8 Network analysis

import altair as alt import networkx as nx import nx_altair as nxa

G = nx.fast_gnp_random_graph(n=50, p=.1) # show graph with nx_altair nxa.draw_networkx(G)

G = nx.Graph() G.add_node("Ada") G.add_node("Bob") G.add_node("Cai") G.add_node("Don") G.add_node("Eva") G.add_edge("Ada", "Bob") G.add_edge("Ada", "Cai") G.add_edge("Ada", "Eva") G.add_edge("Bob", "Cai") G.add_edge("Bob", "Don") G.add_edge("Cai", "Don") nxa.draw_networkx(G)

G = nx.Graph([("Ada", "Bob"), ("Ada", "Cai"), ("Ada", "Eva"), ("Bob", "Cai"), ("Bob", "Don"), ("Cai", "Don")])

G = nx.Graph() G.add_node(1, time='3pm') G.nodes[1]

G.nodes[1]['room'] = 5842 G.nodes.data()

G.add_edge(1, 2, weight=4.7)

G.edges[1, 2]['weight'] = 3.2 G.edges.data()

import requests url = "http://bost.ocks.org/mike/miserables/miserables.json" # Run the HTTP request and transform it into a JSON object. lesmis = requests.get(url).json() # we specify that the dataset is not a multigraph, there are no self-loops # or multiedges, multiple edges between nodes G = nx.readwrite.json_graph.node_link_graph(lesmis, multigraph=False) nxa.draw_networkx(G, node_tooltip="name")

G.number_of_nodes()

G.number_of_edges()

density = nx.density(G) print("Network density:", density)

names = ("Napoleon", "Jondrette") ids = [x for x,y in G.nodes(data=True) if y['name'] in names] ids

path = nx.shortest_path(G, source=ids[0], target=ids[1]) print("Shortest path between {} & {}:".format(names[0], names[1]), path)

names = [ G.nodes[id]["name"] for id in path ] names

print("Length of above path:", len(path)-1)

degrees = dict(G.degree(G.nodes())) # save the degrees as a node attribute nx.set_node_attributes(G, degrees, 'degree') # check what has been saved G.nodes.data()

# reverse sort of the degrees sorted_degree = sorted(degrees.items(), key=lambda x: x[1], reverse=True) # above x[1] refers to degree as items() returns both keys and values in tuples print("Top 10 nodes by degree:\n") for d in sorted_degree[:10]: print( " - {} has {} neighbors".format(G.nodes[d[0]]["name"], d[1]) )

between = nx.betweenness_centrality(G) nx.set_node_attributes(G, between, 'between') sorted_between = sorted(between.items(), key=lambda x: x[1], reverse=True) print("Top 10 nodes by between:\n") for d in sorted_between[:10]: print( " - {}: {} ".format(G.nodes[d[0]]["name"], d[1]) )

nxa.draw_networkx(G, node_tooltip='name').properties(width=500, height=500)

pos = nx.spring_layout(G, iterations=100) nxa.draw_networkx(G, pos, node_tooltip='name').properties(width=500, height=500)

pos = nx.spring_layout(G) nxa.draw_networkx(G, pos, node_tooltip='name').properties(width=500, height=500)

nxa.draw_networkx(G, pos=pos, node_size='degree:Q', node_color='group:N', cmap = "category10", # pass colormap that is used node_tooltip='name:N', linewidths=0, # remove borders from circles ).properties(width=500, height=500)

# rectangular selection in the network view selection = alt.selection_interval(encodings=['x', 'y']) # group selection in the bar chart selection2 = alt.selection_point(fields=['group']) # first we create the force-directed layout chart = nxa.draw_networkx( G, pos=pos, node_size=100, node_color='group:N', width='value:Q', node_tooltip='name', linewidths=0 ) # get node and edge layers from chart edges = chart.layer[0] nodes = chart.layer[1] # group numbers (needed to keep bar chart stable during selections) groups = list(range(1,10)) # separate color definition used across both charts color = alt.Color('group:N', scale=alt.Scale(domain=groups), legend=None) # adjust node opacity and fill color according to selections nodes = nodes.encode( opacity=alt.condition(selection, alt.value(1), alt.value(0.25)), fill=alt.condition(selection2, color, alt.value('lightgray')), ).add_params(selection,selection2) # interactive bar chart bars = alt.Chart(nodes.data).mark_bar().encode( x=alt.X('count()', scale=alt.Scale(domain=(0,20))), y = alt.Y('group:O', scale=alt.Scale(domain=(groups))), color=color, opacity=alt.condition(selection2, alt.value(1), alt.value(0.25)), ).transform_filter(selection).add_params(selection2) # concatenate all layers into one multi-view layout alt.vconcat(edges+nodes, bars)