The document discusses the use of complex network analysis (CNA) for the periodization of post-colonial African history. It explores the theoretical background of historical periodization, proposes modeling historical states as complex networks, and presents two case studies: U.S. voting patterns and African leadership dynamics. The findings suggest that CNA is effective in categorizing historical periods based on community detection methods.

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Using Complex Network Analysis for Periodization of
Post-Colonial African History
Dmitry Zinoviev
Mathematics and Computer Science Department
Suffolk University, Boston, U.S.A.

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Using Complex Network Analysis for Periodization of
Post-Colonial African History
Dmitry Zinoviev
Mathematics and Computer Science Department
Suffolk University, Boston, U.S.A.

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What Is Historical Periodization?
● Periodization is the process of categorizing the past into discrete, contiguous, quantified,
and named blocks of time and the results of such a process.
● Pertains to history (“the past”).
● Corresponds to classification in machine learning (“categorizing … into discretem quantified
blocks”).
● Mostly subjective and arbitrary (though claimed to be “quantified”).
● Periodization is used for understanding and communicating historical phenomena.
● History as a sequence of social formations (Marx, 1844).
● “[History] can exist as a discipline if it develops a theory of periodization” (Koselleck, 2000).
● Also, confronted by some historians as superficial: History is continuous (Jordheim, 2012).

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Formal Definition
● Given:
● [Historical] state St at a discrete time t that includes essential aspects of the society in a specific
territory (Africa, USA, whole world, etc.).
● A measure of similarity of two states mij = m(Si, Sj), such that mij=mji≥0 and mii=0.
● An ordered sequence of states H=S0, S1, S2, … (the history as such).
● Periodization is:
● A mapping {S P}, where P
→P}, where P ⊆ℕ is a set of at least two periods (non-trivial!).
● Such that if Si P
→P}, where P a and Sj P
→P}, where P a, then Sk P
→P}, where P a ∀*k: i<k<j (non-overlapping!).
*Ideally, for all k; practically, for most k’s.
● That minimizes the goal function: F(H, P)=min.

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The Goal Function
● The goal function F(H, P) sets the objective of the periodization: keep similar historical
states within the same historical period and keep different states separate.
● One possible definition:
F(H , P)= ∑
Si ,Sj∈H ,i> j {m(Si , SJ) if P(Si)=P(S j)
−m(Si , SJ ) if P(Si)≠P(S j)}

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Steps in Periodization
● Define the historical states.
● Arbitrary and subjective.
● Part of the history modeling process.
● Examples:
● Having specific rulers and social formations;
● Worshiping specific gods;
● Having particular trade and political relationships;
● Speaking specific languages;
● Using specific materials.
● Define the similarity measure.
● Arbitrary and subjective.
● Part of the history modeling process.
● Prioritization? Quantification?
● Define/select* the goal function.
● Combine and evaluate.

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Proposed Approach
● Model historical states as complex networks and use complex network analysis (CNA) for
periodization.
● Complex networks model binary (and higher degree) relationships that are common in
humanities, as opposed to quantitative relationships.
● Complex networks are intuitive to build and visually appealing.
● Complex networks have established apparatus for community detection.
● Convert periodization to community detection and win!
● Disclosure: I am the author of Complex Network Analysis in Python, published by The
Pragmatic Bookshelf.

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Two Case Studies

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Case Study 1: Federal/State Voting in the U.S.A.
● Time frame: from 1796 to 2022.
● Time step: 4 years.
● Historical state: each U.S. state voting for a particular party at presidential and/or
gubernatorial elections.
● Mathematically: a mapping of U.S. states U to political parties R, Si={Uj R
→P}, where P kP⨉RkG}.
● Similarity measure: the number of U.S. states that changed their voting preferences (Jaccard
distance).
● Construct a dissimilarity-based weighted network of YEARS.
● Apply community detection (e.g., Louvain algorithm that maximizes Newmann
modularity).

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A Network of Years of the U.S. History
1792
1789
1796
1800
1804
1808
1812
1816
1820
1828
1832
1836
1840
1844
1848
1852
1856
1860 1864
1868
1872
1876
1880
1884
1888
1892
1896
1900
1904
1908
1912
1916
1920
1924
1928
1932
1936
1940
1944
1948
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
2008
2012
2016
2020
Three network
communities

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Periodization of U.S. History Based on Voting
???

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Case Study 2: Post-Colonial Africa
● Time range: from 1960 to 2021.
● Time step: 5 years.
● Historical state: having a particular leader
in a particular country.
● Mathematically: a mapping of leaders L to
countries C, Si={Lj C
→P}, where P k}.
● Similarity measure: implicit.
● Connect each independent African head of
state (president/dictator/king/prime
minister) to each of the years they ruled.

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A Network of Years & Leaders
● Time range: from 1960 to 2021.
● Time step: 5 years.
● Historical state: having a particular leader
in a particular country.
● Mathematically: a mapping of leaders L to
countries C, Si={Lj C
→P}, where P k}.
● Similarity measure: implicit.
● Connect each independent African head of
state (president/dictator/king/prime
minister) to each of the years they ruled.

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Projecting the Network
● The network is bipartite: years are connected to leaders but not to other years (which would
be desirable for community detection!)
● Perform two-way projection:
● Use generalized similarity (Kovacs, 2010).
● Construct a single-mode, weighted network of years connected to similar leaders.
● Construct a single-mode, weighted network of leaders that were in power in similar years.
● Eliminate negative weights.
● Eliminate small weights (<W) to avoid cluttered spaghetti-like graphs.
● Perform community detection, as before.

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Periodization of African Post-Colonial History Based on
Leaders
???
???

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Sensitivity Study
● Parameter W affects the density of the
network.
● How does the number of periods and
their boundaries depend on it?
● The chart shows the frequency of
choosing the point as a boundary.
● Denser networks (smaller W) produce
fewer periods (3 vs. 4). However, the
boundaries are remarkably stable.

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Free: Four Gen’s of
African Leaders
● For those unfamiliar with African
political history: the eight red circles
represent the eight Soviet/Russian
leaders, from Khrushchev to Putin.
● Given the extraordinary involvement
of the USSR in the African
decolonization process, I thought they
belonged here.

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Conclusion
● Complex networks can be used to model historical states.
● Complex network analysis can be used to calculate historical periodization.