How to calculate the Precedence Matrix in Python?

Per OP's request in the comments here is a minimalist proof of concept of a precedence matrix in python using a graph structure.

class PrecedenceDiagram():
    def __init__(self, mode = 'relative'):
        # {<str> origin : { <str> destination: <int> frequency, ... } }
        self.graph = dict()
        self.flow_amount = 0
        self.mode = mode
    
    def update(self, origin, destination):
        '''
        increment frequency if origin exists and destination is in
        origin else instantiate origin/destination appropriately
        '''
        if origin in self.graph:
            if destination in self.graph[origin]:
                self.graph[origin][destination] += 1
            else:
                self.graph[origin][destination] = 1
        else:
            self.graph[origin] = dict()
            self.graph[origin][destination] = 1
        self.flow_amount += 1

    def display_precedence(self):
        '''
        display flow frequency
        '''
        print('O','D','f')
        for node, edges in self.graph.items():
            for edge, weight in edges.items():
                if self.mode == 'absolute':
                    print(node, edge, weight)
                elif self.mode == 'relative':
                    print(node, edge, weight/ self.flow_amount)
        print('-'*16)


pm = PrecedenceDiagram(mode='relative')
pm.update('a', 'b')
pm.update('b', 'c')
pm.update('a', 'b')
pm.update('a', 'b')
pm.update('a', 'd')
pm.update('a', 'e')
pm.update('e', 'a')
pm.update('a', 'n')
pm.update('a', 'b')
pm.update('a', 'b')
pm.update('a', 'b')
pm.display_precedence()
pm.mode = 'absolute'
pm.display_precedence()

Using pm4py discover_dfg

Exampleset

import pandas as pd
import pm4py

df = pm4py.format_dataframe(pd.read_csv('https://raw.githubusercontent.com/pm4py/pm4py-core/release/notebooks/data/running_example.csv', sep=';'), case_id='case_id',activity_key='activity', timestamp_key='timestamp')

Converting data to log

from pm4py.objects.conversion.log import converter as log_converter
log = log_converter.apply(df)

discover_dfg(log) will return such a matrix (as a dict) and also a counter maintaining start and end activities.

d = pm4py.discover_dfg(log)[0]

Data Wrangling

df = pd.DataFrame.from_dict(d, orient='index').reset_index()
df.rename(columns={"index" : "Antecedent,Consequent", 0 : "Count"}, inplace=True)
df['Antecedent'], df['Consequent'] = zip(*df["Antecedent,Consequent"])

Final Output