns nodes format nodes={bitcode:edges that represent the bitcode} >>> get_nodes([['ab', 5, '11111'], ['ac', 5, '11111'], ['df', 5, '11111'], ... ['bd', 5, '11111'], ['bc', 5, '11111']]) {'11111': ['ab', 'ac', 'df', 'bd', 'bc']} """ nodes = {} for i, item in enumerate(frequency_table): nodes.setdefault(item[2], []).append(item[0]) return nodes def get_cluster(nodes): """ Returns cluster format cluster:{WT(bitcode):nodes with same WT} """ cluster = {} for key, value in nodes.items(): cluster.setdefault(key.count("1"), {})[key] = value return cluster def get_support(cluster): """ Returns support >>> get_support({5: {'11111': ['ab', 'ac', 'df', 'bd', 'bc']}, ... 4: {'11101': ['ef', 'eg', 'de', 'fg'], '11011': ['cd']}, ... 3: {'11001': ['ad'], '10101': ['dg']}, ... 2: {'10010': ['dh', 'bh'], '11000': ['be'], '10100': ['gh'], ... '10001': ['ce']}, ... 1: {'00100': ['fh', 'eh'], '10000': ['hi']}}) [100.0, 80.0, 60.0, 40.0, 20.0] """ return [i * 100 / len(cluster) for i in cluster] def print_all() -> None: print("\nNodes\n") for key, value in nodes.items(): print(key, value) print("\nSupport\n") print(support) print("\n Cluster \n") for key, value in sorted(cluster.items(), reverse=True): print(key, value) print("\n Graph\n") for key, value in graph.items(): print(key, value) print("\n Edge List of Frequent subgraphs \n") for edge_list in freq_subgraph_edge_list: print(edge_list) def create_edge(nodes, graph, cluster, c1): """ create edge between the nodes """ for i in cluster[c1].keys(): count = 0 c2 = c1 + 1 while c2 < max(cluster.keys()): for j in cluster[c2].keys(): """ creates edge only if the condition satisfies """ if int(i, 2) & int(j, 2) == int(i, 2): if tuple(nodes[i]) in graph: graph[tuple(nodes[i])].append(nodes[j]) else: graph[tuple(nodes[i])] = [nodes[j]] count += 1 if count == 0: c2 = c2 + 1 else: break def construct_graph(cluster, nodes): X = cluster[max(cluster.keys())] cluster[max(cluster.keys()) + 1] = "Header" graph = {} for i in X: if tuple(["Header"]) in graph: graph[tuple(["Header"])].append(X[i]) else: graph[tuple(["Header"])] = [X[i]] for i in X: graph[tuple(X[i])] = [["Header"]] i = 1 while i < max(cluster) - 1: create_edge(nodes, graph, cluster, i) i = i + 1 return graph def myDFS(graph, start, end, path=None): """ find different DFS walk from given node to Header node """ path = (path or []) + [start] if start == end: paths.append(path) for node in graph[start]: if tuple(node) not in path: myDFS(graph, tuple(node), end, path) def find_freq_subgraph_given_support(s, cluster, graph): """ find edges of multiple frequent subgraphs """ k = int(s / 100 * (len(cluster) - 1)) for i in cluster[k].keys(): myDFS(graph, tuple(cluster[k][i]), tuple(["Header"])) def freq_subgraphs_edge_list(paths): """ returns Edge list for frequent subgraphs """ freq_sub_EL = [] for edges in paths: EL = [] for j in range(len(edges) - 1): temp = list(edges[j]) for e in temp: edge = (e[0], e[1]) EL.append(edge) freq_sub_EL.append(EL) return freq_sub_EL def preprocess(edge_array): """ Preprocess the edge array >>> preprocess([['ab-e1', 'ac-e3', 'ad-e5', 'bc-e4', 'bd-e2', 'be-e6', 'bh-e12', ... 'cd-e2', 'ce-e4', 'de-e1', 'df-e8', 'dg-e5', 'dh-e10', 'ef-e3', ... 'eg-e2', 'fg-e6', 'gh-e6', 'hi-e3']]) """ for i in range(len(edge_array)): for j in range(len(edge_array[i])): t = edge_array[i][j].split("-") edge_array[i][j] = t if __name__ == "__main__": preprocess(edge_array) frequency_table = get_frequency_table(edge_array) nodes = get_nodes(frequency_table) cluster = get_cluster(nodes) support = get_support(cluster) graph = construct_graph(cluster, nodes) find_freq_subgraph_given_support(60, cluster, graph) paths: list = [] freq_subgraph_edge_list = freq_subgraphs_edge_list(paths) print_all()